**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:**

- Comprehend the fundamental concepts of differential equations.
- Solve first and second order differential equations and partial differential equations using the concepts developed in the course.
- Apply the concepts of ordinary derivatives and partial derivatives for modeling of physical systems.

**Course outline:**

- First Order Differential Equations
- Variables separable forms,
- Homogenous equations,
- Non-homogenous equations,
- Exact equations,
- Linear equations,
- Solution by substitutions Applications of First Order DE’s
- Modeling with the first order differential equations
- Orthogonal trajectories
- Population dynamics
- Applications of linear equations
- Applications of non-linear equations Higher Order Linear Differential Equations
- Introduction and preliminary theory,
- Initial-value and boundary-value problems,
- Homogenous and non-homogenous equations,
- Method of undetermined coefficients,
- Method of variation of parameters,
- Power series solution Applications of the Second Order Differential Equations
- Spring mass problems,
- RLC Circuit Partial Differential Equations
- Basic concepts,
- Vibrating string,
- Wave equation,
- Separation of variables,
- 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

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