This course includes the study of first order differential equations and higher order differential equations, Laplace transforms. numerical methods, initial vlue and boundary value problems, qualitaitive analysis of solutions and applications of differentials in solving engineering problems.

**Learning Outcomes:**

1. To understand the concepts of matrices and determinants.

2. To understand the concept and use of partial differential equations and their applications.

**Course Outlines: **

1. Linear Algebra: Basic concepts of matrices and determinants, addition, subtraction, multiplication, linear system of equations and their solutions.

2. Gauss elimination tecnique, row reduced echelon form, rank, of the matrices

3. Gauss Jordan method, Determinants, Crammers rule, Eigen values, and Eigen vectors.

4. Vecdtor differential calculus, Gradiant, Divergence and Curl , and concepts of victor integral calculus.

5. Partial Differential equations: Fouriers series, basic concepts of Partial Differential Equations, Wave equations, Heat equation, Laplace's equation, Poisson Equation and Their solutions by using Fourier series, and Laplace transforms.

**Recommended Books**

A First Course in Differential Equations with modeling applications by Dennis G. Zill.

**Suggested Books**

Erwin Kreyszig, "Dvanced Engineering Mathematics, 10th Edition", John Willey & sons.

**Assessment Criteria**

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04

Mid-Term Exam (Term Paper): 30

Final-Term Exam: 50

**Key Dates and Time of Class Meeting**

Tuesday 09:30am-11:00pm

Wednesday 09:30am-11:00pm