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 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