Analytic Methods in Physics
Blackwell Verlag GmbH (Hersteller)
978-3-527-60307-7 (ISBN)
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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.
Charlie Harper, Prof., California State University, Hayward, CA, USA.
VECTOR ANALYSIS
The Cartesian Coordinate System
Differentiation of Vector Functions
Orthogonal Curvilinear Coordinates
Problems
Appedix I: SI Units
Appendix II: Determinants
MODERN ALGEBRAIC METHODS IN PHYSICS
Matrix Analysis
Essentials of Vector Spaces
Essential Algebraic Structures
Problems
FUNCTIONS OF A COMPLEX VARIABLE
Complex Variables and Their Representations
The de Moivre Theorem
Analytic Functions of a Complex Variable
Contour Integrals
The Taylor Series and Zeros of f(z)
The Laurent Expansion
Problems
Appendix: Series
CALCULUS OF RESIDUES
Isolated Singular Points
Evaluation of Residues
The Cauchy Residue Theorem
The Cauchy Principal Value
Evaluation of Definite Integrals
Dispersion Relations
Conformal Transformations
Multi-Valued Functions
Problems
FOURIER SERIES
The Fourier Cosine and Sine Series
Change of Interval
Complex Form of the Fourier Series
Generalized Fourier Series and the Dirac Delta Function
Summation of the Fourier Series
The Gibbs Phenomenon
Summary of Some Properties of Fourier Series
Problems
FOURIER TRANSFORMS
Cosine and Sine Transforms
The Transforms of Derivatives
The Convolution Theorem
Parseval´s Relation
Problems
ORDINARY DIFFERENTIAL EQUATIONSFIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS
The Bernoulli Differential Equation
Second-Order Linear Differential Equations
Some Numerical Methods
Problems
PARTIAL DIFFERENTIAL EQUATIONS
The Method of Separation of Variables
Green´s Functions in Potential Theory
Some Numerical Methods
Problems
SPECIAL FUNCTIONS
The Sturm-Liouville Theory
The Hermite Polynomials
The Helmholtz Differential Equation in Spherical Coordinates and in Cylindrical Coordinates
The Hypergeometric Function
The Confluent Hypergeometric Function
Other Special Functions Used in Physics
Problems
Worksheet 9.1: The Quantum Mechanical Linear Harmonic Oscillator
Workshheet 9.2: The Legendre Differential Equation
Worksheet 9.3: The Laguerre Differential Equation
Workshheet 9.4: The Bessel Differential Equation
Workshheet 9.5: The Hypergeometric Differential Equation
INTEGRAL EQUATIONS
Integral Equations with Separable Kernels and with Displacement Kernels
The Neumann Series Method
The Abel Problem
Problems
APPLIED FUNCTIONAL ANALYSIS
Stationary Values of Certain Functions and Functionals
Hamilton´s Variational Principle in Mechanics
Formulation of Hamiltonian Mechanics
Continous Media and Fields
Transitions to Quantum Mechanics
Problems
GEOMETRIC METHODS IN PHYSICS
Transformation of Coordinates in Linear Spaces
Contravariant and Covariant Tensors
Tensor Algebra
The Line Element
Tensor Calculus
Equation of the Geodesic Line
Special Equations involving the Metric Tensor
Exterior Differential Forms
Problems
References
Index
| Erscheint lt. Verlag | 28.1.2005 |
|---|---|
| Verlagsort | Berlin |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| ISBN-10 | 3-527-60307-7 / 3527603077 |
| ISBN-13 | 978-3-527-60307-7 / 9783527603077 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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