Advanced Partial Differential Equations (MT5013)

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Applied Partial Differential Equations, Richard Haberman.

Linear Partial Differential Equations For Scientists And Engineers, By Tyn Myint U.

The course objectives are to learn the basics analytical methods to solve partial differential equations (PDE). Partial Differential Equations (PDEs) are at the heart of applied mathematics and many other scientific disciplines.

By the end of this course you will have learned:

• Basic concepts of PDE theory

• Analytical methods for solving linear PDEs

• Applications of PDEs.

Quick review of Differential Equations, Introduction, Definitions and terminology of partial differential equations , Solution of first order partial differential equations, Derivation Heat Equation and Wave Equation, Canonical forms, Canonical form, Inverse operator method, Method of Characteristics, The Cauchy Problem, Method of Separation of Variables, Higher Dimensional problems, Non Homogeneous problems in partial differential equations.