Course Details
Subject {L-T-P / C} : MA5303 : Partial Differential Equations { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Jugal Mohapatra
Syllabus
Origin of first-order partial differential equations, Cauchy’s problem, Linear equations, Integral surfaces passing through a given curve, Surfaces orthogonal to a given system of surfaces, Nonlinear partial differential equations of the first-order, Cauchy’s method of characteristics, Compatible systems of first-order equations, Charpit’s method, Jacobi’s method, Second and higher-order equations in physics, Linear partial differential equations, Characteristic curves, Separations of variables, Integral transform method for parabolic, hyperbolic and elliptic equations.
Course Objectives
- Partial differential equations allow deterministic mathematical formulations of phenomena in physics and engineering as well as biological processes among many other scenarios. The objective of this course is to present the main results in the context of partial differential equations that allow learning about these topics.
- To equip students with the concepts of PDEs and how to solve PDEs with different analytical methods. Students also will be introduced to <br />some physical problems in Engineering models that result in PDEs.
Course Outcomes
Apply logical/mathematical thinking: the analytic process. Apply some techniques/ methods to predict the behavior of certain phenomena. Identify real phenomena as models of PDEs.
Essential Reading
- I. N. Sneddon, Elements of Partial Differential Equations, Dover Publications , 2006
- S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications , 1993
Supplementary Reading
- Tyn Myint-U and Lokenath Debnath, Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition, Birkhauser , 2007
- W.A. Strauss, Partial Differential Equations: An Introduction, John Wiley , 1992