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Mathematical methods in physics /
This new book on Mathematical Methods In Physics is intended to be used for a 2-semester course for first year MA or PhD physics graduate students, or senior undergraduates majoring in physics, engineering or other technically related fields. Emphasis has been placed on physics applications, include...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, N.J. :
World Scientific,
©1996.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Ch. 1. Vector analysis. 1.1. Vector algebra. 1.2. Examples and applications. 1.3. Theory of curves in space
- ch. 2. Tensor analysis. 2.1. nth rank tensor. 2.2. 2nd-rank isotropic (invariant) tensor. 2.3. Contraction. 2.4. Outer product theorem. 2.5. 3rd-rank isotropic (invariant) tensor. 2.6. Examples and applications. 2.7. Geometrical representation of tensors. 2.8. Moment of inertia tensor
- ch. 3. Fields. 3.1. Tensor field. 3.2. Gauss' theorem. 3.3. Stokes' theorem. 3.4. Connectivity of space. 3.5. Helmholtz theorem. 3.6. Equivalent forms of Gauss' and Stokes' theorems. 3.7. Maxwell's equations. 3.8. Curvilinear orthogonal coordinate systems
- ch. 4. Matrix and vector algebra in N-dimensional space. 4.1. Algebra of N-dimensional complex space. 4.2. Matrix algebra. 4.3. Examples of matrices. 4.4. Tensor analysis in N-dimensional space. 4.5. Matrices in N-dimensional space. 4.6. Linear independence and completeness.
- Ch. 5. Hilbert space. 5.1. Definitions. 5.2. Weierstrass's theorem. 5.3. Examples of complete orthonormal sets
- ch. 6. Theory of functions of a complex variable. 6.1. Theory of complex variables. 6.2. Analytic functions. 6.3. Applications of analytic functions. 6.4. Integral calculus of complex variables. 6.5. Taylor's theorem. 6.6. Laurent theorem. 6.7. Singularities. 6.8. Liouville theorem. 6.9. Multiple-valued functions. 6.10. Theory of residues. 6.11. Analytic continuation
- ch. 7. Theory of ordinary differential equations. 7.1. Ordinary differential equations in physics. 7.2. Ordinary points and singular points. 7.3. Hermite polynomials. 7.4. Behavior of solutions near singular points. 7.5. Bessel functions
- ch. 8. Theory of partial differential equations. 8.1. Examples of field equations in physics. 8.2. Theory of characteristics
- ch. 9. Heat conduction. 9.1. Fundamental equations. 9.2. Infinite medium. 9.3. Semi-infinite medium.
- Ch. 10. The eigenvalue problem. 10.1. Eigenvalues and eigenfunctions. 10.2. Harmonic oscillator/free particle in a sphere. 10.3. The variational principle
- ch. 11. Wave equations. 11.1. Infinite medium. 11.2. Retarded and advanced D-functions. 11.3. Field due to a moving point charge. 11.4. Finite boundary medium. 11.5. Green's function method applied to Schrodinger's equation and to heat conduction.