Mathematical Methods for Physicists : a Comprehensive Guide.

Author/creator Arfken, George B., 1922-
Other author Weber, Hans Jürgen, 1928-
Format Electronic
Edition7th ed.
Publication InfoBurlington : Elsevier Science, 2012.
Description1 online resource (1,229 pages)
Supplemental ContentElsevier ScienceDirect
Subjects

Contents Front Cover; Mathematical Methods for Physicists: A Comprehensive Guide; Copyright; Table of Contents; Preface; 1 Mathematical Preliminaries; 1.1 Infinite Series; Fundamental Concepts; Comparison Test; Cauchy Root Test; D'Alembert (or Cauchy) Ratio Test; Cauchy (or Maclaurin) Integral Test; More Sensitive Tests; Alternating Series; Absolute and Conditional Convergence; Operations on Series; Improvement of Convergence; Rearrangement of Double Series; 1.2 Series of Functions; Uniform Convergence; Weierstrass M (Majorant) Test; Abel's Test; Properties of Uniformly Convergent Series.
Contents Taylor's Expansion; Power Series; Properties of Power Series; Uniqueness Theorem; Indeterminate Forms; Inversion of Power Series; 1.3 Binomial Theorem; 1.4 Mathematical Induction; 1.5 Operations on Series Expansions of Functions; 1.6 Some Important Series; 1.7 Vectors; Basic Properties; Dot (Scalar) Product; Orthogonality; 1.8 Complex Numbers and Functions; Basic Properties; Functions in the Complex Domain; Polar Representation; Complex Numbers of Unit Magnitude; Circular and Hyperbolic Functions; Powers and Roots; Logarithm; 1.9 Derivatives and Extrema; Stationary Points.
Contents 1.10 Evaluation of IntegralsIntegration by Parts; Special Functions; Other Methods; Multiple Integrals; Remarks: Changes of Integration Variables; 1.11 Dirac Delta Function; Properties of d(x); Kronecker Delta; Additional Readings; 2 Determinants and Matrices; 2.1 Determinants; Homogeneous Linear Equations; Inhomogeneous Linear Equations; Definitions; Properties of Determinants; Laplacian Development by Minors; Linear Equation Systems; Determinants and Linear Dependence; Linearly Dependent Equations; Numerical Evaluation; 2.2 Matrices; Basic Definitions; Equality; Addition, Subtraction.
Contents Multiplication (by a Scalar)Matrix Multiplication (Inner Product); Unit Matrix; Diagonal Matrices; Matrix Inverse; Derivatives of Determinants; Systems of Linear Equations; Determinant Product Theorem; Rank of a Matrix; Transpose, Adjoint, Trace; Operations on Matrix Products; Matrix Representation of Vectors; Orthogonal Matrices; Unitary Matrices; Hermitian Matrices; Extraction of a Row or Column; Direct Product; Functions of Matrices; Additional Readings; 3 Vector Analysis; 3.1 Review of Basic Properties; 3.2 Vectors in 3-D Space; Vector or Cross Product; Scalar Triple Product.
Contents Vector Triple Product; 3.3 Coordinate Transformations; Rotations; Orthogonal Transformations; Reflections; Successive Operations; 3.4 Rotations in R3; 3.5 Differential Vector Operators; Gradient, ; Divergence, ; Curl x ; 3.6 Differential Vector Operators: Further Properties; Successive Applications of; Laplacian; Irrotational and Solenoidal Vector Fields; Maxwell's Equations; Vector Laplacian; Miscellaneous Vector Identities; 3.7 Vector Integration; Line Integrals; Surface Integrals; Volume Integrals; 3.8 Integral Theorems; Gauss' Theorem; Green's Theorem; Stokes' Theorem.
Abstract Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the€key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples.
General note3.9 Potential Theory.
Source of descriptionPrint version record.
Issued in other formPrint version: Arfken, George B. Mathematical Methods for Physicists : A Comprehensive Guide. Burlington : Elsevier Science, ©2012 9780123846549
ISBN9780123846556
ISBN0123846552

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