| Description |
1 online resource (xii, 400 pages) |
| Physical Medium |
polychrome |
| Description |
text file |
| Summary |
"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 physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303"-- Provided by publisher. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical physics.
|
|
Mathematical physics. |
|
Physics -- Data processing.
|
|
Physics -- Data processing. |
|
Numerical analysis.
|
|
Numerical analysis. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Franklin, Joel, 1975- Computational methods for physics. Cambridge : Cambridge University Press, 2013 9781107034303 (DLC) 2013003044 (OCoLC)820434099 |
| ISBN |
9781107058408 (electronic book) |
|
1107058406 (electronic book) |
|
9781107056053 (electronic book) |
|
1107056055 (electronic book) |
|
9781139525398 (electronic book) |
|
1139525395 (electronic book) |
|
9781107059627 |
|
1107059623 |
|
9781107034303 |
|
1107034302 |
|
9781299546035 |
|
129954603X |
|
