Definitions and terminology of differential equations. Methods of solution for first order differential equations: separable, exact, homogeneous, linear and nonlinear Bernoulli equations. Some basic mathematical models.



Second order linear differential equations: homogeneous equations with constant coefficients. Fundamental solutions of linear homogeneous equations, linear independence and the Wronskian, complex roots of the characteristic equation, repeated roots, reduction of order.



Nonhomogeneous equations: method of undetermined coefficients and variation of parameters. Mechanical and electrical vibrations, forced vibrations.



The Laplace Transform: definition of Laplace transform and inverse transform. Properties of Laplace transform. Solution of initial value problems and differential equations with discontinuous forcing functions, Impulse functions.



Systems of linear differential equations: introduction to systems of differential equations and review of eigenvalues and eigenvectors. Methods of solution for complex and repeated eigenvalues. Matrix exponential.



References:

1. Boyce, W.E. & Diprima, R.C. (2006). Elementary Differential Equations and Boundary Value Problems with ODE Architect CD (8th Edition). Wiley & Sons.

2. Zill, D.Z (2001). A First Course in Differential Equations With Modeling Applications (7th Edition). Brooks/Cole Thompson Learning.

3. Edwards, C.H. & Penney, D.E. (1998). Elementary Differential Equations With Boundary Value Problems (4th Edition). Prentice Hall International, Inc.