Advanced Partial Differential Equations
Advanced Partial Differential Equations. Instructor: Dr. Kaushik Bal, Department of Mathematics and Statistics, IIT Kanpur. The precise idea to study partial differential equations is to interpret physical phenomena occurring in nature. Most often the systems encountered fail to admit explicit solutions but fortunately qualitative methods were discovered which does provide ample information about the system without explicitly solving it. In this course we will explore the basic ideas of studying first order equations starting with the inner workings of method of characteristics followed by the three fundamental second order PDEs namely Laplace equation, Heat equation and Wave equation. (from nptel.ac.in)
| Lecture 06 - Introduction to Laplace Equations |
In this lecture, Laplace equations are introduced. Canonical forms are recalled briefly. Poisson Equation, Harmonic functions and their properties are discussed. Several examples and physical problems related to Laplace equation are discussed.
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