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E-grāmata: Guide To Mathematical Methods For Physicists, A: Advanced Topics And Applications

(Univ Of Milano-bicocca, Italy), (Univ Of Rome Tor Vergata, Italy), (Sorbonne Univ, Paris, France)
  • Formāts: 308 pages
  • Sērija : Advanced Textbooks in Physics
  • Izdošanas datums: 29-Aug-2018
  • Izdevniecība: World Scientific Europe Ltd
  • Valoda: eng
  • ISBN-13: 9781786345509
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Guide To Mathematical Methods For Physicists, A: Advanced Topics And ApplicationsPalielināt
  • Formāts: 308 pages
  • Sērija : Advanced Textbooks in Physics
  • Izdošanas datums: 29-Aug-2018
  • Izdevniecība: World Scientific Europe Ltd
  • Valoda: eng
  • ISBN-13: 9781786345509
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This book provides a self-contained and rigorous presentation of the main mathematical tools needed to approach many courses at the last year of undergraduate in Physics and MSc programs, from Electromagnetism to Quantum Mechanics. It complements A Guide to Mathematical Methods for Physicists: With Problems and Solutions with advanced topics and physical applications. The different arguments are organised in three main sections: Complex Analysis, Differential Equations and Hilbert Spaces, covering most of the standard mathematical method tools in modern physics. One of the purposes of the book is to show how seemingly different mathematical tools like, for instance, Fourier transforms, eigenvalue problems, special functions and so on, are all deeply interconnected. It contains a large number of examples, problems and detailed solutions, emphasising the main purpose of relating concrete physical examples with more formal mathematical aspects.

Preface v
Part I Complex Analysis
1(68)
Introduction
3(2)
1 Mapping Properties of Holomorphic Functions
5(20)
1.1 Local Behaviour of Holomorphic Functions
5(9)
1.2 The Riemann Mapping Theorem
14(2)
1.3 Applications of Conformal Mapping
16(7)
1.4 Exercises
23(2)
2 Laplace Transform
25(16)
2.1 The Laplace Transform
25(8)
2.2 Integral Transforms and Differential Equations
33(5)
2.3 Exercises
38(3)
3 Asymptotic Expansions
41(28)
3.1 Asymptotic Series
42(5)
3.2 Laplace and Fourier Integrals
47(4)
3.3 Laplace's Method
51(3)
3.4 Stationary Phase Method
54(3)
3.5 Saddle-Point Method
57(7)
3.6 Exercises
64(5)
Part II Differential Equations
69(102)
Introduction
71(4)
4 The Cauchy Problem for Differential Equations
75(18)
4.1 Cauchy Problem for Ordinary Differential Equations
75(6)
4.2 Second-Order Linear Ordinary Differential Equations
81(4)
4.3 Second-Order Linear Partial Differential Equations
85(5)
4.4 Exercises
90(3)
5 Boundary Value Problems
93(24)
5.1 Boundary Value Problems in One Dimension
94(10)
5.2 Boundary Value Problems for Partial Differential Equations
104(4)
5.3 The Dirichlet Problem for the Sphere
108(4)
5.4 Exercises
112(5)
6 Green Functions
117(30)
6.1 Fundamental Solutions and Green Functions
117(3)
6.2 Linear Ordinary Differential Equations
120(5)
6.3 The Fourier Transform Method
125(3)
6.4 Linear Partial Differential Equations
128(8)
6.5 Green Functions and Linear Response
136(4)
6.6 Green Functions and the Spectral Theorem
140(4)
6.7 Exercises
144(3)
7 Power Series Methods
147(24)
7.1 Ordinary and Singular Points of an Ordinary Differential Equation
147(2)
7.2 Series Solutions for Second-Order Linear Ordinary Differential Equations
149(19)
7.3 Exercises
168(3)
Part III Hilbert Spaces
171(60)
Introduction
173(2)
8 Compact Operators and Integral Equations
175(14)
8.1 Compact Operators
175(6)
8.2 Predholm Equation of Second Type
181(5)
8.3 Exercises
186(3)
9 Hilbert Spaces and Quantum Mechanics
189(42)
9.1 The Schrodinger Equation
189(5)
9.2 Quantum Mechanics and Probability
194(5)
9.3 Spectrum of the Hamiltonian Operator
199(10)
9.4 Heisenberg Uncertainty Principle
209(2)
9.5 Compatible Observables
211(1)
9.6 Time Evolution for Conservative Systems
212(3)
9.7 Dirac Notation
215(2)
9.8 WKB Method
217(9)
9.9 Exercises
226(5)
Part IV Appendices
231(2)
Appendix A Review of Basic Concepts 233(8)
Appendix B Solutions of the Exercises 241(48)
Bibliography 289(2)
Index 291
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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