Computational Methods Using MATLAB®: An introduction for physicists

PRELIMS.pdf
	Preface
	Acknowledgements
	Author biography
		P K Thiruvikraman
CH001.pdf
	Chapter 1 Introduction
		1.1 A note of caution: rounding errors
		1.2 More on the limitations of digital computers
		Exercises:
CH002.pdf
	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
CH003.pdf
	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
CH004.pdf
	Chapter 4 Interpolation
		4.1 Lagrangian interpolation formula
		4.2 The error caused by interpolation
		4.3 Newton’s form of interpolation polynomial
		Exercises
CH005.pdf
	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
		Exercises
CH006.pdf
	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
		Exercises
CH007.pdf
	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
		Exercises
CH008.pdf
	Chapter 8 Applications of Monte Carlo methods
		8.1 Random walks
		8.2 The Ising model
		8.3 Percolation theory
		8.4 Simulated annealing
		Exercises
CH009.pdf
	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
		Exercises
CH010.pdf
	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
		Exercises
CH011.pdf
	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
		Exercises
APP1.pdf
	Chapter
		Chapter 2
		Chapter 3
		Chapter 4
		Chapter 5
		Chapter 6
		Chapter 7
		Chapter 9
		Chapter 10
		Chapter 11