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.

**Pre-requisite:**

Applied Mathematics II

**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 engineering.

**Course Content:**

Differential equation; basic concepts and ideas; geometrical interpretation of first and second order differential equations; separable equations, equations reducible to separable form, exact differential equations, 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, Doperator, complementary functions and particular integrals. Real, complex and repeated roots of characteristics equations. Cauchy equation, nonhomogeneous linear equations. Applications of higher order linear differential equations. Ordinary and regular points and corresponding series solutions; introduction to Laplace transformation.

**Recommended Books:**

1. C.R. Wylie, “Advanced Engineering Mathematics 5th Edition”, McGraw- Hill Education.

2. Erwin Kreyszig, “Advanced Engineering Mathematics 8th Edition”, John Wiley & Sons.

**Assesment 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**

BS Mechanical Technology

Every Thrusday 2:20 pm - 4:50 pm

Commencement of Classes March 15, 2021

Mid Term Examination May 17-21, 2021

Final Term Examination July 12-16, 2021

Declaration of Result July 27, 2021