Computational methods using MATLAB : an introduction for physicists / P. K. Thiruvikraman.

Format:

Book

Author/Creator:

Thiruvikraman, P. K., author.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Physicists.

Physical Description:

1 online resource (258 pages)

Edition:

First edition.

Place of Publication:

Bristol, England : IOP Publishing, [2022]

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. The book is suitable for undergraduates in physics or engineering.

Contents:

Intro

Preface

Acknowledgements

Author biography

P K Thiruvikraman

Chapter 1 Introduction

1.1 A note of caution: rounding errors

1.2 More on the limitations of digital computers

Exercises:

Chapter 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

Programming exercises

Chapter 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

Exercises

Chapter 4 Interpolation

4.1 Lagrangian interpolation formula

4.2 The error caused by interpolation

4.3 Newton's form of interpolation polynomial

Chapter 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

Chapter 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

6.9.1 Limit comparison test

6.9.2 Direct comparison test

6.10 Approximate evaluation of integrals using Taylor series expansion

6.11 The Fourier transform

6.12 Numerical integration using MATLAB

Chapter 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

Chapter 8 Applications of Monte Carlo methods

8.1 Random walks

8.2 The Ising model

8.3 Percolation theory

8.4 Simulated annealing

Chapter 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

Chapter 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

Chapter 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

Chapter

Chapter 2.

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 9

Chapter 10

Chapter 11.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

ISBN:

9780750345385

0750345381

OCLC:

1429732958