Umfang:
Online Ressource (1 v.)
,
Ill.
Ausgabe:
7. ed.
Ausgabe:
Online-Ausg.
ISBN:
9780123846549
Inhalt:
Mathematical Preliminaries -- Determinants and Matrices -- Vector Analysis -- Tensors and Differential Forms -- Vector Spaces -- Eigenvalue Problems -- Ordinary Differential Equations -- Sturm-Liouville Theory -- Partial Differential Equations -- Green's Functions -- Complex Variable Theory -- Further Topics in Analysis -- Gamma Function -- Bessel Functions -- Legendre Functions -- Angular Momentum -- Group Theory -- More Special Functions -- Fourier Series -- Integral Transforms -- Integral Equations -- Calculus of Variations -- Probability and Statistics
Inhalt:
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. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises. Revised and updated version of the leading text in mathematical physics Focuses on problem-solving skills and active learning, offering numerous chapter problems Clearly identified definitions, theorems, and proofs promote clarity and understanding New to this edition: Improved modular chapters New up-to-date examples More intuitive explanations
Anmerkung:
Previous ed.: Amsterdam; London: Elsevier Academic, 2005. - Includes bibliographical references and index. - Description based on print version record
,
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
,
Taylor's ExpansionPower 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
,
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
,
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
,
Vector Triple Product3.3 Coordinate Transformations; Rotations; Orthogonal Transformations; Reflections; Successive Operations; 3.4 Rotations in R3; 3.5 Differential Vector Operators; Gradient, ?; Divergence, ?·; Curl, ?×; 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
,
3.9 Potential Theory
,
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. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises. Revised and updated version of the leading text in mathematical physics Focuses on problem-solving skills and active learning, offering numerous chapter problems Clearly identified definitions, theorems, and proofs promote clarity and understanding New to this edition: Improved modular chapters New up-to-date examples More intuitive explanations
Weitere Ausg.:
ISBN 9780123846549
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Arfken, George B. (George Brown), 1922- Mathematical methods for physicists Oxford : Academic, 2012
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Electronic books
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