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Computational methods using MATLAB : an introduction for physicists
Title
Computational methods using MATLAB : an introduction for physicists / P.K. Thiruvikraman.
ISBN
9780750337915
9780750337908
9780750337892
9780750337922
Publication
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]
Physical Description
1 online resource (various pagings) : illustrations (some color).
Local Notes
Access is available to the Yale community.
Notes
"Version: 202203"--Title page verso.
Access and use
Access restricted by licensing agreement.
Biographical / Historical Note
P.K. Thiruvikraman is currently Professor of Physics at Birla Institute of Technology and Science, Pilani, Hyderabad Campus. He has nearly two decades of experience in teaching courses from many areas of Physics. The author has a PhD in Physics from Mangalore University and a Master's degree in Physics from Indian Institute of Technology, Madras. He has also authored the book A course on Digital Image Processing with MATLAB.
Summary
This book provides an introduction to the computational methods commonly employed by physicists and engineers. The book discusses the details of the numerical algorithms involved and also provides MATLAB code for their implementation.
Variant and related titles
IOP ebooks.
Other formats
Also available in print.
Print version:
Format
Books / Online
Language
English
Added to Catalog
May 13, 2022
Series
[IOP release $release]
IOP ebooks. [2022 collection]
Bibliography
Includes bibliographical references.
Audience
Students in the physical sciences and engineering.
Contents
10. Partial differential equations
10.1. Partial differential equations in physics
10.2. Finite difference method for solving ordinary differential equations
10.3. Finite difference method for solving PDEs
10.4. A finite difference method for PDEs involving both spatial and temporal derivatives
11. Nonlinear dynamics, chaos, and fractals
11.1. History of chaos
11.2. The logistic map
11.3. The Lyapunov exponent
11.4. Differential equations : fixed points
11.5. Fractals
Appendix A. Solutions to selected exercises.
1. Introduction
1.1. A note of caution : rounding errors
1.2. More on the limitations of digital computers
2. Introduction to programming with MATLAB
2.1. Computer programming
2.2. Good programming practices
2.3. Introduction to MATLAB
2.4. HELP on MATLAB
2.5. Variables
2.6. Mathematical operations
2.7. Loops and control statements
2.8. Built-in MATLAB functions
2.9. Some more useful MATLAB commands and programming practices
2.10. Functions
2.11. Using MATLAB for visualisation
2.12. Producing sound using MATLAB
3. Finding the roots and zeros of a function
3.1. The roots of a polynomial
3.2. Graphical method
3.3. Solution of equations by fixed-point iteration
3.4. Bisection
3.5. Descartes' rule of signs
3.6. The Newton-Raphson method
3.7. The false position method
3.8. The secant method
3.9. Applications of root finding in physics
3.10. The finite potential well
3.11. The Kronig-Penney model
4. Interpolation
4.1. Lagrangian interpolation formula
4.2. The error caused by interpolation
4.3. Newton's form of interpolation polynomial
5. Numerical linear algebra
5.1. Solving a system of equations : Gaussian elimination
5.2. Evaluating the determinant of a matrix
5.3. LU decomposition
5.4. Determination of eigenvalues and eigenvectors : the power method
5.5. Convergence of the power method
5.6. Deflation : determination of the remaining eigenvalues
5.7. Curve fitting : the least-squares technique
5.8. Curve fitting : the generalised least-squares technique
6. Numerical integration and differentiation
6.1. Numerical differentiation
6.2. The Richardson extrapolation
6.3. Numerical integration : the area under the curve
6.4. Simpson's rules
6.5. Comparison of quadrature methods
6.6. Romberg integration
6.7. Gaussian quadrature
6.8. Gaussian quadrature for arbitrary limits
6.9. Improper integrals
6.10. Approximate evaluation of integrals using Taylor series expansion
6.11. The Fourier transform
6.12. Numerical integration using MATLAB
7. Monte Carlo integration
7.1. Error in multidimensional integration
7.2. Monte Carlo integration
7.3. Error estimate for Monte Carlo integration
7.4. Importance sampling Monte Carlo
7.5. The Box-Muller method
7.6. The Metropolis algorithm
7.7. Random number generators
7.8. The linear congruential method
7.9. Generalised feedback shift register
8. Applications of Monte Carlo methods
8.1. Random walks
8.2. The Ising model
8.3. Percolation theory
8.4. Simulated annealing
9. Ordinary differential equations
9.1. Differential equations in physics
9.2. The simple Euler method
9.3. The modified and improved Euler methods
9.4. Runge-Kutta methods
9.5. The Taylor series method
9.6. The shooting method
9.7. Applications to physical systems
Subjects
Also listed under
Institute of Physics (Great Britain), publisher.
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