**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. Concept of Sequence and Series

**Text Book**

** ** Erwin Kreyszig, “Advanced Engineering Mathematics 10th Edition”, John Wiley & Son

**Recommended Books:**

**1. **C.R. Wylie, “Advanced Engineering Mathematics 6th Edition”, McGraw- Hill Education

**2. ** Erwin Kreyszig, “Advanced Engineering Mathematics 10th Edition”, John Wiley & Son