Mathematical Methods in the Physical Sciences
Publisher: John Wiley & Sons
Published: 1983
Language: eng
Table of contents: label: 1
title: Infinite Series, Power Series
pagenum: 1; label: 1.
title: The geometric series
pagenum: 1; label: 2.
title: Definitions and notation
pagenum: 3; label: 3.
title: Applications of series
pagenum: 5; label: 4.
title: Convergent and divergent series
pagenum: 5; label: 5.
title: Testing series for convergence; the preliminary test
pagenum: 7; label: 6.
title: Tests for convergence of series of positive terms; absolute convergence
pagenum: 8; label: 7.
title: Alternating series
pagenum: 15; label: 8.
title: Conditionally convergent series
pagenum: 16; label: 9.
title: Useful facts about series
pagenum: 17; label: 10.
title: Power series; interval of convergence
pagenum: 18; label: 11.
title: Theorems about power series
pagenum: 21; label: 12.
title: Expanding functions in power series
pagenum: 22; label: 13.
title: Techniques for obtaining power series expansions
pagenum: 24; label: 14.
title: Questions of convergence and accuracy in computation
pagenum: 29; label: 15.
title: Some uses of series
pagenum: 33; label: 16.
title: Miscellaneous problems
pagenum: 41; label: 2
title: Complex Numbers
pagenum: 43; label: 1.
title: Introduction
pagenum: 43; label: 2.
title: Real and imaginary parts of a complex number
pagenum: 44; label: 3.
title: The complex plane
pagenum: 45; label: 4.
title: Terminology and notation
pagenum: 46; label: 5.
title: Complex algebra
pagenum: 48; label: 6.
title: Complex infinite series
pagenum: 54; label: 7.
title: Complex power series; circle of convergence
pagenum: 56; label: 8.
title: Elementary functions of complex numbers
pagenum: 58; label: 9.
title: Euler's formula
pagenum: 60; label: 10.
title: Powers and roots of complex numbers
pagenum: 63; label: 11.
title: The exponential and trigonometric functions
pagenum: 66; label: 12.
title: Hyperbolic functions
pagenum: 69; label: 13.
title: Logarithms
pagenum: 71; label: 14.
title: Complex roots and powers
pagenum: 72; label: 15.
title: Inverse trigonometric and hyperbolic functions
pagenum: 74; label: 16.
title: Some applications
pagenum: 76; label: 17.
title: Miscellaneous problems
pagenum: 79; label: 3
title: Linear Equations; Vectors, Matrices, and Determinants
pagenum: 81; label: 1.
title: Introduction
pagenum: 81; label: 2.
title: Sets of linear equations, row reduction
pagenum: 82; label: 3.
title: Determinants; Cramer's rule
pagenum: 87; label: 4.
title: Vectors
pagenum: 95; label: 5.
title: Lines and planes
pagenum: 105; label: 6.
title: Matrix operations
pagenum: 113; label: 7.
title: Linear combinations, linear functions, linear operators
pagenum: 127; label: 8.
title: General theory of sets of linear equations
pagenum: 130; label: 9.
title: Special matrices
pagenum: 139; label: 10.
title: Miscellaneous problems
pagenum: 142; label: 4
title: Partial Differentiation
pagenum: 145; label: 1.
title: Introduction and notation
pagenum: 145; label: 2.
title: Power series in two variables
pagenum: 148; label: 3.
title: Total differentials
pagenum: 150; label: 4.
title: Approximate calculations using differentials
pagenum: 154; label: 5.
title: Chain rule or differentiating a function of a function
pagenum: 156; label: 6.
title: Implicit differentiation
pagenum: 159; label: 7.
title: More chain rule
pagenum: 161; label: 8.
title: Application of partial differentiation to maximum and minimum problems
pagenum: 169; label: 9.
title: Maximum and minimum problems with constraints; Lagrange multipliers
pagenum: 172; label: 10.
title: Endpoint or boundary point problems
pagenum: 181; label: 11.
title: Change of variables
pagenum: 186; label: 12.
title: Differentiation of integrals; Leibniz' rule
pagenum: 192; label: 13.
title: Miscellaneous problems
pagenum: 197; label: 5
title: Multiple Integrals; Applications of Integration
pagenum: 201; label: 1.
title: Introduction
pagenum: 201; label: 2.
title: Double and triple integrals
pagenum: 201; label: 3.
title: Applications of integration ; single and multiple integrals
pagenum: 208; label: 4.
title: Change of variables in integralS; Jacobians
pagenum: 217; label: 5.
title: Surface integrals
pagenum: 228; label: 6.
title: Miscellaneous problems
pagenum: 231; label: 6
title: Vector Analysis
pagenum: 235; label: 1.
title: Introduction
pagenum: 235; label: 2.
title: Applications of vector multiplication
pagenum: 235; label: 3.
title: Triple products
pagenum: 237; label: 4.
title: Differentiation of vectors
pagenum: 244; label: 5.
title: Fields
pagenum: 248; label: 6.
title: Directional derivative; gradient
pagenum: 249; label: 7.
title: Some other expressions involving V
pagenum: 254; label: 8.
title: Line integrals
pagenum: 257; label: 9.
title: Green's theorem in the plane
pagenum: 266; label: 10.
title: The divergence and the divergence theorem
pagenum: 271; label: 11.
title: The curl and Stokes' theorem
pagenum: 281; label: 12.
title: Miscellaneous problems
pagenum: 293; label: 7
title: Fourier Series
pagenum: 297; label: 1.
title: Introduction
pagenum: 297; label: 2.
title: Simple harmonic motion and wave motion; periodic functions
pagenum: 297; label: 3.
title: Applications of Fourier series
pagenum: 302; label: 4.
title: Average value of a function
pagenum: 304; label: 5.
title: Fourier coefficients
pagenum: 307; label: 6.
title: Dirichlet conditions
pagenum: 313; label: 7.
title: Complex form of Fourier series
pagenum: 315; label: 8.
title: Other intervals
pagenum: 317; label: 9.
title: Even and odd functions
pagenum: 321; label: 10.
title: An application to sound
pagenum: 328; label: 11.
title: Parseval's theorem
pagenum: 331; label: 12.
title: Miscellaneous problems
pagenum: 334; label: 8
title: Ordinary Differential Equations
pagenum: 337; label: 1.
title: Introduction
pagenum: 337; label: 2.
title: Separable equations
pagenum: 341; label: 3.
title: Linear first-order equations
pagenum: 346; label: 4.
title: Other methods for first order equations
pagenum: 350; label: 5.
title: Second-order linear equations with constant coefficients and zero right-hand side
pagenum: 352; label: 6.
title: Second-order linear equations with constant coefficients and right-hand side not zero
pagenum: 361; label: 7.
title: Other second-order equations
pagenum: 374; label: 8.
title: Miscellaneous problems
pagenum: 379; label: 9
title: Calculus of Variations
pagenum: 383; label: 1.
title: Introduction
pagenum: 383; label: 2.
title: The Euler equation
pagenum: 386; label: 3.
title: Using the Euler equation
pagenum: 389; label: 4.
title: The brachistochrone problem; cycloids
pagenum: 393; label: 5.
title: Several dependent variables; Lagrange's equations
pagenum: 396; label: 6.
title: Isoperimetric problems
pagenum: 401; label: 7.
title: Variational notation
pagenum: 403; label: 8.
title: Miscellaneous problems
pagenum: 404; label: 10
title: Coordinate Transformations; Tensor Analysis
pagenum: 407; label: 1.
title: Introduction
pagenum: 407; label: 2.
title: Linear transformations
pagenum: 409; label: 3.
title: Orthogonal transformations
pagenum: 410; label: 4.
title: Eigenvalues and eigenvectors; diagonalizing matrices
pagenum: 413; label: 5.
title: Applications of diagonalization
pagenum: 420; label: 6.
title: Curvilinear coordinates
pagenum: 426; label: 7.
title: Scale factors and basis vectors for orthogonal systems
pagenum: 428; label: 8.
title: General curvilinear coordinates
pagenum: 429; label: 9.
title: Vector operators in orthogonal curvilinear coordinates
pagenum: 431; label: 10.
title: Tensor analysis—introduction
pagenum: 435; label: 11.
title: Cartesian tensors
pagenum: 437; label: 12.
title: Uses of tensors; dyadics
pagenum: 441; label: 13.
title: General coordinate systems
pagenum: 447; label: 14.
title: Vector operations in tensor notation
pagenum: 452; label: 15.
title: Miscellaneous problems
pagenum: 453; label: 11
title: Gamma, Beta, and Error Functions; Asymptotic Series; Stirling's Formula; Elliptic Integrals and Functions
pagenum: 457; label: 1.
title: Introduction
pagenum: 457; label: 2.
title: The factorial function
pagenum: 457; label: 3.
title: Definition of the gamma function; recursion relation
pagenum: 458; label: 4.
title: The gamma function of negative numbers
pagenum: 460; label: 5.
title: Some important formulas involving gamma functions
pagenum: 461; label: 6.
title: Beta functions
pagenum: 462; label: 7.
title: The relation between the beta and gamma functions
pagenum: 463; label: 8.
title: The simple pendulum
pagenum: 465; label: 9.
title: The error function
pagenum: 467; label: 10.
title: Asymptotic series
pagenum: 469; label: 11.
title: Stirling's formula
pagenum: 472; label: 12.
title: Elliptic integrals and functions
pagenum: 474; label: 13.
title: Miscellaneous problems
pagenum: 481; label: 12
title: Series Solutions of Differential Equations; Legendre Polynomials; Bessel Functions; Sets of Orthogonal Functions
pagenum: 483; label: 1.
title: Introduction
pagenum: 483; label: 2.
title: Legendre's equation
pagenum: 485; label: 3.
title: Leibniz' rule for differentiating products
pagenum: 488; label: 4.
title: Rodrigues' formula
pagenum: 489; label: 5.
title: Generating function for Legendre polynomials
pagenum: 490; label: 6.
title: Complete sets of orthogonal functions
pagenum: 496; label: 7.
title: Orthogonality of the Legendre polynomials
pagenum: 499; label: 8.
title: Normalization of the Legendre polynomials
pagenum: 500; label: 9.
title: Legendre series
pagenum: 502; label: 10.
title: The associated Legendre functions
pagenum: 504; label: 11.
title: Generalized power series or the method of Frobenius
pagenum: 506; label: 12.
title: Bessel's equation
pagenum: 509; label: 13.
title: The second solution of Bessel's equation
pagenum: 512; label: 14.
title: Tables, graphs, and zeros of Bessel functions
pagenum: 514; label: 15.
title: Recursion relations
pagenum: 514; label: 16.
title: A general differential equation having Bessel functions as solutions
pagenum: 516; label: 17.
title: Other kinds of Bessel functions
pagenum: 517; label: 18.
title: The lengthening pendulum
pagenum: 519; label: 19.
title: Orthogonality of Bessel functions
pagenum: 522; label: 20.
title: Approximate formulas for Bessel functions
pagenum: 525; label: 21.
title: Some general comments about series solutions
pagenum: 526; label: 22.
title: Hermite functions; Laguerre functions; ladder operators
pagenum: 530; label: 23.
title: Miscellaneous problems
pagenum: 537; label: 13
title: Partial Differential Equations
pagenum: 541; label: 1.
title: Introduction
pagenum: 541; label: 2.
title: Laplace's equation ; steady-state temperature in a rectangular plate
pagenum: 543; label: 3.
title: The diffusion or heat flow equation; heat flow in a bar or slab
pagenum: 550; label: 4.
title: The wave equation; the vibrating string
pagenum: 554; label: 5.
title: Steady-state temperature in a cylinder
pagenum: 558; label: 6.
title: Vibration of a circular membrane
pagenum: 564; label: 7.
title: Steady-state temperature in a sphere
pagenum: 567; label: 8.
title: Poisson's equation
pagenum: 570; label: 9.
title: Miscellaneous problems
pagenum: 576; label: 14
title: Functions of a Complex Variable
pagenum: 579; label: 1.
title: Introduction
pagenum: 579; label: 2.
title: Analytic functions
pagenum: 580; label: 3.
title: Contour integrals
pagenum: 588; label: 4.
title: Laurent series
pagenum: 592; label: 5.
title: The residue theorem
pagenum: 596; label: 6.
title: Methods of finding residues
pagenum: 598; label: 7.
title: Evaluation of definite integrals by use of the residue theorem
pagenum: 602; label: 8.
title: The point at infinity; residues at infinity
pagenum: 614; label: 9.
title: Mapping
pagenum: 617; label: 10.
title: Some applications of conformal mapping
pagenum: 622; label: 11.
title: Miscellaneous problems
pagenum: 630; label: 15
title: Integral Transforms
pagenum: 635; label: 1.
title: Introduction
pagenum: 635; label: 2.
title: The Laplace transform
pagenum: 639; label: 3.
title: Solution of differential equations by Laplace transforms
pagenum: 642; label: 4.
title: Fourier transforms
pagenum: 647; label: 5.
title: Convolution; Parseval's theorem
pagenum: 655; label: 6.
title: Inverse Laplace transform (Bromwich integral)
pagenum: 662; label: 7.
title: The Dirac delta function
pagenum: 665; label: 8.
title: Green functions
pagenum: 670; label: 9.
title: Integral transform solutions of partial differential equations
pagenum: 676; label: 10.
title: Miscellaneous problems
pagenum: 681; label: 16
title: Probability
pagenum: 685; label: 1.
title: Introduction; definition of probability
pagenum: 685; label: 2.
title: Sample space
pagenum: 687; label: 3.
title: Probability theorems
pagenum: 692; label: 4.
title: Methods of counting
pagenum: 699; label: 5.
title: Random variables
pagenum: 707; label: 6.
title: Continuous distributions
pagenum: 712; label: 7.
title: Binomial distribution
pagenum: 718; label: 8.
title: The normal or Gaussian distribution
pagenum: 723; label: 9.
title: The Poisson distribution
pagenum: 728; label: 10.
title: Applications to experimental measurements
pagenum: 731; label: 11.
title: Miscellaneous problems
pagenum: 737; title: References
pagenum: 741; title: Bibliography
pagenum: 743; title: Answers to Selected Problems
pagenum: 747; title: Index
pagenum: 775