An edition of Mathematical Methods in the Physical Sciences (1966)

Mathematical Methods in the Physical Sciences

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  • ★★★ 3.0 (3 ratings) ·
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Last edited by AgentSapphire
September 28, 2023 | History
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An edition of Mathematical Methods in the Physical Sciences (1966)

Mathematical Methods in the Physical Sciences

by and

  • ★★★ 3.0 (3 ratings) ·
  • 48 Want to read
  • 4 Currently reading
  • 4 Have read

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Publish Date
Publisher
John Wiley & Sons
Language
English

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Subjects

Textbooks, open_syllabus_project, Mathematics, Mathematics textbooks, Physical sciences, Science, mathematics, Mathematical models, Mathematical physics, Mathematics--textbooks, Qa37.3 .b63 2006, 510

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Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
2006, Wiley
in English - 3rd ed.
Libraries near you: WorldCat
Cover of: Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
July 22, 2005, Wiley
in English
Libraries near you: WorldCat
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
2004, Wiley
in English - 3rd ed.
Libraries near you: WorldCat
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
1983, Wiley
in English - 2nd ed.
Libraries near you: WorldCat
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
1983, Wiley
in English - 2nd ed.
Libraries near you: WorldCat
Cover of: Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
1983, John Wiley & Sons
in English
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
1966, Wiley
in English
Libraries near you: WorldCat
Cover of: Mathematical methods in the physical sciences.
Mathematical methods in the physical sciences.
1966, Wiley
in English
Cover of: Mathematical methods in the physical sciences
Mathematical methods in the physical sciences
1966, Wiley
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.
Libraries near you: WorldCat

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Book Details

Table of Contents

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

ID Numbers

Open Library
OL49644693M
Internet Archive
mathematicalmeth00boas

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