Summary

The main objectives of the course are:(a) To introduce students to the language, basic concepts and methods of the theory of ODE.(b) To convey to the students a feeling for the interrelation between pure mathematics and the physical sciences and engineering, and especially, electrical engineering.1. Main notions of ODE. Examples.2. First order differential equations. Cauchy problem. The existence and uniqueness of the solution. Separable equations, homogeneous equations, exact equations, integrating factors, linear equations, Bernoulli equations.3. ODE of higher order. Cauchy problem. The existence and uniqueness of the solution. Reduction of order. Examples.4. Second order linear ODE. Basic theory. Second order linear ODE with constant coefficients. Linear ODE of order n.5. The Laplace Transform. A table of the Laplace transform. The delta-function. The convolution integral. Application of the Laplace transform for solution of ODE. Electrical networks.6. Systems of ODE. Basic theory of systems of first order linear differential equations.Linear systems with constant coefficients.7. Series solutions of ODE.8. Numerical methods.