Analytic Methods in Physics

This Book Presents A Self-contained Treatment Of Invaluable Analytic Methods In Mathematical Physics. It Is Designed For Undergraduate Students And It Contains More Than Enough Material For A Two Semester (or Three Quarter) Course In Mathematical Methods Of Physics. With The Appropriate Selection Of Material, One May Use The Book For A One Semester Or A One Quarter Course. The Prerequisites Or Corequisites Are General Physics, Analytic Mechanics, Modern Physics, And A Working Knowledge Of Differential An Integral Calculus. 1. Vector Analysis -- 2. Modern Algebraic Methods In Physics -- 3. Functions Of A Complex Variable -- 4. Calculus Of Residues -- 5. Fourier Series -- 6. Fourier Transforms -- 7. Ordinary Differential Equations -- 8. Partial Differential Equations -- 9. Special Functions -- 10. Integral Equations -- 11. Applied Functional Analysis -- 12. Geometrical Methods In Physics -- Bibliography-- Index. Charlie Harper. Includes Bibliographical References (p. [317]-319) And Index. Title Preface Contents Chapter 1 Vector Analysis 1.1 Introduction 1.2 The Cartesian Coordinate System 1.3 Differentiation of Vector Functions 1.4 Integration of Vector Functions 1.5 Orthogonal Curvilinear Coordinates 1.6 Problems 1.7 Appendix I: Systbme International (SI) Units 1.8 Appendix 11: Properties of Determinants 1.9 Summary of Some Properties of Determinants Chapter 2 Modern Algebraic Methods in Physics 2.1 Introduction 2.2 Matrix Analysis 2.3 Essentials of Vector Spaces 2.4 Essential Algebraic Structures 2.5 Problems Chapter 3 Functions of a Complex Variable 3.1 Introduction 3.2 Complex Variables and Their Representations 3.3 The de Moivre Theorem 3.4 Analytic Functions of a Complex Variable 3.5 Contour Integrals 3.6 The Taylor Series and Zeros of f (z) 3.7 The Laurent Expansion 3.8 Problems 3.9 Appendix: Series Chapter 4 Calculus of Residues 4.1 Isolated Singular Points 4.2 Evaluation of Residues 4.3 The Cauchy Residue Theorem 4.4 The Cauchy Principal Value 4.5 Evaluation of Definite Integrals 4.6 Dispersion Relations 4.7 Conformal Transformations 4.8 Multi-valued Functions 4.9 Problems Chapter 5 Fourier Series 5.1 Introduction 5.2 The Fourier Cosine and Sine Series 5.3 Change of Interval 5.4 Complex Form of the Fourier Series 5.5 Generalized Fourier Series and the Dirac Delta Function 5.6 Summation of the Fourier Series 5.7 The Gibbs Phenomenon 5.8 Summary of Some Properties of Fourier Series 5.9 Problems Chapter 6 Fourier Transforms 6.1 Introduction 6.2 Cosine and Sine Transforms 6.3 The Transforms of Derivatives 6.4 The Convolution Theorem 6.5 Parseval's Relation 6.6 Problems Chapter 7 Ordinary Differential Equations 7.1 Introduction 7.2 First-Order Linear Differential Equations 7.3 The Bernoulli Differential Equation 7.4 Second-Order Linear Differential Equations 7.5 Some Numerical Methods 7.6 Problems Chapter 8 Partial Differential Equations 8.1 Introduction 8.2 The Method of Separation of Variables 8.3 Green's Functions in Potential Theory 8.4 Some Numerical Methods 8.5 Problems Chapter 9 Special Functions 9.1 Introduction 9.2 The Sturm-Liouville Theory 9.3 The Hermite Polynomials 9.4 The Helmholtz Differential Equation in Spherical Coordinates 9.5 The Helmholtz Differential Equation in Cylindrical Coordinates 9.6 The Hypergeometric Function 9.7 The Confluent Hypergeometric Function 9.8 Other Special Functions used in Physics 9.9 Problems Chapter 10 Integral Equations 10.1 Introduction 10.2 Integral Equations with Separable Kernels 10.3 Integral Equations with Displacement Kernels 10.4 The Neurnann Series Method 10.5 The Abel Problem 10.6 Problems Chapter 11 Applied Functional Analysis 11.1 Introduction 11.2 Stationary Values of Certain Functions and Functionals 11.3 Hamilton's Variational Principle in Mechanics 11.4 Formulation of Harniltonian Mechanics 11.5 Continuous Media and Fields 11.6 Transitions to Quantum Mechanics 11.7 Problems Chapter 12 Geometrical Methods in Physics 12.1 Introduction 12.2 Transformation of Coordinates in Linear Spaces 12.3 Contravariant and Covariant Tensors 12.4 Tensor Algebra 12.5 The Line Element 12.6 Tensor Calculus 12.7 The Equation of the Geodesic Line 12.8 Special Equations Involving the Metric Tensor 12.9 Exterior Differential Forms 12.10 Problems Bibliography Index "This book presents a self-contained treatment of invaluable analytic methods in mathematical physics. It is designed for undergraduate students and it contains more than enough material for a two semester (or three quarter) course in mathematical methods of physics. The prerequisites or corequisites are general physics, analytic mechanics, modern physics, and a working knowledge of differential and integral calculus."--BOOK JACKET