61140 Differential Equations

Course Description

1.Definitions and Terminology: Introduction to the course, Fundamental Concepts and Definitions in ODE, Degree, Order, Solution, Initial Value Problems.
2.First Order ODE: Solving Separable ODE, Solving Exact ODE, Solving Linear ODE, Integrating Factor, Solving Homogeneous ODE, Application Problems Involving Series Circuits by Using Linear ODE.
3.Higher Order ODE: Solving Homogeneous linear Differential Equations and Non-homogeneous Differential Equations.
4.Laplace Transform: Definition of Laplace Transform, Linearity Property, Inverse Laplace Transform, Laplace Transform of Derivatives, First and Second Shifting Theorem, Convolution, Solving ODE by Laplace Transform.
5.Fourier Series: Periodic Functions and Their Graphs, Non-periodic Functions, Full and Half-range Fourier Expansions

Learning Objective

  • At the end of the course, we hope that the students are able to solve all kinds of first order ordinary differential equations. Students also may solve higher order differential equations. Similarly we expect students should know how to use Laplace transform when they are solving ODE. Finally, students will learn some methods involving Fourier series.

Credits

    3

Books for this Course

  • Deferential Equations with Boundary-Value Problems / Fourth Edition
  • Dennis G. Zill and Michael R. Cullen

Times Offered

  • September 2014
  • January 2015

Course Prerequisite

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