This is a lively textbook for an introductory course in numerical methods, MATLAB, and technical computing, with an emphasis on the informed use of mathematical software. The presentation helps readers learn enough about the mathematical functions in MATLAB to use them correctly, appreciate their limitations, and modify them appropriately. The book makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms. It provides more than 70 M-files, which can be downloaded from the text Web site www.mathworks.com/moler. Many of the numerous exercises involve modifying and extending these programs. The topics covered include an introduction to MATLAB; linear equations; interpolation; zeros and roots; least squares; quadrature; ordinary differential equations; Fourier analysis; random numbers; eigenvalues and singular values; and partial differential equations. Motivating applications include modern problems from cryptography, touch-tone dialing, Google page-ranking, atmospheric science and image processing, as well as classical problems from physics and engineering.

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+1Sequence 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 Pagepank and Markov Chains 2.12 Further Reading Exercises 3 Interpolation 3.1 The Interpolating Polynamial 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 fzerotx, feval 4.8 fzerogui 4.9 Value Finding and Reverse Interpolation 4.10 Optimization and fmintx Exercises 5 Least Squares 5.1 Models and Curve Fitting 5.2 Morms 5.3 censusgui 5.4 Househoder Reflections 5.5 The QR Factorization 5.6 Pseudoinverse 5.7 Rank Deficiency 5.8 Separable Least Squares 5.9 Further Reading Exercises 6 Quadrature 6.1 Adaptive Quadrature 6.2 Basic Quadrature Rules 6.3 quadtx, quadgui 6.4 Specifying Integrands 6.5 Performance 6.6 Integrating Discrete Data 6.7 Further Reading Exercises 7 Ordinary Differential Equations 7.1 Integrating Differential Equations 7.2 Systems of Equations 7.3 Linearized 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 Ohter 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 Exercises 10 Eigenvalues and Singular Values 10.1 Eigenvalues and Singular Value Decompositions 10.2 A Small Example 10.3 eigshow 10.4 Characteristic Polynomial 10.5 Symmetric and Hermitian Matrices 10.6 Eigenvalues Sensitivity and Accuracy 10.7 Singular Value Sensitivity and Accuracy 10.8 Fourier Analysis 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 Mermbrane Exercises Bibliography Index

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