Graduate Mathematical Physics
James J. Kelly
Bok Engelsk 2008 · Electronic books.
| Annen tittel | |
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| Utgitt | Hoboken : : Wiley, , 2008.
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| Omfang | 1 online resource (478 p.)
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| Opplysninger | Description based upon print version of record.. - Handbook of Time Series Analysis; Preface; Contents; Note to the Reader; 1 Analytic Functions; 1.1 Complex Numbers; 1.1.1 Motivation and Definitions; 1.1.2 Triangle Inequalities; 1.1.3 Polar Representation; 1.1.4 Argument Function; 1.2 Take Care with Multivalued Functions; 1.3 Functions as Mappings; 1.3.1 Mapping: w = e z; 1.3.2 Mapping: w = Sin[z]; 1.4 Elementary Functions and Their Inverses; 1.4.1 Exponential and Logarithm; 1.4.2 Powers; 1.4.3 Trigonometric and Hyperbolic Functions; 1.4.4 Standard Branch Cuts; 1.5 Sets,Curves,Regions and Domains; 1.6 Limits and Continuity. - 1.12.2 Cauchy Inequality1.12.3 Liouville's Theorem; 1.12.4 Fundamental Theorem of Algebra; 1.12.5 Zeros of Analytic Functions; 1.13 Laurent Series; 1.13.1 Derivation; 1.13.2 Example; 1.13.3 Classification of Singularities; 1.13.4 Poles and Residues; 1.14 Meromorphic Functions; 1.14.1 Pole Expansion; 1.14.2 Example: Tan[z]; 1.14.3 Product Expansion; 1.14.4 Example: Sin[z]; 2 Integration; 2.1 Introduction; 2.2 Good Tricks; 2.2.1 Parametric Differentiation; 2.2.2 Convergence Factors; 2.3 Contour Integration; 2.3.1 Residue Theorem; 2.3.2 Definite Integrals of the Form 0 ∫ 2Π f[sinΘ, cosΘ ∫dΘ. - 1.7 Differentiability1.7.1 Cauchy-Riemann Equations; 1.7.2 Differentiation Rules; 1.8 Properties of Analytic Functions; 1.9 Cauchy-Goursat Theorem; 1.9.1 Simply Connected Regions; 1.9.2 Proof; 1.9.3 Example; 1.10 Cauchy Integral Formula; 1.10.1 Integration Around Nonanalytic Regions; 1.10.2 Cauchy Integral Formula; 1.10.3 Example:Yukawa Field; 1.10.4 Derivatives of Analytic Functions; 1.10.5 Morera's Theorem; 1.11 Complex Sequences and Series; 1.11.1 Convergence Tests; 1.11.2 Uniform Convergence; 1.12 Derivatives and Taylor Series for Analytic Functions; 1.12.1 TaylorSeries. - 2.3.3 Definite Integrals of the Form -∞∫∞ f[x]dx2.3.4 Fourier Integrals; 2.3.5 CustomContours; 2.4 Isolated Singularities on the Contour; 2.4.1 Removable Singularity; 2.4.2 Cauchy Principal Value; 2.5 Integration Around a Branch Point; 2.6 Reduction to Tabulated Integrals; 2.6.1 Example: -∞∫∞ e -x4 dx; 2.6.2 Example: The Beta Function; 2.6.3 Example: -0 ∫ ∞ ωn/eβω -1 dω; 2.7 Integral Representations for Analytic Functions; 2.8 Using MATHEMATICA to Evaluate Integrals; 2.8.1 Symbolic Integration; 2.8.2 Numerical Integration; 2.8.3 Further Information; 3 Asymptotic Series; 3.1 Introduction. - 3.2 Method of Steepest Descent3.2.1 Example: Gamma Function; 3.3 Partial Integration; 3.3.1 Example: Complementary Error Function; 3.4 Expansion of an Integrand; 3.4.1 Example: Modified Bessel Function; 4 Generalized Functions; 4.1 Motivation; 4.2 Properties of the Dirac Delta Function; 4.3 Other Useful Generalized Functions; 4.3.1 Heaviside Step Function; 4.3.2 Derivatives of the Dirac Delta Function; 4.4 Green Functions; 4.5 Multidimensional Delta Functions; 5 Integral Transforms; 5.1 Introduction; 5.2 Fourier Transform; 5.2.1 Motivation; 5.2.2 Definition and Inversion. - 5.2.3 Basic Properties. - This up-to-date textbook on mathematical methods of physics is designed for a one-semester graduate or two-semester advanced undergraduate course. The formal methods are supplemented by applications that use MATHEMATICA to perform both symbolic and numerical calculations.The book is written by a physicist lecturer who knows the difficulties involved in applying mathematics to real problems. As many as 40 exercises are included at the end of each chapter. A student CD includes a basic introduction to MATHEMATICA, notebook files for each chapter, and solutions to selected exercises.*
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 3527406379. - 9783527406371
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