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| Introduction Introduction to MATLAB� | |
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| MATLAB� Commands for Display and Plotting | |
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| Creating MATLAB� Programs | |
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| MATLAB� Programming Language | |
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| Problem Solving and Programming (Optional) | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Numbers and Vectors Properties of Real Numbers | |
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| MATLAB� Computer Numbers (Optional) | |
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| Complex Numbers | |
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| Vectors in Two Dimensions and Three Dimensions | |
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| Vectors in Higher Dimensions | |
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| MATLAB� Vectors | |
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| Complex Vectors | |
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| Vector Spaces | |
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| Vector Spaces of Functions | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Matrices Basic Properties of Matrices | |
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| MATLAB� Matrix Operations | |
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| Square and Symmetric Matrices | |
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| Determinants and Matrix Inverses | |
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| Orthogonal and Triangular Matrices | |
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| Systems of Linear Equations | |
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| MATLAB� Matrix Functions | |
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| Linear Transformations | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Eigenvalues and Eigenvectors General Discussion of Eigenvalues | |
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| Eigenvalues and Eigenvectors | |
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| Matrix Eigenvalue Theorems | |
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| Complex Vectors and Matrices | |
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| MATLAB� Commands for Eigenvectors | |
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| Matrix Calculus | |
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| Similar and Diagonalizable Matrices | |
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| Special Matrices and Their Eigenvalues (Optional) | |
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| Applications to Differential Equations | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Linear Differential Equations Classification of Differential Equations | |
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| Linear Differential Equations | |
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| Higher Order Differential Equations | |
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| Second Order Differential Equations | |
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| Particular Solutions of Differential Equations | |
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| Systems of Differential Equations | |
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| MATLAB� Solutions of Systems of Differential Equations | |
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| Homogeneous Systems with Repeated Eigenvalues | |
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| Nonhomogeneous Systems of Differential Equations | |
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| Transforming Differential Equations | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Advanced Differential Equations Functions and Differential Equations | |
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| Sequences and Series | |
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| Taylor Series | |
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| Numerical Methods for Differential Equations | |
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| Stiff Differential Equations | |
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| Vector Equations | |
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| Boundary Value Problems | |
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| Equations with Variable Coefficients | |
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| Bessel and Legendre Equations | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Approximation of Functions Polynomial Interpolation | |
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| Interpolation by Spline Functions | |
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| Least-Squares Curve Fitting | |
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| Orthogonal Functions | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Fourier Analysis Fourier Series | |
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| Properties of Fourier Series | |
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| Fourier Transforms | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Laplace Transforms Definition and Properties of the Laplace Transform | |
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| Computation of Inverse Laplace Transforms | |
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| MATLAB� and Laplace Transforms | |
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| Applications to Differential Equations | |
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| Applications of Laplace Transforms to Linear Systems | |
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| Relationship of Fourier and Laplace Transforms | |
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| Summary of Laplace Transform Properties | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| Discrete Systems Introduction to the Sequences and Discrete Functions | |
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| Linear Difference Equations | |
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| Approximation to Differential Equations | |
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| Smoothing and Digital Filters | |
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| Introduction to z-Transforms | |
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| MATLAB� Commands for Discrete Systems | |
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| z-Transform Solution of Difference Equations | |
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| Applications of z-transforms to Linear Discrete Systems | |
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| Frequency Response and Fourier Analysis | |
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| Summary of z-transform Properties | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated Bibliography | |
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| The Discrete Fourier Transform and the Fft Frequency Analysis of Signals | |
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| Discrete and Fast Fourier Transforms | |
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| MATLAB� Fourier Commands | |
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| Practical Signal Analysis | |
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| Practical Signal Sampling and DFT Errors | |
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| Analysis of DFT for Computation (Optional) | |
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| Reinforcement Exercises and Exploration Problems | |
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| Annotated | |