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La biblioteca di EY: sezione Matematica

Indice

Sommario:

Questo articolo raccoglie una richiesta fattami da Zeno, il grande admin: pubblicare sul mio blog una versione adattata ad articolo di un mio post, tramite il quale consigliavo dei libri di matematica, partendo da un livello piuttosto semplice fino ad arrivare ad un livello piuttosto avanzato.

L'articolo contiene un totale di sedici libri: quattro di livello base, cinque di livello intermedio, cinque di livello avanzato e, infine, due libri riguardanti l'uso di programmi per la matematica al calcolatore.

Per ogni libro viene riportata l'indicazione della lingua in cui è stato scritto e della sua difficoltà (per esempio se l'inglese è discorsivo o tecnico), il suo codice ISBN e il suo indice, per intero, oppure il riferimento al proprio sito web.

Anche all'interno dei vari livelli che ho individuato la complessità è crescente: il primo della lista è il libro più semplice, poi si va verso quello più approfondito.

I libri che riporto qui non sono libri di matematica teorica, ma libri di matematica applicata, dato il carattere tecnico del sito.

Per una più facile ed agevole ricerca del libro interessato, consiglio l'utilizzo del comando "mostra indice", in alto a destra in questa pagina, vicino al comando per convertire l'articolo in formato pdf.

Buona consultazione!

Libri di livello base:

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JOHN BIRD, Engineering Mathematics, Newnes

lingua: inglese tecnico per tutta la famiglia.
ISBN: 0 7506 5776 6

Ecco un libro assolutamente di base, ma che vi stupirà non soltanto per la sua completezza, ma anche per la chiarezza di esposizione e la presenza di esercizi davvero mirati alla comprensione. Questo libro vi darà le basi per poter leggere ed interpretare la lingua tecnico/scientifica senza problemi. Potrete parlare con matematici/fisici/ingegneri senza problemi, inceppamenti e incomprensioni varie ed eventuali.

Indice:

Preface xi
Part I Number and Algebra
Revision of fractions, decimals and percentages 1
1.1 Fractions 1
1.2 Ratio and proportion 3
1.3 Decimals 4
1.4 Percentages 7
2 Indices and standard form 9
2.1 Indices 9
2.2 Worked problems on indices 9
2.3 Further worked problems on indices 11
2.4 Standard form 13
2.5 Worked problems on standard form 13
2.6 Further worked problems on standard form 14
3 Computer numbering systems 16
3.1 Binary numbers 16
3.2 Conversion of binary to decimal 16
3.3 Conversion of decimal to binary 17
3.4 Conversion of decimal to binary via octal 18
3.5 Hexadecimal numbers 20
4 Calculations and evaluation of formulae 24
4.1 Errors and approximations 24
4.2 Use of calculator 26
4.3 Conversion tables and charts 28
4.4 Evaluation of formulae 30
5 Algebra 34
5.1 Basic operations 34
5.2 Laws of Indices 36
5.3 Brackets and factorisation 38
5.4 Fundamental laws and precedence 40
5.5 Direct and inverse proportionality 42
6 Further Algebra 44
6.1 Polynomial division 44
6.2 The factor theorem 46
6.3 The remainder theorem 48
7 Partial Fractions 51
7.1 Introduction to partial fractions 51
7.2 Worked problems on partial fractions with linear factors 51
7.3 Worked problems on partial fractions with repeated linear factors 54
7.4 Worked problems on partial fractions with quadratic factors 55
8 Simple equations 57
8.1 Expressions, equations and identities 57
8.2 Worked problems on simple equations 57
8.3 Further worked problems on simple equations 59
8.4 Practical problems involving simple equations 61
8.5 Further practical problems involving simple equations 62
9 Simultaneous equations 65
9.1 Introduction to simultaneous equations 65
9.2 Worked problems on simultaneous equations in two unknowns 65
9.3 Further worked problems on simultaneous equations 67
9.4 More difficult worked problems on simultaneous equations 69
9.5 Practical problems involving simultaneous equations
10 Transposition of formulae 74
10.1 Introduction to transposition of formulae 74
10.2 Worked problems on transposition of formulae 74
10.3 Further worked problems on transposition of fonnulae 75
10.4 Harder worked problems on transposition of formulae 77
11 Quadratic equations 80
11.1 Introduction to quadratic equations 80
11.2 Solution of quadratic equations by factorisation 80
11.3 Solution of quadratic cquations by 'completing thc square' 82
11.4 Solution of quadratic equations by formula 84
11.5 Practical problems involving quadratic equations 85
11.6 The solution of linear and quadratic equations simultaneously 87
12 Logarithms 89
12.1 Introduction to logarithms 89
12.2 Laws of logarithms 89
12.3 Indicial equations 92
12.4 Graphs of logarithmic functions 93
13 Exponential functions 95
13.1 The exponential function 95
13.2 Evaluating exponcntial functions 95
13.3 The power series for e^x 96
13.4 Graphs of exponential functions 98
13.5 Naperian logarithms 100
13.6 Evaluating Neperian logarithms 100
13.7 Laws of growth and decay 102
14 Number sequences 106
14.1 Arithmetic progressions 106
14.2 Worked problems on arithmctic progression 106
14.3 Further worked problems on arithmetic progressions 107
14.4 Geometric progressions 109
14.5 Worked problems on geomctric progressions 110
14.6 Further worked problems on geometric progressions 111
14.7 Combinations and permutations 112
15 The binomial series 114
15.1 Pascal's Triangle 114
15.2 The binomial series 115
15.3 Worked problems on the binomial series 115
15.4 Further worked problems on the binomial series 117
15.5 Pratical problems involving the binomial theorem 120
16 Solving equations by iterative methods 123
16.1 Introduction to iterative methods 123
16.2 The Newton-Raphson method 123
16.3 Worked problems on the Newton-Raphson method 123
Multiple choice questions on chapters 1 to 16 127
Part 2 Mensuration 131
17 Areas of plane figures 131
17.1 Mensuration 131
17.2 Properties of quadrilaterals 131
17.3 Worked problems on areas of plane figures 132
17.4 Further worked problems on areas of plane figures 135
17.5 Workcd problems on areas of composite figures 137
17.6 Arcas of similar shapes 138
18 The circle and its properties 139
18.1 Introduction 139
18.2 Properties of circles 139
18.3 Arc length and area of a scctor 140
18.4 Worked problems on arc length and sector of a circle 141
18.5 The equation of a circle 143
19 Volumes and surface areas of common solids 145
19.1 Volumcs and surface areas of regular solids 145
19.2 Worked problems on volumes and surface areas of regular solids 145
19.3 Further worked problems on volumes and surface areas of regular solids 147
19.4 Volumes and surface areas of frusta of pyramids and cones 151
19.5 The frustum and zone of a sphere 155
19.6 Prismoidal rule 157
19.7 Volumes of similar shapes 159
20 Irregular areas and volumes and meanvalues of waveforms 161
20.1 Arcas of irregular figures 161
20.2 Volumes of irrcgular solids 163
20.3 The mean or average value of a waveform 164
Part 3 Trigonometry 171
21 Introduction to trigonometry 171
21.1 Trigonometry 171
21.2 Thc theorem of Pythagoras 171
21.3 Trigonometric ratios of acute angles 172
21.4 Fractional and surd forms of trigonometric ratios 174
21.5 Solution of right-angled triangles 175
21.6 Angles of elevation and depression 176
21.7 Evaluating trigonometrie ratios of any angles 178
21.8 Trigonometric approximations for small angles 181
22 Trigonometric waveforms 182
22.1 Graphs of trigonomctric functions 182
22.2 Angles of any magnitude 182
22.3 Thc production of a sine and cosine wave 185
22.4 Sine and cosine curvcs 185
22.5 Sinusoidal form Asin(wl ± a) 189
22.6 Waveform harmonics 192
23 Cartesian and polar co-ordinates 194
23.1 Introduction 194
23.2 Changing from Cartesian into polar co-ordinates 194
23.3 Changing from polar into Cartesian co-ordinates 196
23.4 Use of R -> P and P -> R functions on calculators 197
24 Triangles and some practical applications 199
24.1 Sine and cosine rules 199
24.2 Area of any triangle 199
24.3 Worked problems on the solution of triangles and their areas 199
24.4 Further worked problems on the solution of triangles and their areas 201
24.5 Pratical situations involving trigonometry 203
24.6 Further practical situations involving trigonometry 205
25 Trigonometric identities and equations 208
25.1 Trigonometric identities 208
25.2 Worked problems on trigonometric identities 208
25.3 Trigonometric equations 209
25.4 Worked problcms (i) on trigonometric equations 210
25.5 Worked problems (ii) on trigonometric equations 211
25.6 Worked problems (iii) on trigonometric equations 212
25.7 Worked problems (iv) on trigonometric equations 212
26 Compound angles 214
26.1 Compound angle formulae 214
26.2 Conversion of a sin(wt) + b cos (wt) into R sin(wt+a) 216
26.3 Double angles 220
26.4 Changing products of sines and cosines into sums or differences 221
26.5 Changing sums or differences of sines and cosines into products 222
Multiple choice questions on chapters 17 to 26 225
Part 4 Graphs 231
27 Straight line graphs 231
27.1 Introduction to graphs 231
27.2 The straight line graph 231
27.3 Practical problems involving straight line graphs 237
28 Reduction of non-linear laws to linear form 243
28.1 Determination of law 243
28.2 Determination of law involving logarithms 246
29 Graphs with logarithmic scales 251
29.1 Logarithmic scales 251
29.2 Graphs of the form y = a x^n 251
29.3 Graphs of the fonn y = a b^x 254
29.4 Graphs of the foml y = a e^(kx) 255
30 Graphical solution of equations 258
30.1 Graphical solution of simultaneous equations 258
30.2 Graphical solution of quadratic equations 259
30.3 Graphical solution of linear and quadratic equations simultaneously 263
30.4 Graphical solution of cubic equations 264
31 Functions and their curves 266
31.1 Standard curves 266
31.2 Simple transformations 268
31.3 Periodic functions 273
31.4 Continuous and discontinuous functions 273
31.5 Even and odd functions 273
31.6 Inverse functions 275
Part 5 Vectors 281
32 Vectors 281
32.1 Introduction 281
32.2 Vcctor addition 281
32.3 Resolution of vectors 283
32.4 Vector subtraction 284
33 Cumbination uf waveforms 287
33.1 Combination of two periodic functions 287
33.2 Plotting periodic functions 287
33.3 Determining resultant phasors by calculation 288
Part 6 Complex Numbers 291
34 Complex numbers 291
34.1 Cartesian complex numbers 291
34.2 The Argand diagram 292
34.3 Addition and subtraction of complex numbers 292
34.4 Multiplication and division of complex numbers 293
34.5 Complex equations 295
34.6 The polar form of a complex number 296
34.7 Multiplication and division in polar form 298
34.8 Applications of complex numbers 299
35 De Moivre's theorem 303
35.1 Introduction 303
35.2 Powers of complex numbers 303
35.3 Roots of complcx numbers 304
Part 7 Statistics 307
36 Presentation of statistical data 307
36.1 Some statistical tcrminology 307
36.2 Presentation of ungrouped data 308
36.3 Presentation of grouped data 312
37 Measures of central tendency and dispersion 319
37.1 Measures of central tendency 319
37.2 Mean, median and mode for discrete data 319
37.3 Mean, median and mode for grouped law 320
37.4 Standard deviation 322
37.5 Quartiles, deciles and percentiles 324
38 Probability 326
38.1 Introduction to probability 326
38.2 Laws of probability 326
38.3 Worked problems on probability 327
38.4 Further worked problems on probability 329
38.5 Permutations and combinations 331
39 The binomial and Poisson distribution 333
39.1 The binomial distribution 333
39.2 The Poisson distribution 336
40 The normal distribution 340
40.1 Introduction to normal distribution 340
40.2 Testing for a normal distribution 344
41 Linear correlation 347
41.1 Introduction to linear correlation 347
41.2 The product-moment formula for determining the linear correlation coefficient 347
41.3 The significance of a coefficient of correlation 348
41.4 Worked problems on linear correlation 348
42 Linear regression 351
42.1 Introduction to linear regression 351
42.2 The least-squares regression lines 351
42.3 Worked problems on linear regression 352
43 Sampling and estimation theories 356
43.1 Introduction 356
43.2 Sampling distributions 356
43.3 The sampling distribution of the means 356
43.4 The estimation of population parameters based on a large sample size 359
43.5 Estimating the mean of a population based on a small sample size 364
Multiple choice questions on chapters 27 to 43 369
Part 8 Differential Calculus 375
44 Introduction to differentiation 375
44.1 Introduction to calculus 375
44.2 Functional notation 375
44.3 The gradient of a curve 376
44.4 Differentiation from first principles 377
44.5 Differentiation of y = a x^n by the general rule 379
44.6 DiITerentiation of sine and cosine functions 380
44.7 Differentiation of e^(a x) and ln(a x) 382
45 Methods of differentiation 384
45.1 Differentiation of common functions 384
45.2 Differentiation of a product 386
45.3 Differentiation of a quotient 387
45.4 Function of a function 389
45.5 Successive differentiation 390
46 Some applications of differentiation 392
46.1 Rates of change 392
46.2 Velocity and acceleration 393
46.3 Turning points 396
46.4 Practical problems involving maximum and minimum values 399
46.5 Tangents and normals 403
46.6 Small changes 404
Part 9 Integral Calculus 407
47 Standard integration 407
47.1 The process of integration 407
47.2 The general solution of integrals of the form a x^n 407
47.3 Standard integrals 408
47.4 Definition integrals 411
48 Integration using algebraic substitutions 414
48.1 Introduction 414
48.2 Algebraic substitutions 414
48.3 Worked problems on integration using algebraic substitutions 414
48.4 Further worked problems on integration using algebraic substitutions 416
48.5 Change of limits 416
49 Integration using trigonometric substitutions 418
49.1 Introduction 418
49.2 Worked problems on integration of sin^2(x), cos^2(x), tan^2(x) and cot^2(x) 418
49.3 Worked problems on powers of sines and cosines 420
49.4 Worked problems on integration of products of sines and cosines 421
49.5 Worked problems on integration using the sin(t) substitution 422
49.6 Worked problems on integration using the tan(t) substitution 424
50 Integration using partial fractions 426
50.1 Introduction 426
50.2 Worked problems on integration using partial fractions with linear factors 426
50.3 Worked problems on integration using partial fractions with repeated linear factors 427
50.4 Worked problems on integration using partial fractions with quadratic factors 428
51 The t = (Theta/2) substitution 430
51.1 Introduction 430
51.2 Worked problems on the t = tan(Theta/2) substitution 430
51.3 Further worked problems on the t = tan(Theta/2) substitution 432
52 Integration by parts 434
52.1 Introduction 434
52.2 Worked problems on integration by parts 434
52.3 Further worked problems on integration by parts 436
S3 Numerical integration 439
53.1 Introduction 439
53.2 The trapezoidal rule 439
53.3 The mid-ordinate rule 441
53.4 Simpson's rule 443
54 Areas under and between curves 448
54.1 Area under a curve 448
54.2 Worked problems on the area under a curve 449
54.3 Further worked problems on the area under a curve 452
54.4 The area between curves 454
55 Mean and root mean square values 457
55.1 Mean or average values 457
55.2 Root mean square values 459
56 Volumes of solids of revolution 461
56.1 Introduction 461
56.2 Worked problems on volumes of solids of revolution 461
56.3 Further worked problems on volumes of solids of revolution 463
57 Centroids of simple shapes 466
57.1 Centroids 466
57.2 The first moment of area 466
57.3 Centroid of area between a curve and the x-axis 466
57.4 Ccnlfoid of area between a curve and the y-axis 467
57.5 Worked problems of ccntroids of simple shapes 467
57.6 Further worked problems on centroids of simple shapes 468
57.7 Theorem of Pappus 471
58 Second moments of area 475
58.1 Second moments of area and radius of gyration 475
58.2 Second moment of area of regular sections 475
58.3 Parallel axis theorem 475
58.4 Perpendicular axis theorem 476
58.5 Summary of derived results 476
58.6 Worked problems on second moments of area of regular sections 476
58.7 Worked problems on second moments of areas of composite areas 480
Part 10 Further Number and Algebra 483
59 Boolesn algebra and logic circuits 483
59.1 Boolean algebra and switching circuits 483
59.2 Simplifying Boolean expressions 488
59.3 Laws and rules of Boolean algebra 488
59.4 De Morgan's laws 490
59.5 Karnaugh maps 491
59.6 Logic circuits 495
59.7 Universal logic circuits 500
60 The theory of matrices and determinants 504
60.1 Matrix notation 504
60.2 Addition, subtraction and multiplication of matrices 504
60.3 The unit matrix 508
60.4 The determinant of a 2 by 2 matrix 508
60.5 The inverse or reciprocal of a 2 by 2 matrix 509
60.6 The determinant of a 3 by 3 matrix 510
60.7 The inverse or reciprocal of a 3 by 3 matrix 511
61 The solution of simultaneous equations by matrices and determinants 514
61.1 Solution of simultaneous equations by matrices 514
61.2 Solution of simultaneous equations by determinants 516
61.3 Solution of simultaneous equations using Cramers rule 520
Multiple choice questions on chapters 44-61 522
Answers to multiple choice questions 526
index 527

Nota: Esiste una nuova edizione del testo, che potrete trovare qui. Questa ultima nuova edizione non è significativamente diversa dalla precedente, qui riportata, se non che viene indicato l'avvenuto incorporamento dell' errata-corrige, nel nuovo testo. Potete quindi scegliere se risparmiare qualcosa comprando l'edizione vecchia oppure investire qualche soldino in più, a fronte di una maggiore comodità.

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Dr Steven lan Barry & Dr Stephen Alan Davis ,ESSENTIAL MATHEMATICAL SKILLS for engineering, science and applied mathematics , UNSW Press.

lingua: inglese tecnico.
ISBN: 0 86840 565 5.

Questo libro riporta le prime cose da sapere e da ricordare per poter argomentare il linguaggio matematico. E' leggermente più approfondito del precedente, seppur non di molto.

Ecco l'indice, per farsi la propria idea:

Preface ............................................ ix
1 Algebra and Geometry
1.1 Elementary Notation .................................. 1
1.2 Fractions ........................................ 2
1.3 Modulus ......................................... 3
1.4 Inequalities ....................................... 3
1.5 Expansion and Factorisation .............................. 4
1.5.1 Binomial Expansion .............................. 5
1.5.2 Factorising Polynomials ............................ 6
1.6 Partial Fractions ..................................... 6
1.7 Polynomial Division .................................. 9
1.8 Surds .......................................... 10
1.8.1 Rafionalising Surd Denominators ....................... 10
1.9 Quadratic Equation ................................... 11
1.10 Summation ....................................... 12
1.11 Factorial Notation .................................... 12
1.12 Permutations ...................................... 13
1.13 Combinations ...................................... 13
1.14 Geometry ........................................ 14
1.14.1 Circles ..................................... 15
1.15 Example Questions ................................... 16
2 Functions and Graphs 17
2.1 The Basic Functions and Curves ............................ 17
2.2 Function Properties ................................... 18
2.3 Straight Lines ...................................... 21
2.4 Quadratics ........................................ 22
2.5 Polynomials ....................................... 23
2.6 Hyperbola ........................................ 24
2.7 Exponential and Logarithm Functions ......................... 25
2.8 Trigonometric Functions ................................ 26
2.9 Circles .......................................... 27
2.10 Ellipses ......................................... 28
2.11 Example Questions ................................... 29
3 Transcendental Functions 31
3.1 Exponential Function .................................. 31
3.2 Index Laws ....................................... 32
3.3 Logarithm Rules .................................... 33
3.4 Trigonometric Functions ................................ 35
3.5 Trigonometric Identities ................................ 36
3.6 Hyperbolic Functions .................................. 38
3.7 Example Questions ................................... 39
4 Differentiation 41
4.1 First Principles ..................................... 41
4.2 Linearity ......................................... 42
4.3 Simple Derivatives ................................... 43
4.4 Product Rule ...................................... 43
4.5 Quotient Rule ...................................... 44
4.6 Chain Rule ....................................... 45
4.7 Implicit Differentiation ................................. 46
4.8 Parametric Differentiation ............................... 47
4.9 Second Derivative .................................... 47
4.10 Stationary Points .................................... 48
4.11 Example Questions ................................... 50
5 Integration 51
5.1 Antidifferentiation ................................... 51
5.2 Simple Integrals ..................................... 52
5.3 The Definite Integral .................................. 53
5.4 Areas .......................................... 55
5.5 Integration by Substitution ............................... 56
5.6 Integration by Parts ................................... 57
5.7 Example Questions ................................... 58
6 Matrices 59
6.1 Addition ......................................... 59
6.2 Multiplication ...................................... 60
6.3 Identity ......................................... 61
6.4 Transpose ........................................ 62
6.5 Determinants ...................................... 63
6.5.1 Cofactor Expansion ............................... 64
6.6 Inverse .......................................... 65
6.6.1 Two by Two Matrices .............................. 66
6.6.2 Partitioned Matrix ............................... 66
6.6.3 Cofactors Matrix ................................ 67
6.7 Matrix Manipulation .................................. 68
6.8 Systems of Equations .................................. 70
6.9 Eigenvalues and Eigenvectors .............................. 73
6.10 Trace .......................................... 74
6.11 Symmetric Matrices ................................... 74
6.12 Diagonal Matrices .................................... 74
6.13 Example Questions ................................... 75
7 Vectors 77
7.1 Vector Notation ..................................... 77
7.2 Addition and Scalar Multiplication ........................... 78
7.3 Length .......................................... 79
7.4 Cartesian Unit Vectors ................................. 80
7.5 Dot Product ....................................... 80
7.6 Cross Product ...................................... 82
7.7 Linear Independence .................................. 83
7.8 Example Questions ................................... 86
8 Asymptotics and Approximations 87
8.1 Limits .......................................... 87
8.2 L'Hopital's Rule ..................................... 88
8.3 Taylor Series ...................................... 88
8.4 Asymptofics ....................................... 89
8.5 Example Questions ................................... 90
9 Complex Numbers 91
9.1 Definition ........................................ 91
9.2 Addition and Multiplication .............................. 92
9.3 Complex Conjugate ................................... 92
9.4 Euler's Equation ..................................... 93
9.5 De Moivre's Theorem .................................. 94
9.6 Example Questions ................................... 95
10 Differential Equations 97
10.1 First Order Differential Equations ........................... 97
10.1.1 Integrable .................................... 97
10.1.2 Separable .................................... 98
10.1.3 Integrating Factor ................................ 99
10.2 Second Order Differential Equations .......................... 100
10.2.1 Homogeneous ................................. 100
10.2.2 Inhomogeneous ................................. 102
10.3 Example Questions ................................... 105
11 Multivariable Calculus 107
11.1 Partial Differentiation .................................. 107
11.2 Grad, Div and Curl ................................... 108
11.3 Double Integrals ..................................... 111
11.4 Example Questions ................................... 114
12 Numerical Skills 115
12.1 Integration ........................................ 115
12.2 Differentiation ...................................... 116
12.3 Newton's Method .................................... 117
12.4 Differential Equations .................................. 118
12.5 Fourier Series ...................................... 119
12.5.1 Even Fourier Series ............................... 120
12.5.2 Odd Fourier Series ............................... 121
12.6 Example Questions ................................... 122
13 Practice Tests 123
13.1 Test 1: First Year -- Semester One ........................... 124
13.2 Test 2: First Year -- Semester One ........................... 125
13.3 Test 3: First Year -- Semester Two ........................... 126
13.4 Test 4: First Year -- Semester Two ........................... 127
13.5 Test 5: Second Year ................................... 128
13.6 Test 6: Second Year ................................... 129
14 Answers 131
15 Other Essential Skills 143 [Nota: sono pagine lasciate in bianco per poter scrivere i propri appunti]
Index 146


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Robert Kaplan and Ellen Kaplan, The Art of the Infinite - The Pleasures of Math, Oxford university press

lingua: inglese discorsivo.
ISBN: 0-19-514743-X

Ecco un libro che NON è un libro tecnico, ma non per questo è meno importante. Non troverete ricette o metodi ma dalla lettura imparerete cosa significa ragionare come un matematico e apprezzerete la matematica come strumento di pensiero e di fantasia. Indispensabile per tenere la mente aperta senza rischiare che il cervello possa cadervi fuori. Leggetelo d'estate sdraiati su un'amaca in un posto sperduto e vi perderete ancora di più ... comincerete a ragionare da matematici! Indispensabile per un tecnico.

Da pagina 167:

 The motto which I should adopt against a course calculated to stop
the progress of discovery would be—remember √(-1).
—Augustus de Morgan

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John B.Reade,Calculus with Complex Numbers Taylor & Francis

lingua: inglese tecnico.
ISBN: 041530847X

Mai più senza numeri complessi! Dopo aver studiato questo libro, che contiene tutto ciò che può servire ad un tecnico riguardo a numeri complessi, non potrete più dire di non saperli (se è vero che non li sapete...). E' un libro introduttivo perché non contiene le trasformate integrali e altri operatori utili al fisico o all'ingegnere.

Ecco l'indice del libro:

Preface
1 Complex numbers
2 Complex functions
3 Derivatives
4 Integrals
5 Evaluation of finite real integrals
6 Evaluation of infinite real integrals
7 Summation of series
8 Fundamental theorem of algebra
Solutions to examples
Appendix 1: Cauchy's theorem
Appendix 2: Half residue theorem
Bibliography
Index ofsymbols and abbreviations
General index

Libri di livello intermedio:

Se siete riusciti ad arrivare vivi fin qui, come prima cosa prendetevi un gelato, e come seconda studiatevi questo libro:

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Peter J. Olver,Cheri Shakiban, Applied Linear Algebra Pearson

lingua: inglese tecnico.
ISBN: 0131473824

Questo libro insegna a cavarsela con l'algebra lineare, abilità tecnica fondamentale. Su questo sito potete leggere l'indice. Mentre su questo potete trovare la pagina in cui Olver parla del suo libro, pubblica l'errata corrige e tante tante altre informazioni. Presenta anche altri libri, di livello un po' più avanzato. Utile e bella è questa pagina, sempre di Olver, attraverso la quale si possono leggere i capitoli non pubblicati del libro, da scaricare prima che diventino un nuovo libro pubblicato. I capitoli non pubblicati appartengono ad un livello un po' alto rispetto a questa fascia. Riuscirete a comprenderli pienamente al livello successivo.

Passiamo all'analisi, materia che risulta essere fondamentale per tutta la fisica e l'ingegneria.

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Giovanni Prodi, Lezioni di analisi matematica: 2, Bollati Boringheri

lingua: italiano tecnico, non tradotto.
ISBN: 8833958124

Per una volta, un buon libro in Italiano di Analisi 2. Scritto dal fratello dell'ex presidente del consiglio [no, no, non quello del Bunga Bunga...] Su questo sito troverete la recensione della Bollati Boringheri. Presenti moltissimi esempi ed esercizi.

Argomenti trattati:

1 Successioni e serie di funzioni
2 Spazi metrici
3 Funzioni di più variabili
4 Equazioni differenziali ordinarie
5 Curve ed integrali curvilinei
6 Forme differenziali lineari
7 Integrali multipli
8 Superfici e integrali di superficie
9 Funzioni implicite

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Christopher J. Zarowski,An Introduction to Numerical Analysis for Electrical and Computer Engineers ,Wiley

lingua: inglese tecnico.
ISBN: 0-471-46737-5

Un libro di Analisi Numerica, una disciplina che richiede conoscenze intermedie e non di base, per poter essere studiata.

Indice:

Preface xiii
1 Functional Analysis Ideas 1
1.1 Introduction 1
1.2 Some Sets 2
1.3 Some Special Mappings: Metrics, Norms, and Inner Products 4
1.3.1 Metrics and Metric Spaces 6
1.3.2 Norms and Normed Spaces 8
1.3.3 Inner Products and Inner Product Spaces 14
1.4 The Discrete Fourier Series (DFS) 25
Appendix 1.A Complex Arithmetic 28
Appendix 1.B Elementary Logic 31
References 32
Problems 33
2 Number Representations 38
2.1 Introduction 38
2.2 Fixed-Point Representations 38
2.3 Floating-Point Representations 42
2.4 Rounding Effects in Dot Product Computation 48
2.5 Machine Epsilon 53
Appendix 2.A Review of Binary Number Codes 54
References 59
Problems 59
3 Sequences and Series 63
3.1 Introduction 63
3.2 Cauchy Sequences and Complete Spaces 63
3.3 Pointwise Convergence and Uniform Convergence 70
3.4 Fourier Series 73
3.5 Taylor Series 78
3.6 Asymptotic Series 97
3.7 More on the Dirichlet Kernel 103
3.8 Final Remarks 107
Appendix 3.A COordinate Rotation DI gital Computing (CORDIC) 107
3.A.1 Introduction 107
3.A.2 The Concept of a Discrete Basis 108
3.A.3 Rotating Vectors in the Plane 112
3.A.4 Computing Arctangents 114
3.A.5 Final Remarks 115
Appendix 3.B Mathematical Induction 116
Appendix 3.C Catastrophic Cancellation 117
References 119
Problems 120
4 Linear Systems of Equations 127
4.1 Introduction 127
4.2 Least-Squares Approximation and Linear Systems 127
4.3 Least-Squares Approximation and Ill-Conditioned Linear Systems 132
4.4 Condition Numbers 135
4.5 LU Decomposition 148
4.6 Least-Squares Problems and QR Decomposition 161
4.7 Iterative Methods for Linear Systems 176
4.8 Final Remarks 186
Appendix 4.A Hilbert Matrix Inverses 186
Appendix 4.B SVD and Least Squares 191
References 193
Problems 194
5 Orthogonal Polynomials 207
5.1 Introduction 207
5.2 General Properties of Orthogonal Polynomials 207
5.3 Chebyshev Polynomials 218
5.4 Hermite Polynomials 225
5.5 Legendre Polynomials 229
5.6 An Example of Orthogonal Polynomial Least-Squares Approximation 235
5.7 Uniform Approximation 238
References 241
Problems 241
6 Interpolation 251
6.1 Introduction 251
6.2 Lagrange Interpolation 252
6.3 Newton Interpolation 257
6.4 Hermite Interpolation 266
6.5 Spline Interpolation 269
References 284
Problems 285
7 Nonlinear Systems of Equations 290
7.1 Introduction 290
7.2 Bisection Method 292
7.3 Fixed-Point Method 296
7.4 Newton–Raphson Method 305
7.4.1 The Method 305
7.4.2 Rate of Convergence Analysis 309
7.4.3 Breakdown Phenomena 311
7.5 Systems of Nonlinear Equations 312
7.5.1 Fixed-Point Method 312
7.5.2 Newton–Raphson Method 318
7.6 Chaotic Phenomena and a Cryptography Application 323
References 332
Problems 333
8 Unconstrained Optimization 341
8.1 Introduction 341
8.2 Problem Statement and Preliminaries 341
8.3 Line Searches 345
8.4 Newton’s Method 353
8.5 Equality Constraints and Lagrange Multipliers 357
Appendix 8.A MATLAB Code for Golden Section Search 362
References 364
Problems 364
9 Numerical Integration and Differentiation 369
9.1 Introduction 369
9.2 Trapezoidal Rule 371
9.3 Simpson’s Rule 378
9.4 Gaussian Quadrature 385
9.5 Romberg Integration 393
9.6 Numerical Differentiation 401
References 406
Problems 406
10 Numerical Solution of Ordinary Differential Equations 415
10.1 Introduction 415
10.2 First-Order ODEs 421
10.3 Systems of First-Order ODEs 442
10.4 Multistep Methods for ODEs 455
10.4.1 Adams–Bashforth Methods 459
10.4.2 Adams–Moulton Methods 461
10.4.3 Comments on the Adams Families 462
10.5 Variable-Step-Size (Adaptive) Methods for ODEs 464
10.6 Stiff Systems 467
10.7 Final Remarks 469
Appendix 10.A MATLAB Code for Example 10.8 469
Appendix 10.B MATLAB Code for Example 10.13 470
References 472
Problems 473
11 Numerical Methods for Eigenproblems 480
11.1 Introduction 480
11.2 Review of Eigenvalues and Eigenvectors 480
11.3 The Matrix Exponential 488
11.4 The Power Methods 498
11.5 QR Iterations 508
References 518
Problems 519
12 Numerical Solution of Partial Differential Equations 525
12.1 Introduction 525
12.2 A Brief Overview of Partial Differential Equations 525
12.3 Applications of Hyperbolic PDEs 528
12.3.1 The Vibrating String 528
12.3.2 Plane Electromagnetic Waves 534
12.4 The Finite-Difference (FD) Method 545
12.5 The Finite-Difference Time-Domain (FDTD) Method 550
Appendix 12.A MATLAB Code for Example 12.5 557
References 560
Problems 561
13 An Introduction to MATLAB 565
13.1 Introduction 565
13.2 Startup 565
13.3 Some Basic Operators, Operations, and Functions 566
13.4 Working with Polynomials 571
13.5 Loops 572
13.6 Plotting and M-Files 573
References 577
Index 579


________________________________________________________________________________________________

T.T. Soong,FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS,Wiley

lingua: inglese tecnico.
ISBN: 0-470-86813-9

Un buon libro di probabilità e statistica, con numerosi esempi ed esercizi, per fornire i fondamenti di queste discipline, non banali e non di livello base. Alcuni esercizi di questo libro li trovo un po' difficili rispetto al livello del testo.

Indice:

PREFACE xiii
1 INTRODUCTION 1
1.1 Organization of Text 2
1.2 Probability Tables and Computer Software 3
1.3 Prerequisites 3
PART A: PROBABILITY AND RANDOM VARIABLES 5
2 BASIC PROBABILITY CONCEPTS 7
2.1 Elements of Set Theory 8
2.1.1 Set Operations 9
2.2 Sample Space and Probability Measure 12
2.2.1 Axioms of Probability 13
2.2.2 Assignment of Probability 16
2.3 Statistical Independence 17
2.4 Conditional Probability 20
Reference 28
Further Reading 28
Problems 28
3 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 37
3.1 Random Variables 37
3.2 Probability Distributions 39
3.2.1 Probability Distribution Function 39
3.2.2 Probability Mass Function for Discrete Random Variables 41
3.2.3 Probability Density Function for Continuous Random Variables 44
3.2.4 Mixed-Type Distribution 46
3.3 Two or More Random Variables 49
3.3.1 Joint Probability Distribution Function 49
3.3.2 Joint Probability Mass Function 51
3.3.3 Joint Probability Density Function 55
3.4 Conditional Distribution and Independence 61
Further Reading and Comments 66
Problems 67
4 EXPECTATIONS AND MOMENTS 75
4.1 Moments of a Single Random Variable 76
4.1.1 Mean, Median, and Mode 76
4.1.2 Central Moments, Variance, and Standard Deviation 79
4.1.3 Conditional Expectation 83
4.2 Chebyshev Inequality 86
4.3 Moments of Two or More Random Variables 87
4.3.1 Covariance and Correlation Coefficient 88
4.3.2 Schwarz Inequality 92
4.3.3 The Case of Three or More Random Variables 92
4.4 Moments of Sums of Random Variables 93
4.5 Characteristic Functions 98
4.5.1 Generation of Moments 99
4.5.2 Inversion Formulae 101
4.5.3 Joint Characteristic Functions 108
Further Reading and Comments 112
Problems 112
5 FUNCTIONS OF RANDOM VARIABLES 119
5.1 Functions of One Random Variable 119
5.1.1 Probability Distribution 120
5.1.2 Moments 134
5.2 Functions of Two or More Random Variables 137
5.2.1 Sums of Random Variables 145
5.3 m Functions of n Random Variables 147
Reference 153
Problems 154
6 SOME IMPORTANT DISCRETE DISTRIBUTIONS 161
6.1 Bernoulli Trials 161
6.1.1 Binomial Distribution 162
6.1.2 Geometric Distribution 167
6.1.3 Negative Binomial Distribution 169
6.2 Multinomial Distribution 172
6.3 Poisson Distribution 173
6.3.1 Spatial Distributions 181
6.3.2 The Poisson Approximation to the Binomial Distribution 182
6.4 Summary 183
Further Reading 184
Problems 185
7 SOME IMPORTANT CONTINUOUS DISTRIBUTIONS 191
7.1 Uniform Distribution 191
7.1.1 Bivariate Uniform Distribution 193
7.2 Gaussian or Normal Distribution 196
7.2.1 The Central Limit Theorem 199
7.2.2 Probability Tabulations 201
7.2.3 Multivariate Normal Distribution 205
7.2.4 Sums of Normal Random Variables 207
7.3 Lognormal Distribution 209
7.3.1 Probability Tabulations 211
7.4 Gamma and Related Distributions 212
7.4.1 Exponential Distribution 215
7.4.2 Chi-Squared Distribution 219
7.5 Beta and Related Distributions 221
7.5.1 Probability Tabulations 223
7.5.2 Generalized Beta Distribution 225
7.6 Extreme-Value Distributions 226
7.6.1 Type-I Asymptotic Distributions of Extreme Values 228
7.6.2 Type-II Asymptotic Distributions of Extreme Values 233
7.6.3 Type-III Asymptotic Distributions of Extreme Values 234
7.7 Summary 238
References 238
Further Reading and Comments 238
Problems 239
PART B: STATISTICAL INFERENCE, PARAMETER ESTIMATION, AND MODEL VERIFICATION 245
8 OBSERVED DATA AND GRAPHICAL REPRESENTATION 247
8.1 Histogram and Frequency Diagrams 248
References 252
Problems 253
9 PARAMETER ESTIMATION 259
9.1 Samples and Statistics 259
9.1.1 Sample Mean 261
9.1.2 Sample Variance 262
9.1.3 Sample Moments 263
9.1.4 Order Statistics 264
9.2 Quality Criteria for Estimates 264
9.2.1 Unbiasedness 265
9.2.2 Minimum Variance 266
9.2.3 Consistency 274
9.2.4 Sufficiency 275
9.3 Methods of Estimation 277
9.3.1 Point Estimation 277
9.3.2 Interval Estimation 294
References 306
Further Reading and Comments 306
Problems 307
10 MODEL VERIFICATION 315
10.1 Preliminaries 315
10.1.1 Type-I and Type-II Errors 316
10.2 Chi-Squared Goodness-of-Fit Test 316
10.2.1 The Case of Known Parameters 317
10.2.2 The Case of Estimated Parameters 322
10.3 Kolmogorov–Smirnov Test 327
References 330
Further Reading and Comments 330
Problems 330
11 LINEAR MODELS AND LINEAR REGRESSION 335
11.1 Simple Linear Regression 335
11.1.1 Least Squares Method of Estimation 336
11.1.2 Properties of Least-Square Estimators 342
11.1.3 Unbiased Estimator for 2 345
11.1.4 Confidence Intervals for Regression Coefficients 347
11.1.5 Significance Tests 351
11.2 Multiple Linear Regression 354
11.2.1 Least Squares Method of Estimation 354
11.3 Other Regression Models 357
Reference 359
Further Reading 359
Problems 359
APPENDIX A: TABLES 365
A.1 Binomial Mass Function 365
A.2 Poisson Mass Function 367
A.3 Standardized Normal Distribution Function 369
A.4 Student’s t Distribution with n Degrees of Freedom 370
A.5 Chi-Squared Distribution with n Degrees of Freedom 371
A.6 D2 Distribution with Sample Size n 372
References 373
APPENDIX B: COMPUTER SOFTWARE 375
APPENDIX C: ANSWERS TO SELECTED PROBLEMS 379
Chapter 2 379
Chapter 3 380
Chapter 4 381
Chapter 5 382
Chapter 6 384
Chapter 7 385
Chapter 8 385
Chapter 9 385
Chapter 10 386
Chapter 11 386
SUBJECT INDEX 389

________________________________________________________________________________________________

kA Kit Tung, Partial differential equations and Fourier analysis

lingua: inglese tecnico.
ISBN: NA

Le equazioni differenziali alle derivate parziali sono un argomento davvero interessante e davvero sorprendente per il numero di applicazioni in campo fisico. Quelle lineari non possono non essere nel bagaglio culturale matematico di qualunque tecnico.

Potete consultare qui l'intero libro. Il primo capitolo effettua una review delle equazioni differenziali ordinarie, il secondo invece tratta le origini fisiche delle equazioni differenziali alle derivate parziali confrontandole con quelle ordinarie. Gli altri capitoli entrano nel merito e discutono le tecniche di soluzione, anche tramite l'analisi di Fourier.

Libri di livello avanzato:

Dopo tutta questa faticaccia potete prendervi una meritatissima vacanza.

________________________________________________________________________________________________

Carl M. Bender, Steven A. Orszag, ADVANCED MATHEMATICAL METHODS FOR SCIENTISTS AND ENGINEERS McGRAW-HILL BOOK COMPANY

lingua: inglese tecnico.
ISBN: 0-07-004452-X

Un libro bello, bello, bello di matematica avanzata, dai fondamenti delle equazioni differenziali e ai metodi perturbativi fino alle approssimazioni WKB, con tutte le discussioni sui fenomeni di tunnelling. Non sempre semplicissimo ma davvero bello.

Preface
PART I
FUNDAMENTALS
1 Ordinary Differential Equations
2 Difference Equations
PART II
LOCAL ANALYSIS
3 Approximate Solution of Linear Differential Equations
4 Approximate Solution of Nonlinear Differential Equations
5 Approximate Solution of Difference Equations
6 Asymptotic Expansion of Integrals
PART III
PERTURBATION METHODS
7 Perturbation Series
8 Summation of Series
PART IV
GLOBAL ANALYSIS
9 Boundary Layer Theory
10 WKB Theory

________________________________________________________________________________________________

M. Taylor,Partial Differential Equations Vol 1 - Basic Theory - Springer

lingua: inglese tecnico.
ISBN: 978-1-4419-7054-1

Ecco un ottimo libro di livello avanzato sulle equazioni differenziali alle derivate parziali. In pratica si tratta di una introduzione più rigorosa e più dettagliata rispetto a quella presente nell'ultimo libro di livello intermedio.

Indice:

Contents of Volumes II and III xi
Preface . . xiii
1 Basic Theory of ODE and Vector Fields . 1
1 The derivative 3
2 Fundamental local existence theorem for ODE . 9
3 Inverse function and implicit function theorems 12
4 Constant-coefficient linear systems; exponentiation of matrices 16
5 Variable-coefficient linear systems of ODE: Duhamel’s principle . 26
6 Dependence of solutions on initial data and on other parameters. . 31
7 Flows and vector fields . 35
8 Lie brackets . 40
9 Commuting flows; Frobenius’s theorem 43
10 Hamiltonian systems . 47
11 Geodesics . 51
12 Variational problems and the stationary action principle . 59
13 Differential forms 70
14 The symplectic form and canonical transformations . 83
15 First-order, scalar, nonlinear PDE . 89
16 Completely integrable hamiltonian systems 96
17 Examples of integrable systems; central force problems . 101
18 Relativistic motion . 105
19 Topological applications of differential forms 110
20 Critical points and index of a vector field . 118
A Nonsmooth vector fields . 122
References . . 125
2 The Laplace Equation and Wave Equation . 127
1 Vibrating strings and membranes. . 129
2 The divergence of a vector field . 140
3 The covariant derivative and divergence of tensor fields . 145
4 The Laplace operator on a Riemannian manifold 153
5 The wave equation on a product manifold and energy conservation 156
6 Uniqueness and finite propagation speed . 162
7 Lorentz manifolds and stress-energy tensors . 166
8 More general hyperbolic equations; energy estimates 172
viii Contents
9 The symbol of a differential operator and a general
Green–Stokes formula . 176
10 The Hodge Laplacian on k-forms . 180
11 Maxwell’s equations . 184
References . . 194
3 Fourier Analysis, Distributions,and Constant-Coefficient Linear PDE . 197
1 Fourier series . 198
2 Harmonic functions and holomorphic functions in the plane 209
3 The Fourier transform. . 222
4 Distributions and tempered distributions 230
5 The classical evolution equations . 244
6 Radial distributions, polar coordinates, and Bessel functions. . 263
7 The method of images and Poisson’s summation formula . 273
8 Homogeneous distributions and principal value distributions . 278
9 Elliptic operators . 286
10 Local solvability of constant-coefficient PDE 289
11 The discrete Fourier transform 292
12 The fast Fourier transform . 301
A The mighty Gaussian and the sublime gamma function. . 306
References . . 312
4 Sobolev Spaces 315
1 Sobolev spaces on Rn 315
2 The complex interpolation method . . 321
3 Sobolev spaces on compact manifolds . . 328
4 Sobolev spaces on bounded domains . 331
5 The Sobolev spaces Hs
6 The Schwartz kernel theorem. . 345
7 Sobolev spaces on rough domains . 349
References . . 351
5 Linear Elliptic Equations 353
1 Existence and regularity of solutions to the Dirichlet problem 354
2 The weak and strong maximum principles 364
3 The Dirichlet problem on the ball in Rn 373
4 The Riemann mapping theorem (smooth boundary) . 379
5 The Dirichlet problem on a domain with a rough boundary . 383
6 The Riemann mapping theorem (rough boundary) . 398
7 The Neumann boundary problem . 402
8 The Hodge decomposition and harmonic forms 410
9 Natural boundary problems for the Hodge Laplacian 421
10 Isothermal coordinates and conformal structures on surfaces . 438
11 General elliptic boundary problems . 441
12 Operator properties of regular boundary problems . 462
Contents ix
A Spaces of generalized functions on manifolds with boundary . 471
B The Mayer–Vietoris sequence in deRham cohomology . . 475
References . . 478
6 Linear Evolution Equations . 481
1 The heat equation and the wave equation on bounded domains . 482
2 The heat equation and wave equation on unbounded domains 490
3 Maxwell’s equations . 496
4 The Cauchy–Kowalewsky theorem . 499
5 Hyperbolic systems 504
6 Geometrical optics . 510
7 The formation of caustics 518
8 Boundary layer phenomena for the heat semigroup . . 535
A Some Banach spaces of harmonic functions . . 541
B The stationary phase method 543
References . . 545
A Outline of Functional Analysis 549
1 Banach spaces 549
2 Hilbert spaces 556
3 Fr´echet spaces; locally convex spaces . 561
4 Duality 564
5 Linear operators 571
6 Compact operators . 579
7 Fredholm operators 593
8 Unbounded operators 596
9 Semigroups . 603
References . . 615
B Manifolds, Vector Bundles, and Lie Groups . 617
1 Metric spaces and topological spaces . 617
2 Manifolds . 622
3 Vector bundles 624
4 Sard’s theorem. . 626
5 Lie groups 627
6 The Campbell–Hausdorff formula 630
7 Representations of Lie groups and Lie algebras 632
8 Representations of compact Lie groups . 636
9 Representations of SU(2) and related groups . 641
References . . 647
Index 649[/code]


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M. Taylor,Partial Differential Equations Vol 2 - Qualitative Studies of Linear Equations- Springer

Il secondo volume approfondisce quanto trattato nel primo. Sono introdotte le tecniche analitiche e gli operatori pseudodifferenziali, incluse le misure di Wiener. Interessantissime le discussioni sugli operatori ellittici, la teoria dello scattering, la teoria degli operatori di Dirac, la teoria del moto Browniano e le equazioni della diffusione.

lingua: inglese tecnico.
ISBN: 1441970517

Indice:

Qualitative Studies of Linear Equations
7 Pseudodifferential Operators
8 Spectral Theory
9 Scattering by Obstacles
10 Dirac Operators and Index Theory
11 Brownian Motion and Potential Theory
12 The 3-Neumann Problem
C Connections and Curvature

________________________________________________________________________________________________

M. Taylor,Partial Differential Equations Vol 3 - Non linear equation - Springer

lingua: inglese tecnico.
ISBN: 0387946527

Questo è un libro di livello davvero avanzato: vengono discusse le equazioni alle derivate parziali non lineari. Ho deciso di inserire questo libro per continuità con gli altri due, altrimenti non l'avrei fatto. Si discute la meccanica relativistica e numerosi problemi di geometria differenziale, come il problema delle superifici minime e le mappe armoniche. Vengono studiati anche i problemi di diffusione non lineare, spazi di Sobolev,spazi di Holder, spazi di Hardy e di Morrey. Vengono trattati gli operatori paradifferenziali tramite molecolarità di calcolo. Molto faticoso e per veri duri. Do not try this at home.

________________________________________________________________________________________________

Eugenio Hernftndez, A First Course on WAVELETS, CRC Press

lingua: inglese tecnico, ogni tanto, forse, un po' troppo spagnoleggiante (ma per un Italiano è un bene).
ISBN: 0-8493-8274-2

Vi siete mai chiesti cosa sono le wavelets? Le mother-function? Le father-function (sì, ci sono anche loro)? Volete diventare dei veri esperti nel campo dell'analisi dei segnali? questo libro fa decisamente per voi.

Bases for L2(R)
1.1 Preliminaries
1.2 Orthonormal bases generated by a single function; the Balian- Low theorem
1.3 Smooth projections on L2(R)
1.4 Local sine and cosine bases and the construction of some wavelets
1.5 The unitary folding operators and the smooth projections
1.6 Notes and references
2 Multiresolution analysis and the construction of wavelets
2.1 Multiresolution analysis
2.2 Construction of wavelets from a multiresolution analysis
2.3 The construction of compactly supported wavelets
2.4 Better estimates for the smoothness of compactly supported wavelets
2.5 Notes and references Band-limited wavelets
3.1 Orthonormality
3.2 Completeness
3.3 The Lemari-Meyer wavelets revisited
3.4 Characterization of some band-limited wavelets
3.5 Notes and references
4 Other constructions of wavelets
4.1 Franklin wavelets on the real line
4.2 Spline wavelets on the real line
4.3 Orthonormal bases of piecewise linear continuous functions for L2
4.4 Orthonormal bases of periodic splines
4.5 Periodization of wavelets defined on the real line
4.6 Notes and references Representation of functions by wavelets
5.1 Bases for Banach spaces
5.2 Unconditional bases for Banach spaces
5.3 Convergence of wavelet expansions in LP(R)
5.4 Pointwise convergence of wavelet expansions
5.5 H and B on R
5.6 Wavelets as unconditional bases for H' and LP
5.7 Notes and references
Characterizations of function spaces using wavelets
6.1 Wavelets and sampling theorems
6.2 Littlewood-Paley theory
6.3 Necessary tools
6.4 The Lebesgue spaces
6.5 The Hardy space
6.6 The Sobolev spaces
6.7 The Lipschitz spaces , and the Zygmund class A. (R)

Programmi per la matematica:

In questa sezione volevo inserire qualche libro, destinato al matematico di professione, per imparare ad usare i tool più belli di manipolazione matematica. La preghiera è però di non usarli se non si ha ben chiaro che cosa si stia facendo. Troppe volte mi è capitato di vedere persone che trovavano risultati un po' "esotici" senza rendersi minimamente conto del madornale errore (velocità complesse o pari a 4c, Energie di TJ, Temperature pari a -100K, rendimenti pari a 10, probabilità negative...). Purtroppo però molto spesso le cose non vanno così bene. Capita, talvolta, che il risultato sia verosimile ma errato e, da questa eventualità, non c'è difesa se non quella data dall'occhio esperto e dal controllo attento di chi inserisce il modello fisico all'interno del tool matematico. Gli inglesi dicono "do not toy with fire".

________________________________________________________________________________________________

Ferdinand E Cap, MATHEMATICAL METHODS in PHYSICS and ENGINEERING with MATHEMATICA, CHAPMAN & HALL/CRC, A CRC Press Company.

lingua: inglese tecnico.
ISBN: 1-58488-402-9

Un bel libro con un sacco di problemi risolti con Mathematica, il famoso tool di Stephen Wolfram. Armatevi di the e biscottini per sopportare le lunghe attese date dalla ricerca della soluzione di qualche annoso problema... E' utile togliersi qualche curiosità su alcuni problemi riportati su questo libro, facendo fare tutti i conti a Mathematica!

Contents
Introduction
1.1 What is a boundary problem?
1.2 Classification of partial differential equations
1.3 Types of boundary conditions and the collocation method
1.4 Differential equations as models for nature
2 Boundary problems of ordinary differential equations
2.1 Linear differential equations
2.2 Solving linear differential equations
2.3 Differential equations of physics and engineering
2.4 Boundary value problems and eigenvalues
2.5 Boundary value problems as initial value problems
2.6 Nonlinear ordinary differential equations
2.7 Solutions of nonlinear differential equations
Partial differential equations
3.1 Coordinate systems and separability
3.2 Methods to reduce partial to ordinary differential equations
3.3 The method of characteristics
3.4 Nonlinear partial differential equations
4 Boundary problems with one closed boundary
4.1 LAPLACE and POISSON equations
4.2 Conformal mapping in two and three dimensions
4.3 D'ALEMBERT wave equation and string vibrations
4.4 HELMHOLTZ equation and membrane vibrations
4.5 Rods and the plate equation
4.6 Approximation methods
4.7 Variational calculus
4.8 Collocation methods
Boundary problems with two closed boundaries
5.1 Inseparable problems
5.2 Holes in the domain. Two boundaries belonging to different
coordinate systems .
5.3 Corners in the boundary
Nonlinear boundary problems
6.1 Some definitions and examples
6.2 Moving and free boundaries
6.3 Waves of large amplitudes. Solirons
6.4 The rupture of an embankment-type water dam
6.5 Gas flow with combustion
References
Appendix

________________________________________________________________________________________________

J. Manassah, Elem. Math. and Comp. Tools for Engineers using MATLAB ,CRC Press

lingua: inglese tecnico.
ISBN: 0-8493-1080-6

Una rapida occhiata all'indice di questo libro vi farà pienamente comprendere quanti problemi possano essere trattati con Matlab.

1. Introduction to MATLAB® and Its Graphics Capabilities
1.1 Getting Started
1.2 Basic Algebraic Operations and Functions
1.3 Plotting Points
1.3.1 Axes Commands
1.3.2 Labeling a Graph
1.3.3 Plotting a Point in 3-D
1.4 M-files
1.5 MATLAB Simple Programming
1.5.1 Iterative Loops
1.5.2 If-Else-End Structures
1.6 Array Operations
1.7 Curve and Surface Plotting
1.7.1 x-y Parametric Plot
1.7.2 More Parametric Plots in 2-D
1.7.3 Plotting a 3-D Curve
1.7.4 Plotting a 3-D Surface
1.8 Polar Plots
1.9 Animation
1.10 Histograms
1.11 Printing and Saving Work in MATLAB
1.12 MATLAB Commands Review
2. Difference Equations
2.1 Simple Linear Forms
2.2 Amortization
2.3 An Iterative Geometric Construct: The Koch Curve
2.4 Solution of Linear Constant Coefficients Difference Equations
2.4.1 Homogeneous Solution
2.4.2 Particular Solution
2.4.3 General Solution
2.5 Convolution-Summation of a First-Order System with Constant Coefficients
2.6 General First-Order Linear Difference Equations*
2.7 Nonlinear Difference Equations
2.7.1 Computing Irrational Numbers
2.7.2 The Logistic Equation2.8 Fractals and Computer Art
2.8.1 Mira’s Model
2.8.2 Hénon’s Model
2.9 Generation of Special Functions from Their Recursion Relations
3. Elementary Functions and Some of Their Uses
3.1 Function Files
3.2 Examples with Affine Functions
3.3 Examples with Quadratic Functions
3.4 Examples with Polynomial Functions
3.5 Examples with Trigonometric Functions
3.6 Examples with the Logarithmic Function
3.6.1 Ideal Coaxial Capacitor
3.6.2 The Decibel Scale
3.6.3 Entropy
3.7 Examples with the Exponential Function
3.8 Examples with the Hyperbolic Functions and Their Inverses
3.8.1 Capacitance of Two Parallel Wires
3.9 Commonly Used Signal Processing Functions
3.10 Animation of a Moving Rectangular Pulse
3.11 MATLAB Commands Review
4. Numerical Differentiation, Integration, and Solutions of Ordinary Differential Equations
4.1 Limits of Indeterminate Forms
4.2 Derivative of a Function
4.3 Infinite Sums
4.4 Numerical Integration
4.5 A Better Numerical Differentiator
4.6 A Better Numerical Integrator: Simpson’s Rule
4.7 Numerical Solutions of Ordinary Differential Equations
4.7.1 First-Order Iterator
4.7.2 Higher-Order Iterators: The Runge-Kutta Method
4.7.3 MATLAB ODE Solvers
4.8 MATLAB Commands Review
5. Root Solving and Optimization Methods
5.1 Finding the Real Roots of a Function
5.1.1 Graphical Method
5.1.2 Numerical Methods
5.1.3 MATLAB fsolve and fzero Built-in Functions
5.2 Roots of a Polynomial5.3 Optimization Methods
5.3.1 Graphical Method
5.3.2 Numerical Methods
5.3.3 MATLAB fmin and fmins Built-in Function
5.4 MATLAB Commands Review
6. Complex Numbers
6.1 Introduction
6.2 The Basics
6.2.1 Addition
6.2.2 Multiplication by a Real or Imaginary Number
6.2.3 Multiplication of Two Complex Numbers
6.3 Complex Conjugation and Division
6.3.1 Division
6.4 Polar Form of Complex Numbers
6.4.1 New Insights into Multiplication and Division
of Complex Numbers
6.5 Analytical Solutions of Constant Coefficients ODE
6.5.1 Transient Solutions
6.5.2 Steady-State Solutions
6.5.3 Applications to Circuit Analysis
6.6 Phasors
6.6.1 Phasor of Two Added Signals
6.7 Interference and Diffraction of ElectromagneticWaves
6.7.1 The ElectromagneticWave
6.7.2 Addition of ElectromagneticWaves
6.7.3 Generalization to N-waves
6.8 Solving ac Circuits with Phasors: The Impedance Method
6.8.1 RLC Circuit Phasor Analysis
6.8.2 The Infinite LC Ladder
6.9 Transfer Function for a Difference Equation wit Constant Coefficients
6.10 MATLAB Commands Review
7. Vectors
7.1 Vectors in Two Dimensions (2-D)
7.1.1 Addition
7.1.2 Multiplication of a Vector by a Real Number
7.1.3 Cartesian Representation
7.1.4 MATLAB Representation of the Above Results
7.2 Dot (or Scalar) Product
7.2.1 MATLAB Representation of the Dot Product
7.3 Components, Direction Cosines, and Projections
7.3.1 Components7.3.2 Direction Cosines
7.3.3 Projections
7.4 The Dirac Notation and Some General Theorems*
7.4.1 Cauchy-Schwartz Inequality
7.4.2 Triangle Inequality
7.5 Cross Product and Scalar Triple Product*
7.5.1 Cross Product
7.5.2 Geometric Interpretation of the Cross Product
7.5.3 Scalar Triple Product
7.6 Vector Valued Functions
7.7 Line Integral
7.8 Infinite Dimensional Vector Spaces*
7.9 MATLAB Commands Review
8. Matrices
8.1 Setting up Matrices
8.1.1 Creating Matrices in MATLAB
8.2 Adding Matrices
8.3 Multiplying a Matrix by a Scalar
8.4 Multiplying Matrices
8.5 Inverse of a Matrix
8.6 Solving a System of Linear Equations
8.7 Application of Matrix Methods
8.7.1 dc Circuit Analysis
8.7.2 dc Circuit Design
8.7.3 ac Circuit Analysis
8.7.4 Accuracy of a Truncated Taylor Series
8.7.5 Reconstructing a Function from Its Fourier Components
8.7.6 Interpolating the Coefficients of an (n – 1)-degree Polynomial from n Points
8.7.7 Least-Square Fit of Data
8.8 Eigenvalues and Eigenvectors*
8.8.1 Finding the Eigenvalues of a Matrix
8.8.2 Finding the Eigenvalues and Eigenvectors Using MATLAB
8.9 The Cayley-Hamilton and Other Analytical Techniques*
8.9.1 Cayley-Hamilton Theorem
8.9.2 Solution of Equations of the Form
8.9.3 Solution of Equations of the Form
8.9.4 Pauli Spinors
8.10 Special Classes of Matrices*
8.10.1 Hermitian Matrices
8.10.2 Unitary Matrices
8.10.3 Unimodular Matrices
8.11 MATLAB Commands Review
9. Transformations
9.1 Two-dimensional (2-D) Geometric Transformations
9.1.1 Polygonal Figures Construction
9.1.2 Inversion about the Origin and Reflection about the Coordinate Axes
9.1.3 Rotation around the Origin
9.1.4 Scaling
9.1.5 Translation
9.2 Homogeneous Coordinates
9.3 Manipulation of 2-D Images
9.3.1 Geometrical Manipulation of Images
9.3.2 Digital Image Processing
9.3.3 Encrypting an Image
9.4 Lorentz Transformation*
9.4.1 Space-Time Coordinates
9.4.2 Addition Theorem for Velocities
9.5 MATLAB Commands Review
10. A Taste of Probability Theory
10.1 Introduction
10.2 Basics
10.3 Addition Laws for Probabilities
10.4 Conditional Probability
10.4.1 Total Probability and Bayes Theorems
10.5 Repeated Trials
10.5.1 Generalization of Bernoulli Trials
10.6 The Poisson and the Normal Distributions
10.6.1 The Poisson Distribution
10.6.2 The Normal Distributio Supplement: Review of Elementary Functions
S.1 Affine Functions
S.2 Quadratic Functions
S.3 Polynomial Functions
S.4 Trigonometric Functions
S.5 Inverse Trigonometric Functions
S.6 The Natural Logarithmic Function
S.7 The Exponential Function
S.8 The Hyperbolic Functions
S.9 The Inverse Hyperbolic Functions
Appendix: Some Useful Formulae
Addendum: MATLAB 6
Selected References

Conclusioni:

Concludo con alcune citazioni, utili per meglio comprendere il linguaggio matematico, del matematico statunitense Sean Mauch:


Phrases often have different meanings in mathematics than in everyday usage. Here I have collected definitions of some mathematical terms which might confuse the novice.


  • beyond the scope of this text: Beyond the comprehension of the author.


  • difficult: Essentially impossible. Note that mathematicians never refer to problems they have solved as being difficult. This would either be boastful, (claiming that you can solve difficult problems), or self-deprecating, admitting that you found the problem to be difficult).


  • interesting: This word is grossly overused in math and science. It is often used to describe any work that the author has done, regardless of the work's significance or novelty. It may also be used as a synonym for difficult. It has a completely different meaning when used by the non-mathematician. When I tell people that I am a mathematician they typically respond with: "That must be interesting.", which means: "I don't know anything about math or what mathematicians do." I typically answer, "No. Not really."


  • non-obvious or non-trivial: Real fuckin' hard.


  • one can prove that . . . : The "one" that proved it was a genius like Gauss. The phrase literally means "you haven't got a chance in hell of proving that . . . "


  • simple: Mathematicians communicate their prowess to colleagues and students by referring to all problems as simple or trivial. If you ever become a math professor, introduce every example as being "really quite trivial."


Una volta si diceva "e non finisce qui". Per adesso, invece, la cosa finisce proprio qui. Questo però non vuol dire che, nel caso in cui mi venga in mente qualche altro bel libro che mi è piaciuto studiare, non possa nuovamente rendervi partecipi di un po' di quella che, per me, è bella matematica.

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di ,

"un grammo di osservazione non vale una tonnellata di teoria?" Che ti devo dire, è diventato simpatico già dall'intro di wikipedia: "astronomo, divulgatore scientifico e autore di fantascienza statunitense."

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di ,

Grazie Sjuanez!
Se ti è piaciuta quella frase, prova a cercare fra le citazioni di Sagan
Ciao,
Pietro.

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di ,

Ma come ho fatto a perdermi questo articolo finora? Grazie Pietro! PS: "Indispensabile per tenere la mente aperta senza rischiare che il cervello possa cadervi fuori." Fantastica! Penso che la riciclerò alla prossima riunione!!!

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di ,

meglio cosi'..., perche' molti ci fanno i "caconi" con i libri stranieri. Comunque a parte la sterilizzazione universitaria, a cui credo solo per una certa percentuale, ci sono ottimi testi di matematica in italiano. Magari facendo uno sforzo in piu' potresti aiutare tanta gente che sa studiare solo in italiano. Molta di questa vuole imparare solo cose a livello basilare, quelle che servono, per lavorare a livello di elettronica, elettrotecnica, non il teorema del Lerch, gli integrali di Lebesgue, o l'integrazione di astruse equazioni differenziali: vogliono sapere derivate, limiti, integrali comuni, la trasformata di Laplace e di Fourier. Ma con questo, non voglio condizionare il tuo pensiero, come io ho il mio. Sono anni che sono nel mondo del lavoro nell'elettronica degli apparati militari e sapessi quante pubblicazioni e libri stranieri, soprattutto in americano ed in inglese ho letto, ma ho sempre apprezzato la pubblicazione in italiano, perche' completamente comprensibile senza equivoci per uno che vive qui in italia. Comunque anche gli italiani "gliel'ammollano"... Auguri per le tue attivita' e senza spirito polemico, era solo per esprimere il mio punto di vista, che e' umano e relativo, come gli altri.

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di ,

Ho inserito l'unico libro in Italiano che mi piace, di matematica. Purtroppo la matematica Italiana soffre della settorializzazione universitaria e purtroppo anche un po' di obsolescenza, per i molti conosciuti motivi. Quindi, secondo me, l'Italia non riesce più a produrre testi rimarchevoli, che, qualora ci fossero, inserirei più che volentieri (dura realtà). Avrei forse potuto inserire qualche testo della scuola russa (ma anche per loro si trovano solo traduzioni in Inglese, non volendo mettere l'edizione scritta in russo), purtroppo però, sugli argomenti di punta (PDE e NLPDE) non sono più molto più aggiornati e i grandi classici che trattano gli argomenti di base sono difficili da reperire.

Sono stato selettivo verso i testi in Inglese, forse, ma l'ho fatto perchè sono tanti (quindi è facile trovare buoni testi) e l'Inglese è una lingua ampiamente diffusa. Discriminatorio non credo, perchè avrei più che volentieri inserito altri testi in Italiano, se ne avessi trovati di validi. Non ho pensato di inserire altre lingue (ci sono dei buoni testi in Francese, per esempio) per non inserire troppi testi e non creare dei doppioni su testi equivalenti. Infine, non avendo consigliato di buttare via i propri testi di letteratura Italiana (che è molto bella) in favore di quella anglosassone, ma avendo consigliato testi tecnici, credo di non essere un "fanatico intellettuale" :-)
Ciao,
Pietro.

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di ,

Ma e' necessario sapere la matematica da libri in inglese. Premetto che leggo molte cose in inglese per lavoro, di tutto dalla sicurezza, lla fisica, alla matematica, ecc. Cio' mi sembra un po' selettivo e discriminatorio, soprattutto verso la grande fascia di lettori che vogliono imparare con la nostra lingua, dato che siamo in italia. Su, mettici qualche testo in italiano, ce ne sono tanti ottimi. Non sconfiniamo, almeno spero di no, nel fanatismo intellettuale.

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di ,

Grazie kotek!!!

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di ,

Ottima rassegna!

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di ,

Io sto ancora ridendo...

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di ,

Comunque che DD non sia veramente specialista di nulla è la barzelletta del secolo...

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di ,

Ecco infatti... per ora che sto studiando comunicazioni elettriche mi piacerebbe approfondire questo argomento per estenderlo alla teoria dei segnali... purtroppo mi sa che per ora devo rinunciare, prima di tutto perché non ritengo di avere il bagaglio teorico adeguato, e poi il tempo tiranno che mi manca a causa del lavoro :((( p.s. ho appena aperto il capitolo del libro di F.M. del mio docente che tratta Wavelet e analisi multi-risoluzione e sto leggendo x curiosità qualcosa, imbattendomi in cose del tipo: operatori di annichilazione e creazione, vettore vacuum, tight frame, MRA di Haar... HO CHIUSO IL LIBRO!!! Ihihihihih :P:P

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di ,

@DD: si potrebbe fare un libro con tutti i tuoi consigli e commenti del forum, EY edizioni. Credo che sarebbe molto bello e molto utile. Il mio contributo potrebbe essere quello di darti una mano nella raccolta e organizzazione, non credo molto di più.
BTW, grazie a tutti ragazzi, siete fantastici!

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di ,

@Lele:Grazie a te!
@Jordan20:Sì, si usano molto in Fisica Matematica, in meccanica quantistica e, più in generale, in modellistica quando si ha un variazionale tempo-frequenza del segnale. Il loro limite più grande è che sono soggette al principio di indeterminazione, scalare e vettoriale. Sono molto utili anche in analisi armonica per le alte frequenze per creare modelli di propagazione ondulatoria.
@sebago:Messere, volger lo palato allo oppressor anglofono l'è cosa dura, in particolar pella Italiana lingua, le cui gesta scienzifiche, poeticali e musiche riempirommi il cuor delle passate gesta, ma lo diniego ha come maleconseguenzia la presa in retroposizione, per li motivi già dispiegati dal poeta DD. Vi esorto dunque, o cavalier, che farete pure che domane o l'altro l'anglofon volgo se ne venga con voi a dimorare, di parer che il godimento vi accompagni nelle brave e balsame letture.

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di ,

@sebago: la mia impressione è che i libri italiani, ahinoi, siano molto legati alle deprimenti vicende degli ordinamenti universitari, con il risultato che non si scrivono più libri di ampio respiro, almeno così mi sembra. Per ciò che riguarda alcuni classici russi di matematica e fisica, le edizioni Mir ne avevano proposto una traduzione italiana, ormai da ricercarsi sulle bancarelle. Però permettimi un consiglio: non chiuderti ai libri in inglese, ti perderesti dei libri straordinari! Per quel che riguarda invece un "mio" libro, devo darti una delusione: molto probabilmente non ci sarà mai ;-) Il motivo principale è che non saprei su cosa scriverlo, non sono veramente specialista di nulla. Il secondo è che per scrivere un *buon* libro ci va tempo, molto tempo, diciamo due-dieci anni, a seconda di quanto tempo uno ci può dedicare, e considerando quanto sono ondivago nelle passioni scientifiche, non me la sentirei di impegnarmi per così tanto tempo su un progetto. E per finire: bravo Pietro! :-)

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di ,

All'ultimo momento mi è scappato il tasto "invia" ma volevo aggiungere: a quando un libro di Pietro Baima o di DirtyDeeds o di Carloc o di ... ? (non cito RenzoDF perché, suo dicere, è un idraulico...) Ri-ciao

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di ,

Bell'elenco, Pietro. Una curiosità: ma nell'italica lingua, ad esclusione di quello di Giovanni Prodi, niente altro? Chi non è anglofono (e non ha intenzione di diventarlo, come il sottoscritto) deve dunque sottomettersi, obtorto collo, all'odiata albione? Possibile che in questa top list siano pressoché assenti i matematici italiani (ovvero: siamo dunque così scarsi a livello internazionale)? Ciao

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di ,

Bellissima rassegna Pietro!!! Le wavelets e la teoria che ci sta attorno è qualcosa di molto interessante... le ho sentite nominare per la prima volta dal mio docente di Fisica Matematica che ne ha fatto qualche cenno... ed ho seguito una volta un seminario all'università in merito a questo tema (ma ho capito veramente pochissimo :PPP)

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di ,

Utile e interessante rassegna. Grazie Pietro ;)

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