Mathematics Matrices and Linear Algebra Function Summary Matrices in MATLAB Creation Addition and Subtraction Vector Products and Transpose Matrix Multiplication The Identity Matrix The Kronecker Tensor Product Vector and Matrix Norms Solving Linear Equations Overview Square Systems Overdetermined Systems Underdetermined Systems Inverses and Determinants Overview Pseudoinverses Cholesky, LU, and QR Factorizations Cholesky Factorization LU Factorization QR Factorization Matrix Powers and Exponentials Eigenvalues Singular Value Decomposition Polynomials and Interpolation Polynomials Polynomial Function Summary Representing Polynomials Polynomial Roots Characteristic Polynomials Polynomial Evaluation Convolution and Deconvolution Polynomial Derivatives Polynomial Curve Fitting Partial Fraction Expansion Interpolation Interpolation Function Summary One-Dimensional Interpolation Two-Dimensional Interpolation Comparing Interpolation Methods Interpolation and Multidimensional Arrays Triangulation and Interpolation of Scattered Data Tessellation and Interpolation of Scattered Data in Higher Dimensions Selected Bibliography Data Analysis and Statistics Column-Oriented Data Sets Basic Data Analysis Functions Function Summary Covariance and Correlation Coefficients Finite Differences Data Preprocessing Missing Values Removing Outliers Regression and Curve Fitting Polynomial Regression Linear-in-the-Parameters Regression Multiple Regression Case Study: Curve Fitting Polynomial Fit Analyzing Residuals Exponential Fit Error Bounds The Basic Fitting Interface Difference Equations and Filtering Fourier Analysis and the Fast Fourier Transform (FFT) Function Summary Introduction Magnitude and Phase of Transformed Data FFT Length Versus Speed Function Functions Function Summary Representing Functions in MATLAB Plotting Mathematical Functions Minimizing Functions and Finding Zeros Minimizing Functions of One Variable Minimizing Functions of Several Variables Setting Minimization Options Finding Zeros of Functions Tips Troubleshooting Converting Your Optimization Code to MATLAB Version 5 Syntax Numerical Integration (Quadrature) Example: Computing the Length of a Curve Example: Double Integration Differential Equations Initial Value Problems for ODEs and DAEs ODE Function Summary Introduction to Initial Value ODE Problems Initial Value Problem Solvers Representing ODE Problems Improving ODE Solver Performance Examples: Applying the ODE Initial Value Problem Solvers Questions and Answers, and Troubleshooting Boundary Value Problems for ODEs BVP Function Summary Introduction to Boundary Value ODE Problems Boundary Value Problem Solver Representing BVP Problems Making a Good Initial Guess Improving BVP Solver Performance Partial Differential Equations PDE Function Summary Introduction to PDE Problems MATLAB Partial Differential Equation Solver Representing PDE Problems Improving PDE Solver Performance Example: Electrodynamics Problem Selected Bibliography Sparse Matrices Function Summary Introduction Sparse Matrix Storage General Storage Information Creating Sparse Matrices Importing Sparse Matrices from Outside MATLAB Viewing Sparse Matrices Information About Nonzero Elements Viewing Sparse Matrices Graphically The find Function and Sparse Matrices Example: Adjacency Matrices and Graphs Introduction to Adjacency Matrices Graphing Using Adjacency Matrices The Bucky Ball An Airflow Model Sparse Matrix Operations Computational Considerations Standard Mathematical Operations Permutation and Reordering Factorization Simultaneous Linear Equations Eigenvalues and Singular Values Selected Bibliography