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Computational methods for physics /
"There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physica...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Structure and teaching; Website and materials; Acknowledgements; 1 Programming overview; 1.1 Arithmetic operations; 1.2 Comparison operations; 1.3 Variables; 1.4 Control structures; 1.5 Functions; 1.6 Input and output; 1.7 Recursion; 1.8 Function pointers; 1.9 Mathematica-specific array syntax; 1.10 Implementations and pseudo-code; 1.11 Timing and operation counts; 1.12 Units and dimensions; Problems; Lab problems; 2 Ordinary differential equations; 2.1 Physical motivation; 2.2 The Verlet method; 2.3 Discretization; 2.4 Runge-Kutta methods.
- 2.5 Stability of numerical methods2.6 Multi-step methods; Further reading; Problems; Lab problems; 3 Root-finding; 3.1 Physical motivation; 3.2 Finding roots; Further reading; Problems; Lab problems; 4 Partial differential equations; 4.1 Physical motivation; 4.2 Finite difference in one dimension; 4.3 Finite difference in two dimensions; 4.4 Examples; Further reading; Problems; Lab problems; 5 Time-dependent problems; 5.1 Physical motivation; 5.2 Exactly solvable cases; 5.3 Discretization and methods; 5.4 Crank-Nicolson for the Schrodinger equation; Further reading; Problems; Lab problems.
- 6 Integration6.1 Physical motivation; 6.2 One-dimensional quadrature; 6.3 Interpolation; 6.4 Higher-dimensional quadrature; 6.5 Monte Carlo integration; Problems; Lab problems; 7 Fourier transform; 7.1 Fourier transform; 7.2 Power spectrum; 7.3 Fourier series; 7.4 Discrete Fourier transform; 7.5 Recursion; 7.6 FFT algorithm; 7.7 Applications; Further reading; Problems; Lab problems; 8 Harmonic oscillators; 8.1 Physical motivation; 8.2 Three balls and two springs; 8.3 Solution for a particular case; 8.4 General solution; 8.5 Balls and springs in D=3; Further reading; Problems; Lab problems.
- 9 Matrix inversion9.1 Definitions and points of view; 9.2 Physical motivation; 9.3 How do you invert a matrix?; 9.4 Determinants; 9.5 Constructing A-1; Further reading; Problems; Lab problems; 10 The eigenvalue problem; 10.1 Fitting data; 10.2 Least squares; 10.3 The eigenvalue problem; 10.4 Physical motivation; 10.5 The power method; 10.6 Simultaneous iteration and QR iteration; 10.7 Quantum mechanics and perturbation; Further reading; Problems; Lab problems; 11 Iterative methods; 11.1 Physical motivation; 11.2 Iteration and decomposition; 11.3 Krylov subspace; Further reading; Problems.
- Lab problems12 Minimization; 12.1 Physical motivation; 12.2 Minimization in one dimension; 12.3 Minimizing u(x); 12.4 Nonlinear least squares; 12.5 Line minimization; 12.6 Monte Carlo minimization; Further reading; Problems; Lab problems; 13 Chaos; 13.1 Nonlinear maps; 13.2 Periodicity and doubling; 13.3 Characterization of chaos; 13.4 Ordinary differential equations; 13.5 Fractals and dimension; Further reading; Problems; Lab problems; 14 Neural networks; 14.1 A neural network model; 14.2 Training; 14.3 Example and interpretation; 14.4 Hidden layers; 14.5 Usage and caveats.