EM2105 Differential Equations

Objectives:

The course provides various mathematical concepts and analysis methods in differential equations  in the engineering context.
 

Pre-requisite:

EM1204
 

Credit Hours:

3
 

Contact Hours:

45 hours of Lectures
15 hours of Assignments/Tutorials
 

Course Marks

70%  Final Exam
30% Course Work
 

Text & References

-       C. Henry Edwards, David E. Penney, “Elementary Differential Equations with Boundary Value Problems”, 4/e. Prentice-Hall, 2000, ISBN 0-13-011301-8

-       Jack L. Goldberg, Merle C. Potter, “Differential Equations: A Systems Approach” , 1/e, Prentice-Hall, 1998, ISBN 0-13-211319-8
 

Description:

Differential equations of first order, differential equations of second order, Differential equations of n order linear differential equations, system of ordinary differential equations, application to those different types of equations.
 

Outlines

First-Order Differential Equations.
Preliminaries. Definitions. The First-Order Linear Equation. Applications of First-Order Linear Equations. Nonlinear Equations of First Order.
Second-Order Linear Equations.
Introduction. Sectionally Continuous Functions. Linear Differential Operators. Linear Independence and the Wronskian. The Nonhomogeneous Equation. Constant Coefficient Equations. Spring-Mass Systems in Free Motion. The Electric Circuit. Undetermined Coefficients. The Spring-Mass System: Forced Motion. The Cauchy-Euler Equation. Variation of Parameters.
Higher Order Equations.
Introduction. The Homogeneous Equation. The Nonhomogeneous Equation. Companion Systems. Homogeneous Companion Systems. Variation of Parameters