Building on the concepts imparted in courses Applied Mathematics – I and Applied Mathematics – II, this course will cover the areas of complex variables, the need for complex variables, an introduction to sequences and series and their wide spread applications in evaluation of complex integrals and solutions of differential equations. A lot of emphasis will be placed on formulation of problems in the above areas. The main reason for solving differential equations is to try to learn something about an underlying physical process that the equation is believed to model. Examples include exponential decay and growth models, spring-mass systems, and electrical circuits. Students will also be exposed to various tools available today to solve complex differential equations, once formulated properly.
COURSE LEARNING OUTCOMES
On Successful Completion of the course the students should be able to
• Understand the concepts of infinite sequences and sum of infinite series
• Learn the need for complex numbers and use of complex numbers in problem solving
• Understand the concept of tangent plane and normal to surfaces in space
• Solve problems of Maximizing and minimizing functions of two or more variables
• Solve first order differential equations and learn their use in solving problems in finance and physics
• Solve second order linear differential equations and learn their applications in vibrating strings and electrical networks