**Introduction:**

This course includes the study of first order differential equations, higher order linear

differential equations, Laplace transforms, numerical methods, boundary value and initial value

problems, qualitative analysis of solutions, and applications of differential in solving engineering problems.

**Prerequisite:**

Mathematics I

**Learning Outcomes**

Differential equations will provide students with the needed working knowledge of advanced mathematical concepts and an awareness of their relationship to complex problems. Students wishing to major in the sciences or engineering are required to study differential equations. It provides a solid foundation for further study in mathematics, the sciences, and

**Contents**

** **Differential equation; basic concepts and ideas; geometrical interpretation of first and second order differential equations(D.E) , **S**eparable equations, Reducible to Separable form, Exact D. E, integrated factors.. Linear first order differential equations, Bernoulli‟s differential equation. Families of curves, orthogonal trajectories and applications of differential equations of first order to relevant engineering systems.** **Homogeneous linear differential equations of second order, homogeneous equations with constant coefficients, the general solutions, Initial and boundary value problems, D- operator, complementary functions and particular integrals. Real, complex and repeated roots of characteristics equations. Cauchy equation, non-homogeneous linear equations. Applications of higher order linear differential equations. Ordinary and regular points and corresponding series solutions;** **Legendre equations and Legendre's polynomial,Bessel equations, Bessel Function of first kind. Gaussian Elimination Techniques, RREF, Rank of Matrix, Inverse of Matrix by Using G. E. Application of Eign Value and Eign Vectors

**Text Book**

** **Advanced Engineering Mathematics 8PthP by Erwin Kreyszig, Edition John Wiley & Sons

**Recommended Books:**

**1. **Advanced Engineering Mathematics 5PthP by ** **C.R. Wylie Edition McGraw Hill Education

**2. **Advanced Engineering Mathematics 8PthP by Erwin Kreyszig, Edition John Wiley & Sons

**PPT/Handouts**

**ASSEMENT CRITERIA:**

Sessional:20 %(Assignments 5% , Quiz 5% ,Class Attendance/Class Participation/Presentation 10%)

Mid Term Paper:30%

Final Term: 50 %

Every Thursday from 9:30 AM to 11:00 AM

Every Friday from 8: 00 AM to 9:30 AM

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 3, 2020