### Differential Equations (MATH-121)

Description and Objectives:

To develope an understanding of the knowledge/skill of Mathematics and to apply these in engineering problems.

Pre requisite:

None

Learning Outcomes:

1.Comprehend the fundamental concepts of differential equations.

2.Solve first and second order differential equations and partial differential equations using the concepts developed in the course.

3.Apply the concepts of ordinary derivatives and partial derivatives for modeling of physical systems.

Course outline:

1.First Order Differential Equations

2.Variables separable forms,

3.Homogenous equations,

4.Non-homogenous equations,

5.Exact equations,

6.Linear equations,

7.Solution by substitutions Applications of First Order DE’s

8.Modeling with the first order differential equations

9.Orthogonal trajectories

10.Population dynamics

11.Applications of linear equations

12.Applications of non-linear equations Higher Order Linear Differential Equations

13.Introduction and preliminary theory,

14.Initial-value and boundary-value problems,

15.Homogenous and non-homogenous equations,

16.Method of undetermined coefficients,

17.Method of variation of parameters,

18.Power series solution Applications of the Second Order Differential Equations

19.Spring mass problems,

20.RLC Circuit Partial Differential Equations

21.Basic concepts,

22.Vibrating string,

23.Wave equation,

24.Separation of variables,

25.Heat equation solution by separation of variables

Recommended books:

Advanced Engineering Mathematics by Erwin Kreyszig, 10th Ed. Willey 2014. ISBN 978-0-470- 91361-1.

Assessment Criteria:

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam: 30

Final-Term Exam: 50

Key Dates and Time of Class Meeting:

Monday 09:30 AM-11:00 AM

Tuesday 09:30AM-11:00 AM

Commencement of Classes March 15, 2021

Mid Term Examination May 17 to May 21, 2021

Final Term Examination July 12-16, 2021

Declaration of Result July 27, 2021