### Applied Mathematics-II (MATH-122)

Description and Objective:

To develope an understanding of the knowledge/skill of Mathematics and to apply these in engineering problems.

Pre requisite:

Applied Mathematics I

Learning Outcomes:

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

Course Outline:

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, Bernoullill's differential equation. Families of cuives, 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 vahe 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.

Recommended Books:

1. C.R. Wiley, "Advanced Engineering Mathematics 6th Edition". McGraw-Hill Education

2. E. Kreyszig, "Advanced Engineering Mathematics 10th Edition", John Wiley & Sons

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:

Friday                                                    08:00 AM-11:00 AM (Section A)

Friday                                                    02:00 PM-05:00 PM (Section B)

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