### Differential Equations (MATH-121)

Description and Objective:

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:

1. 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

Thursday                                                 11:00 AM-12:30 PM

Commencement of Classes                                                   March 02, 2020

Mid Term Examination                                                            April 27 to May 04, 2020

Final Term Examination                                                          June 22-26, 2020

Declaration of Result                                                              July 03, 2020