Textbook: Differential Equations, Computing and Modeling by C.H Edwards Jr. and D. E.Penney, Prentice-Hall, 1999; Coursepack: Computer Laboratory Projects for ODE?s by Alterman and Doering
Cognizant Faculty:
Description:
After an introduction to complex numbers, the first half of the course is devoted to topics in linear algebra, including systems of linear algebraic equations, vector spaces, linear dependence, bases, dimension, matrix algebra, determinants, eigenvalues, and eigenvectors. In the second half, these tools are applied to the solution of linear systems of ordinary differential equations. Nonlinear systems of ordinary differential equations and Laplace transform methods
Course Topics:
Complex Numbers
First order (separable, linear) equations, slope fields.
Modeling and numerical methods.
Higher order linear ODE?s free and forced oscillations.
Linear systems of ODE?s and matrix algebra
Nonlinear systems and applications
Laplace transform methods including delta functions.
Computer labs (MATLAB):
Euler?s method and RC circuits
Higher order numerical methods (improved Euler, Runge-Kutta)
Systems and oscillations(free and damped, driven, resonance)
Nonlinear systems (nonlinear oscillations and impulse response)
Course Objectives:
To teach the students the fundamentals and applications of Ordinary Differential equations and Linear Algebra.
To teach the students applications of the above topics to engineering problems using MATLAB computer software.
Course Outcomes:
Assessment Tools: