| First-Order Differential Equations / 1： |
| Differential Equations and Mathematical Model |
| Integrals as General and Particular Solutions |
| Direction Fields and Solution Curves |
| Separable Equations and Applications |
| Linear First-Order Equations |
| Substitution Methods and Exact Equations |
| Mathematical Models and Numerical Methods / 2： |
| Population Models |
| Equilibrium Solutions and Stability |
| Acceleration-Velocity Models |
| Numerical Approximation: Euler's Method |
| A Closer Look at the Euler Method |
| The Runge-Kutta Method |
| Linear Systems and Matrices / 3： |
| Introduction to Linear Systems |
| Matrices and Gaussian Elimination |
| Reduced Row-Echelon Matrices |
| Matrix Operations |
| Inverses of Matrices |
| Determinants |
| Linear Equations and Curve Fitting |
| Vector Spaces / 4： |
| The Vector Space R |
| The Vector Space Rn and Subspaces |
| Linear Combinations and Independence of Vectors |
| Bases and Dimension for Vector Spaces |
| General Vector Spaces |
| Linear Equations of Higher Order / 5： |
| Introduction: Second-Order Linear Equations |
| General Solutions of Linear Equations |
| Homogeneous Equations with Constant Coefficients |
| Mechanical Vibrations |
| Undetermined Coefficients and Variation of Parameters |
| Forced Oscillations and Resonance |
| Eigenvalues and Eigenvectors / 6： |
| Introduction to Eigenvalues |
| Diagonalization of Matrices |
| Applications Involving Powers of Matrices |
| Linear Systems of Differential Equations / 7： |
| First-Order Systems and Applications |
| Matrices and Linear Systems |
| The Eigenvalue Method for Linear Systems |
| Second-Order Systems and Mechanical Applications |
| Multiple Eigenvalue Solutions |
| Numerical Methods for Systems |
| Matrix Exponential Methods / 8： |
| Matrix Exponentials and Linear Systems |
| Nonhomogeneous Linear Systems |
| Spectral Decomposition Methods |
| Nonlinear Systems and Phenomena / 9： |
| Stability and the Phase Plane |
| Linear and Almost Linear Systems |
| Ecological Models: Predators and Competitors |
| Nonlinear Mechanical Systems |
| Laplace Transform Methods / 10： |
| Laplace Transforms and Inverse Transforms |
| Transformation of Initial Value Problems |
| Translation and Partial Fractions |
| Derivatives, Integrals, and Products of Transforms |
| Periodic and Piecewise Continuous Forcing Functions |
| Power Series Methods / 11： |
| Introduction and Review of Power Series |
| Power Series Solutions |
| Frobenius Series Solutions |
| Bessel's Equation |
| References for Further Study |
| The Existence and Uniqueness of Solutions / Appendix A： |
| Theory of Determinants / Appendix B： |
| Answers to Selected Problems |
| Index |
| First-Order Differential Equations / 1： |
| Differential Equations and Mathematical Model |
| Integrals as General and Particular Solutions |
| Direction Fields and Solution Curves |
| Separable Equations and Applications |
| Linear First-Order Equations |
