First Order Linear Differential Equations: Integrating factor method; First Order Linear Differential Equations: Separable equations, Exact equations and integrating factors; Second Order Linear Differential Equations: Linear dependence and independence. Homogenous Equations: General solutions; Solution of Homogeneous Equations: Constant coefficients; Solution of Homogeneous Equations: Non-Constant coefficients; Solution of non-Homogeneous Equations: method of undetermined coefficients and variation of parameters; Introduction and Euler method; Midpoint rule and Runge Kutta methods; Singular points and Stability; Singularities of nonlinear systems and Bifurcations; Limit cycles and the Duffing equations; Introduction to calculus of variations.
Suggested Text:
- Advanced Engineering Mathematics by Michael D. Greenberg, second edition, Prentice Hall.