Numerical Computing with MATLAB revised in 2013

Preface
1 Introduction to MATLAB
1.1 The Golden Ratio
1.2 Fibonacci Numbers
1.3 Fractal Fern
1.4 Magic Squares
1.5 Cryptography
1.6 The 3n+l Sequence
1.7 Floating-Point Arithmetic
1.8 Further Reading
Exercises
2 Linear Equations
2.1 Solving Linear Systems
2.2 The MATLAB Backslash Operator
2.3 A 3-by-3 Example
2.4 Permutation and Triangular Matrices
2.5 LU Factorization
2.6 Why Is Pivoting Necessary?
2.7 lutx, bslashtx, lugui
2.8 Effect of Roundoff Errors
2.9 Norms and Condition Numbers
2.10 Sparse Matrices and Band Matrices
2.11 PageRank and Markov Chains
2.12 Further Reading
Exercises
3 Interpolation
3.1 The Interpolating Polynomial
3.2 Piecewise Linear Interpolation
3.3 Piecewise Cubic Hermite Interpolation
3.4 Shape-Preserving Piecewise Cubic
3.5 Cubic Spline
3.6 pchiptx, splinetx
3.7 interpgui
Exercises
4 Zeros and Roots
4.1 Bisection
4.2 Newton's Method
4.3 A Perverse Example
4.4 Secant Method
4.5 Inverse Quadratic Interpolation
4.6 Zeroin
4.7 fzerctx
4.8 fzeregui
4.9 Value Finding and Reverse Interpolation
4.10 Optimization and fmintx
Exercises
5 Least Squares
5.1 Models and Curve Fitting
5.2 Ncrms
5.3 censusgui
5.4 Householder Reflections
5.5 The QR Factorization
5.6 Pseu doinverse
5.7 Rank Deficiency
5.8 Separable Least Squares
5.9 b-hrther Reading
Exercises
6 Quadrature
6.1 Adaptive Quadrature
6.2 Basic Quadrature Rules
6.3 qusdtx, quadgui
6.4 Specifying Integrands
6.5 Performance
6.6 Integrating Discrete Data
6.7 Further Reading
Exelcises
7 Ordinary Differential Equations
7.1 Integrating Differential Equations
7.2 Systems of Equations
7.3 Lineari2ed Differential Equations
7.4 Single-Step Methods
7.5 The BS23 Algorithm
7.6 ode23tx
7.7 Examples
7.8 Lorenz Attractor
7.9 Stiffness
7.10 Events
7.11 Multistep Methods
7.12 The MATLAB ODE Solvers
7.13 Errors
7.14 Performance
7.15 Further Reading
Exercises
8 Fourier Analysis
8.1 Touch-Tone Dialing
8.2 Finite Fourier Transform
8.3 fftgui
8.4 Sunspots
8.5 Periodic Time Series
8.6 Fast Finite Fourier Transform
8.7 ffttx
8.8 fftmatrix
8.9 Other Fourier Transforms and Series
8.10 Further Reading
Exercises
9 Random Numbers
9.1 Pseudorandom Numbers
9.2 Uniform Distribution
9.3 Normal Distribution
9.4 randtx, randntx
9.5 Twister
Exercises
10 Eigenvalues and Singular Values
10.1 Eigenvalue and Singular Value Decompositions
10.2 A Small Example
10.3 eigshow
10.4 Characteristic Polynomial
10.5 Symmetric and Hermitian Matrices
10.6 Eigenvalue Sensitivity and Accuracy
10.7 Singular Value Sensitivity and Accuracy
10.8 Jordan and Schur Forms
10.9 The QR Algorithm
10.10 eigsvdgui
10.11 Principal Components
10.12 Circle Generator
10.13 Further Reading
Exercises
11 Partial Differential Equations
11.1 Model Problems
11.2 Finite Difference Methods
11.3 Matrix Representation
11.4 Numerical Stability
11.5 The L-Shaped Membrane
Exercises
Bibliography
Index