Engineering Mathematics I

At the end of the course, the students should be able to: 1. solve qualitative problems based on vector and matrix analyses such as linear independence and dependence of vectors, rank etc; 2. describe the concepts of limit theory and nth order differential equations and their applications to physical phenomena; 3. solve the problems of differentiation of functions of two variables and know about the maximization and minimization of functions of several variables; 4. describe the applications of double and triple integration in finding the area and volume of engineering solids, and explain the qualitative applications of Gauss, Stoke’s and Green’s theorem; 5. explain ordinary differential equations and applications, and develop a mathematical model of linear differential equations, as well as appreciate the necessary and sufficient conditions for total differential equations; and 6. analyse basic engineering models through partial differential equations such as wave equation, heat conduction equation, etc., as well as fourier series, initial conditions and its applications to different engineering processes.

Limits, continuity, differentiation, introduction to linear first order differential equations, partial and total derivatives, composite functions, matrices and determinants, vector algebra, vector calculus, directional derivatives.