1. Introduction to Differential Equations. Introduction. Direction Fields. 2. First Order Linear Differential Equations. Existence and Uniqueness. First Order Linear Homogeneous Differential Equations. Nonhomogeneous Differential Equations. Introduction to Mathematical Models. Mixing Problems and Cooling Problems. 3. First Order Nonlinear Differential Equations. Existence and Uniqueness. Separable First Order Equations. Exact Differential Equations. Bernoulli Equations. The Logistic Population Model. One-Dimensional Motion with Air Resistance. One-Dimensional Dynamics with Distance as the Independent Variable. Euler's Method. 4. Second Order Linear Differential Equations. Introduction. Existence and Uniqueness. The General Solution of Homogeneous Equations. Fundamental Sets and Linear Independence. Constant Coefficient Homogeneous Equations. Real Repeated Roots; Reduction of Order. Complex Roots. Unforced Mechanical Vibrations. The General Solution of the Linear Nonhomogeneous Equation. The Method of Undetermined Coefficients. The Method of Variation of Parameters. Forced Mechanical Vibrations, Electrical Networks, and Resonance. 5. Higher Order Linear Differential Equations. Existence and Uniqueness. The General Solution ofnth Order Linear Homogeneous Equation. Fundamental Sets and Linear Independence. Constant Coefficient Homogeneous Equations. Nonhomogeneous Linear Equations. 6. First Order Linear Systems. The Calculus of Matrix Functions. Existence and Uniqueness. Homogeneous Linear Systems. Fundamental Sets and Linear Independence. Constant Coefficient Homogeneous Systems. Complex Eigenvalues. Repeated Eigenvalues. Nonhomogeneous Linear Systems. Euler's Method for Systems of Differential Equations. Diagonalization. Functions of a Matrix and the Exponential Matrix. 7. Laplace Transforms. The Laplace Transform. LaplaKohler, Werner E. is the author of 'Elementary Differential Equations With Boundary Value Problems', published 2003 under ISBN 9780321121646 and ISBN 0321121643.