ElectroYou - la comunità dei professionisti del mondo elettrico

da **PietroBaima** » 23 ott 2012, 4:43

Ciao a tutti!

Un po' di tempo fa qualcuno, tipo

Lele_u_biddrazzu era curioso di sapere una lista di miei libri di matematica. Non me ne sono dimenticato, e quindi ora ... la posto.

Non so se l'argomento possa interessare anche a gli altri utenti che parteciparono a quella discussione:

IsidoroKZ,

asdf e

v0id.

Magari anche

Chiodo è interessato.

All'interno dei vari livelli 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.

Libri di livello base:

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:
Codice: Seleziona tutto
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
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:
Codice: Seleziona tutto
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
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 $\sqrt{-1}$ .
—Augustus de Morgan
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:
Codice: Seleziona tutto
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:
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.
Qui potete leggere l'indice.
Mentre Qui 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.
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...]
Ecco la recensione della Bollati Boringheri. Presenti moltissimi esempi ed esercizi.

Argomenti trattati:
Codice: Seleziona tutto
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
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.

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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.

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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 questo libro qui.
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.

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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.

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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
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

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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 un po' troppo Spagnolo (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.

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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 di questi problemi senza doversi perdere nei conti.

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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.

Codice: Seleziona tutto
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

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

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 signicance 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.

Ciao a tutti!
O_/

da **Lele_u_biddrazzu** » 23 ott 2012, 9:15

Grazie

PietroBaima, una raccolta davvero esaustiva e completa direi ;-)

Vorrei segnalare un paio di testi che ho avuto modo di apprezzare per il loro modo "applicativo" di trasmettere le nozioni, sto parlando dei due volumi di Engineering Mathematics di K.A. Stroud ;-)

Sito web · da **admin** » 23 ott 2012, 10:22

Altro post-articolo: inseriscilo nel tuo blog,

PietroBaima ;-)

da **Chiodo** » 23 ott 2012, 22:24

Grazie veramente :) ..faro tesoro dei consigli...io aggiungerei (anche se in lingua italiana)essendo di scuola patavina che la bibbia dell'analisi matematica e' il de marco..attualmente e pubblicato dalla zanichellu in 3 volumi..si chiamano:
Analisi Uno
Analisi Due (parte prima)
Analisi Due (parte second
Io personalmente non ho studiato analisi su questi, li ho letti in biblioteca x la rigirosita e la completezza eccellente in ogni cosa...ricchissimo di esempi e di esercizi..
Per questi ultimi in piu ci sono due libri dello stesso autore scritto in collaborazione con carlo mariconda (mio ex prof)..sempre editi dalla zanichelli sono:
Calcolo di funzioni in una variabile
Calcolo di funzioni in piu variabili

da **v0id** » 24 ott 2012, 0:10

Che dire, se non grazie mille! =D>

Alla fine me la son cavata col Canuto Tabacco di Analisi 2, libro di testo dell'esame più altre integrazioni di appunti/dispense/libri trovati qua e là. Domani con calma se ho tempo e mi ricordo ( #-o

) posto tutto, chissà non possa tornare utile anche ad altri!

:ok:

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