- Browse
- » Mathematical methods for physicists
Mathematical methods for physicists
Author
Publisher
Varies, see individual formats and editions
Publication Date
Varies, see individual formats and editions
Language
English
Find It Now
Embry Riddle Aero University - CIRCCOLL - Circulating Collection
QA37.2.A74 1985
1 available
QA37.2.A74 1985
1 available
Embry Riddle Aero University - CIRCCOLL - Circulating Collection
QA37.3.A74 2001
1 available
QA37.3.A74 2001
1 available
More Details
Contributors
ISBN
9780120598267
9780120598250
9780120598205
9780120598250
9780120598205
Description
Loading Description...
Table of Contents
From the Book - Regular Print - Fifth edition.
1 Vector Analysis 1 --
1.2 Rotation of the Coordinate Axes 8 --
1.3 Scalar or Dot Product 13 --
1.4 Vector or Cross Product 19 --
1.5 Triple Scalar Product, Triple Vector Product 27 --
1.6 Gradient, [down triangle, open] 35 --
1.7 Divergence, [down triangle, open] 40 --
1.8 Curl, [down triangle, open] x 44 --
1.9 Successive Applications of [down triangle, open] 51 --
1.10 Vector Integration 55 --
1.11 Gauss's Theorem 61 --
1.12 Stokes's Theorem 65 --
1.13 Potential Theory 69 --
1.14 Gauss's Law, Poisson's Equation 80 --
1.15 Dirac Delta Function 84 --
1.16 Helmholtz's Theorem 96 --
2 Curved Coordinates, Tensors 103 --
2.1 Orthogonal Coordinates 103 --
2.2 Differential Vector Operators 108 --
2.3 Special Coordinate Systems: Introduction 113 --
2.4 Circular Cylindrical Coordinates 114 --
2.5 Spherical Polar Coordinates 121 --
2.6 Tensor Analysis 131 --
2.7 Contraction, Direct Product 137 --
2.8 Quotient Rule 139 --
2.9 Pseudotensors, Dual Tensors 141 --
2.10 Non-Cartesian Tensors 150 --
2.11 Tensor Derivative Operators 160 --
3 Determinants and Matrices 165 --
3.1 Determinants 165 --
3.2 Matrices 174 --
3.3 Orthogonal Matrices 192 --
3.4 Hermitian Matrices, Unitary Matrices 206 --
3.5 Diagonalization of Matrices 213 --
3.6 Normal Matrices 227 --
4 Group Theory 237 --
4.1 Introduction to Group Theory 237 --
4.2 Generators of Continuous Groups 242 --
4.3 Orbital Angular Momentum 258 --
4.4 Angular Momentum Coupling 263 --
4.5 Homogeneous Lorentz Group 275 --
4.6 Lorentz Covariance of Maxwell's Equations 278 --
4.7 Discrete Groups 286 --
5 Infinite Series 303 --
5.2 Convergence Tests 306 --
5.3 Alternating Series 322 --
5.4 Algebra of Series 325 --
5.5 Series of Functions 329 --
5.6 Taylor's Expansion 334 --
5.7 Power Series 346 --
5.8 Elliptic Integrals 354 --
5.9 Bernoulli Numbers, Euler-Maclaurin Formula 360 --
5.10 Asymptotic Series 373 --
5.11 Infinite Products 381 --
6 Functions of a Complex Variable I 389 --
6.1 Complex Algebra 390 --
6.2 Cauchy-Riemann Conditions 399 --
6.3 Cauchy's Integral Theorem 404 --
6.4 Cauchy's Integral Formula 411 --
6.5 Laurent Expansion 416 --
6.6 Mapping 425 --
6.7 Conformal Mapping 434 --
7 Functions of a Complex Variable II 439 --
7.1 Singularities 439 --
7.2 Calculus of Residues 444 --
7.3 Dispersion Relations 469 --
7.4 Method of Steepest Descents 477 --
8 Differential Equations 487 --
8.1 Partial Differential Equations 487 --
8.2 First-Order Differential Equations 496 --
8.3 Separation of Variables 506 --
8.4 Singular Points 516 --
8.5 Series Solutions
Frobenius's Method
518 --
8.6 A Second Solution 533 --
8.7 Nonhomogeneous Equation
Green's Function
548 --
8.8 Numerical Solutions 567 --
9 Sturm-Liouville Theory 575 --
9.1 Self-Adjoint ODEs 575 --
9.2 Hermitian Operators 588 --
9.3 Gram-Schmidt Orthogonalization 596 --
9.4 Completeness of Eigenfunctions 604 --
9.5 Green's Function
Eigenfunction Expansion
616 --
10 Gamma-Factorial Function 631 --
10.1 Definitions, Simple Properties 631 --
10.2 Digamma and Polygamma Functions 643 --
10.3 Stirling's Series 649 --
10.4 Beta Function 654 --
10.5 Incomplete Gamma Function 660 --
11 Bessel Functions 669 --
11.1 Bessel Functions of the First Kind J[subscript v](x) 669 --
11.2 Orthogonality 688 --
11.3 Neumann Functions, Bessel Functions of the Second Kind 694 --
11.4 Hankel Functions 702 --
11.5 Modified Bessel Functions I[subscript v](x) and K[subscript v](x) 709 --
11.6 Asymptotic Expansions 716 --
11.7 Spherical Bessel Functions 722 --
12 Legendre Functions 739 --
12.1 Generating Function 739 --
12.2 Recurrence Relations 748 --
12.3 Orthogonality 755 --
12.4 Alternate Definitions 767 --
12.5 Associated Legendre Functions 771 --
12.6 Spherical Harmonics 786 --
12.7 Orbital Angular Momentum Operators 792 --
12.8 Addition Theorem for Spherical Harmonics 796 --
12.9 Integrals of Three Ys 802 --
12.10 Legendre Functions of the Second Kind 806 --
12.11 Vector Spherical Harmonics 813 --
13 Special Functions 817 --
13.1 Hermite Functions 817 --
13.2 Laguerre Functions 828 --
13.3 Chebyshev Polynomials 839 --
13.4 Hypergeometric Functions 850 --
13.5 Confluent Hypergeometric Functions 855 --
14 Fourier Series 863 --
14.1 General Properties 863 --
14.2 Advantages, Uses of Fouries Series 870 --
14.3 Applications of Fourier Series 874 --
14.4 Properties of Fourier Series 886 --
14.5 Gibbs Phenomenon 893 --
14.6 Discrete Fourier Transform 898 --
15 Integral Transforms 905 --
15.1 Integral Transforms 905 --
15.2 Development of the Fourier Integral 909 --
15.3 Fourier Transforms
Inversion Theorem
911 --
15.4 Fourier Transform of Derivatives 920 --
15.5 Convolution Theorem 924 --
15.6 Momentum Representation 928 --
15.7 Transfer Functions 935 --
15.8 Laplace Transforms 938 --
15.9 Laplace Transform of Derivatives 946 --
15.10 Other Properties 953 --
15.11 Convolution or Faltungs Theorem 965 --
15.12 Inverse Laplace Transform 969 --
16 Integral Equations 983 --
16.2 Integral Transforms, Generating Functions 991 --
16.3 Neumann Series, Separable Kernels 997 --
16.4 Hilbert-Schmidt Theory 1009 --
17 Calculus of Variations 1017 --
17.1 A Dependent and an Independent Variable 1018 --
17.2 Applications of the Euler Equation 1023 --
17.3 Several Dependent Variables 1031 --
17.4 Several Independent Variables 1036 --
17.5 Several Dependent and Independent Variables 1038 --
17.6 Lagrangian Multipliers 1039 --
17.7 Variation With Constraints 1045 --
17.8 Rayleigh-Ritz Variational Technique 1052 --
18 Nonlinear Methods and Chaos 1059 --
18.2 Logistic Map 1060 --
18.3 Sensitivity to Initial Conditions 1064 --
18.4 Nonlinear Differential Equations 1068 --
Appendix 1 Real Zeros of a Function 1085 --
Appendix 2 Gaussian Quadrature 1089.
Excerpt
Loading Excerpt...
Author Notes
Loading Author Notes...
Reviews from GoodReads
Loading GoodReads Reviews.
Staff View
Loading Staff View.