Textbook

Preface
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Preliminaries
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Vectors and Matrices
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MATLAB
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Special Kinds of Matrices
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The Geometry of Vector Operations
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Solving Linear Equations
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The Geometry of Low-Dimensional Solutions
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Linear Equations with Special Coefficients
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Uniqueness of Reduced Echelon Form
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Matrices and Linearity
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Matrix Mappings
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The Principle of Superposition
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Determinants of 2 × 2 Matrices
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Solving Ordinary Differential Equations
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A Single Differential Equation
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Graphing Solutions to Differential Equations
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Phase Space Pictures and Equilibria
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Separation of Variables
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Uncoupled Linear Systems of Two Equations
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Coupled Linear Systems
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The Initial Value Problem and Eigenvectors
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Eigenvalues of 2 × 2 Matrices
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Initial Value Problems Revisited
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Vector Spaces
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Vector Spaces and Subspaces
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Construction of Subspaces
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Dimension and Bases
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Closed Form Solutions for Planar ODEs
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The Initial Value Problem
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Closed Form Solutions by the Direct Method
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Solutions Using Matrix Exponentials
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Linear Normal Form Planar Systems
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Similar Matrices
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Formulas for Matrix Exponentials
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Second Order Equations
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Qualitative Theory of Planar ODEs
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Sinks, Saddles, and Sources
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Phase Portraits of Sinks
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Phase Portraits of Nonhyperbolic Systems
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Determinants and Eigenvalues
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Determinants
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Eigenvalues
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Existence of Determinants
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Linear Maps and Changes of Coordinates
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Linear Mappings and Bases
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Orthogonality
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Least Squares Fitting of Data
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Symmetric Matrices
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Autonomous Planar Nonlinear Systems
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Bifurcation Theory
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The Continuous Flow Stirred Tank Reactor
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Saddle-Node Bifurcations Revisited
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Matrix Normal Forms
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Markov Matrix Theory
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Proof of Jordan Normal Form
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Higher Dimensional Systems
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MATLAB ODE
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Linear Differential Equations
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Solving Systems in Original Coordinates
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Higher Order Equations
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Linear Differential Operators
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Undetermined Coefficients
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Periodic Forcing and Resonance
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Laplace Transforms
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The Method of Laplace Transforms
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Laplace Transforms and Their Computation
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Partial Fractions
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RLC Circuits
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Additional Techniques for Solving ODEs
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Nonconstant Coefficient Linear Equations
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Variation of Parameters for Systems
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The Wronskian
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Higher Order Equations
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Simplification by Substitution
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Exact Differential Equations
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Numerical Solutions of ODEs
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A Description of Numerical Methods
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Error Bounds for Euler’s Method
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Local and Global Error Bounds
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Overall
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