Matrices and Linear Algebra

    Function Summary
    Matrices in MATLAB
        Creating Matrices
        Adding and Subtracting Matrices
        Vector Products and Transpose
        Multiplying Matrices
        The Identity Matrix
        The Kronecker Tensor Product
        Vector and Matrix Norms

    Solving Linear Systems of Equations
        Computational Considerations
        General Solution
        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
        Fitting a Curve to Data
        Setting Minimization Options
        Output Functions
        Finding Zeros of Functions
        Tips
        Troubleshooting

    Numerical Integration (Quadrature)
        Example: Computing the Length of a Curve
        Example: Double Integration

    Parameterizing Functions Called by Function Functions
        Providing Parameter Values Using Nested Functions
        Providing Parameter Values to Anonymous Functions

Differential Equations

    Initial Value Problems for ODEs and DAEs
        ODE Function Summary
        Introduction to Initial Value ODE Problems
        Solvers for Explicit and Linearly Implicit ODEs
        Examples: Solving Explicit ODE Problems
        Solver for Fully Implicit ODEs
        Example: Solving a Fully Implicit ODE Problem
        Changing ODE Integration Properties
        Examples: Applying the ODE Initial Value Problem Solvers
        Questions and Answers, and Troubleshooting

    Initial Value Problems for DDEs
        DDE Function Summary
        Introduction to Initial Value DDE Problems
        DDE Solver
        Solving DDE Problems
        Discontinuities
        Changing DDE Integration Properties

    Boundary Value Problems for ODEs
        BVP Function Summary
        Introduction to Boundary Value ODE Problems
        Boundary Value Problem Solver
        Solving BVP Problems
        Using Continuation to Make a Good Initial Guess
        Solving Singular BVPs
        Solving Multi-Point BVPs
        Changing BVP Integration Properties

    Partial Differential Equations
        PDE Function Summary
        Introduction to PDE Problems
        MATLAB Partial Differential Equation Solver
        Solving PDE Problems
        Evaluating the Solution at Specific Points
        Changing PDE Integration Properties
        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

    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

Nondouble Data Types

    Introduction
    Integer Mathematics
        Integer Data Types
        Largest and Smallest Values for Integer Data Types
        Integer Arithmetic
        Example -- Digitized Signals
        Warnings for Integer Data Types

    Single-Precision Mathematics
        Data Type single
        Single-Precision Arithmetic
        The Function eps
        Example -- Writing M-Files for Different Data Types
        Largest and Smallest Numbers of Type double and single
        References

Examples