Exercises and Problems in Mathematical Methods of Physics
This book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics. This mission is retained in this book. The structure of the book is one that keeps pedagogical principles in mind...
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2020, 2020
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| Edition: | 2nd ed. 2020 |
| Series: | Undergraduate Lecture Notes in Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1 Hilbert spaces
- 1.1 Complete sets, Fourier expansions
- 1.1.1 Preliminary notions. Subspaces. Complete sets
- 1.1.2 Fourier expansions
- 1.1.3 Harmonic functions; Dirichlet and Neumann Problems
- 1.2 Linear operators
- 1.2.1 Linear operators defined giving T en = vn, and related Problems
- 1.2.2 Operators of the form T x = v(w;x) and T x = ån vn(wn;x)
- 1.2.3 Operators of the form T f (x) = j(x) f (x)
- 1.2.4 Problems involving differential operators
- 1.2.5 Functionals
- 1.2.6 Time evolution Problems. Heat equation
- 1.2.7 Miscellaneous Problems
- 2 Functions of a complex variable
- 2.1 Basic properties of analytic functions
- 2.2 Evaluation of integrals by complex variable methods
- 2.3 Harmonic functions and conformal mappings
- 3 Fourier and Laplace transforms. Distributions
- 3.1 Fourier transform in L1(R) and L2(R)
- 3.1.1 Basic properties and applications
- 3.1.2 Fourier transform and linear operators in L2(R)
- 3.2 Tempered distributions and Fourier transforms
- 3.2.1 General properties
- 3.2.2 Fourier transform, distributions and linear operators
- 3.2.3 Applications to ODE’s and related Green functions
- 3.2.4 Applications to general linear systems and Green functions
- 3.2.5 Applications to PDE’s
- 3.3 Laplace transforms
- vvi Contents
- Groups, Lie algebras, symmetries in physics
- 4.1 Basic properties of groups and representations
- 4.2 Lie groups and algebras
- 4.3 The groups SO3; SU2; SU3
- 4.4 Other direct applications of symmetries to physics
- Answers and Solutions.