Cover of: Mathematical Methods in the Physical Sciences by Mary L. Boas
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Mathematical Methods in the Physical Sciences

2nd ed.
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This edition was published in by Wiley in New York.

Written in English

793 pages

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Edition Availability
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
2006, Wiley
in English - 3rd ed.
Cover of: Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
July 22, 2005, Wiley
in English
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
2004, Wiley
in English - 3rd ed.
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
1983, Wiley
in English - 2nd ed.
Cover of: Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
1983, Wiley
in English - 2nd ed.
Cover of: Mathematical methods in the physical sciences
Cover of: Mathematical methods in the physical sciences.
Cover of: Mathematical methods in the physical sciences
Cover of: Mathematical methods in the physical sciences, by Mary L. Boas
Mathematical methods in the physical sciences, by Mary L. Boas
Publish date unknown, Wiley & Sons
in English - 2nd ed.

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Mathematical Methods in the Physical Sciences

2nd ed.

This edition was published in by Wiley in New York.


Table of Contents

1 Infinite Series, Power Series 1
1. The geometric series 1
2. Definitions and notation 3
3. Applications of series 5
4. Convergent and divergent series 5
5. Testing series for convergence; the preliminary test 7
6. Tests for convergence of series of positive terms; absolute convergence 8
7. Alternating series 15
8. Conditionally convergent series 16
9. Useful facts about series 17
10. Power series; interval of convergence 18
11. Theorems about power series 21
12. Expanding functions in power series 22
13. Techniques for obtaining power series expansions 24
14. Questions of convergence and accuracy in computation 29
15. Some uses of series 33
16. Miscellaneous problems 41
2 Complex Numbers 43
1. Introduction 43
2. Real and imaginary parts of a complex number 44
3. The complex plane 45
4. Terminology and notation 46
5. Complex algebra 48
6. Complex infinite series 54
7. Complex power series; circle of convergence 56
8. Elementary functions of complex numbers 58
9. Euler's formula 60
10. Powers and roots of complex numbers 63
11. The exponential and trigonometric functions 66
12. Hyperbolic functions 69
13. Logarithms 71
14. Complex roots and powers 72
15. Inverse trigonometric and hyperbolic functions 74
16. Some applications 76
17. Miscellaneous problems 79
3 Linear Equations; Vectors, Matrices, and Determinants 81
1. Introduction 81
2. Sets of linear equations, row reduction 82
3. Determinants; Cramer's rule 87
4. Vectors 95
5. Lines and planes 105
6. Matrix operations 113
7. Linear combinations, linear functions, linear operators 127
8. General theory of sets of linear equations 130
9. Special matrices 139
10. Miscellaneous problems 142
4 Partial Differentiation 145
1. Introduction and notation 145
2. Power series in two variables 148
3. Total differentials 150
4. Approximate calculations using differentials 154
5. Chain rule or differentiating a function of a function 156
6. Implicit differentiation 159
7. More chain rule 161
8. Application of partial differentiation to maximum and minimum problems 169
9. Maximum and minimum problems with constraints; Lagrange multipliers 172
10. Endpoint or boundary point problems 181
11. Change of variables 186
12. Differentiation of integrals; Leibniz' rule 192
13. Miscellaneous problems 197
5 Multiple Integrals; Applications of Integration 201
1. Introduction 201
2. Double and triple integrals 201
3. Applications of integration ; single and multiple integrals 208
4. Change of variables in integralS; Jacobians 217
5. Surface integrals 228
6. Miscellaneous problems 231
6 Vector Analysis 235
1. Introduction 235
2. Applications of vector multiplication 235
3. Triple products 237
4. Differentiation of vectors 244
5. Fields 248
6. Directional derivative; gradient 249
7. Some other expressions involving V 254
8. Line integrals 257
9. Green's theorem in the plane 266
10. The divergence and the divergence theorem 271
11. The curl and Stokes' theorem 281
12. Miscellaneous problems 293
7 Fourier Series 297
1. Introduction 297
2. Simple harmonic motion and wave motion; periodic functions 297
3. Applications of Fourier series 302
4. Average value of a function 304
5. Fourier coefficients 307
6. Dirichlet conditions 313
7. Complex form of Fourier series 315
8. Other intervals 317
9. Even and odd functions 321
10. An application to sound 328
11. Parseval's theorem 331
12. Miscellaneous problems 334
8 Ordinary Differential Equations 337
1. Introduction 337
2. Separable equations 341
3. Linear first-order equations 346
4. Other methods for first order equations 350
5. Second-order linear equations with constant coefficients and zero right-hand side 352
6. Second-order linear equations with constant coefficients and right-hand side not zero 361
7. Other second-order equations 374
8. Miscellaneous problems 379
9 Calculus of Variations 383
1. Introduction 383
2. The Euler equation 386
3. Using the Euler equation 389
4. The brachistochrone problem; cycloids 393
5. Several dependent variables; Lagrange's equations 396
6. Isoperimetric problems 401
7. Variational notation 403
8. Miscellaneous problems 404
10 Coordinate Transformations; Tensor Analysis 407
1. Introduction 407
2. Linear transformations 409
3. Orthogonal transformations 410
4. Eigenvalues and eigenvectors; diagonalizing matrices 413
5. Applications of diagonalization 420
6. Curvilinear coordinates 426
7. Scale factors and basis vectors for orthogonal systems 428
8. General curvilinear coordinates 429
9. Vector operators in orthogonal curvilinear coordinates 431
10. Tensor analysis—introduction 435
11. Cartesian tensors 437
12. Uses of tensors; dyadics 441
13. General coordinate systems 447
14. Vector operations in tensor notation 452
15. Miscellaneous problems 453
11 Gamma, Beta, and Error Functions; Asymptotic Series; Stirling's Formula; Elliptic Integrals and Functions 457
1. Introduction 457
2. The factorial function 457
3. Definition of the gamma function; recursion relation 458
4. The gamma function of negative numbers 460
5. Some important formulas involving gamma functions 461
6. Beta functions 462
7. The relation between the beta and gamma functions 463
8. The simple pendulum 465
9. The error function 467
10. Asymptotic series 469
11. Stirling's formula 472
12. Elliptic integrals and functions 474
13. Miscellaneous problems 481
12 Series Solutions of Differential Equations; Legendre Polynomials; Bessel Functions; Sets of Orthogonal Functions 483
1. Introduction 483
2. Legendre's equation 485
3. Leibniz' rule for differentiating products 488
4. Rodrigues' formula 489
5. Generating function for Legendre polynomials 490
6. Complete sets of orthogonal functions 496
7. Orthogonality of the Legendre polynomials 499
8. Normalization of the Legendre polynomials 500
9. Legendre series 502
10. The associated Legendre functions 504
11. Generalized power series or the method of Frobenius 506
12. Bessel's equation 509
13. The second solution of Bessel's equation 512
14. Tables, graphs, and zeros of Bessel functions 514
15. Recursion relations 514
16. A general differential equation having Bessel functions as solutions 516
17. Other kinds of Bessel functions 517
18. The lengthening pendulum 519
19. Orthogonality of Bessel functions 522
20. Approximate formulas for Bessel functions 525
21. Some general comments about series solutions 526
22. Hermite functions; Laguerre functions; ladder operators 530
23. Miscellaneous problems 537
13 Partial Differential Equations 541
1. Introduction 541
2. Laplace's equation ; steady-state temperature in a rectangular plate 543
3. The diffusion or heat flow equation; heat flow in a bar or slab 550
4. The wave equation; the vibrating string 554
5. Steady-state temperature in a cylinder 558
6. Vibration of a circular membrane 564
7. Steady-state temperature in a sphere 567
8. Poisson's equation 570
9. Miscellaneous problems 576
14 Functions of a Complex Variable 579
1. Introduction 579
2. Analytic functions 580
3. Contour integrals 588
4. Laurent series 592
5. The residue theorem 596
6. Methods of finding residues 598
7. Evaluation of definite integrals by use of the residue theorem 602
8. The point at infinity; residues at infinity 614
9. Mapping 617
10. Some applications of conformal mapping 622
11. Miscellaneous problems 630
15 Integral Transforms 635
1. Introduction 635
2. The Laplace transform 639
3. Solution of differential equations by Laplace transforms 642
4. Fourier transforms 647
5. Convolution; Parseval's theorem 655
6. Inverse Laplace transform (Bromwich integral) 662
7. The Dirac delta function 665
8. Green functions 670
9. Integral transform solutions of partial differential equations 676
10. Miscellaneous problems 681
16 Probability 685
1. Introduction; definition of probability 685
2. Sample space 687
3. Probability theorems 692
4. Methods of counting 699
5. Random variables 707
6. Continuous distributions 712
7. Binomial distribution 718
8. The normal or Gaussian distribution 723
9. The Poisson distribution 728
10. Applications to experimental measurements 731
11. Miscellaneous problems 737
References 741
Bibliography 743
Answers to Selected Problems 747
Index 775

Edition Notes

Bibliography: p. [743]-746.
Includes index.

Classifications

Dewey Decimal Class
510
Library of Congress
QA37.2 .B59 1983

The Physical Object

Pagination
xx, 793 p. :
Number of pages
793

ID Numbers

Open Library
OL3159558M
Internet Archive
mathematicalmeth00boas
ISBN 10
0471044091
LC Control Number
83001226
Library Thing
76041
Goodreads
774911

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