Course Tittle: PARTIAL DFFERENTIAL EQUATIONS

Course Code: MATH-405

Credit Hours: 03

DESCRIPTION & OBJECTIVES

The course aim at developing understanding about fundamental concepts of PDEs theory, identification and classification of their different types, how they arises in applications, and analytical methods for solving them. Special emphasis would be on Wave, Heat and Laplace equations.

Recommended Books:

1. Humi M, Miller W.B; Boundary Value Problems and Partial Differential Equations. PWS-KENT Publishing Company, 1991.
2. Myint UT, Partial Differential Equations for Scientists and Engineers, 3rd edition, North Holland, Amsterdam,   1987.
3. Dennis G. Zill, Michael R. Cullen, Differential equations with boundary value problems, Brooks Cole, 2008.  
4. John Polking, Al Boggess, Differential Equations with Boundary Value Problems, 2nd Edition, Pearson, July 28, 2005.
5. J. Wloka, Partial Differential Equations, Cambridge University press, 1987.

CONTENTS

First order PDEs: Introduction, formation of PDEs, solutions of PDEs of first order, The Cauchy’s problem for quasilinear first order PDEs, First order nonlinear equations, Special types of first order equations.Second order PDEs: Basic concepts and definitions, Mathematical problems, Linear operators, Superposition, Mathematical models: The classical equations, the vibrating string, the vibrating membrane, conduction of heat solids, canonical forms and variable, PDEs of second order in two independent variables with constant and variable coefficients, Cauchy’s problem for second order PDEs in two independent variables .Methods of separation of variables:  Solutions of elliptic, parabolic and hyperbolic PDEs in Cartesian and cylindrical coordinates. Laplace transform: Introduction and properties of Laplace transform, transforms of elementary functions, periodic functions, error function and Dirac delta function, inverse Laplace transform, convolution theorem, solution of PDEs by Laplace transform, Diffusion and wave equations. Fourier transforms: Fourier integral representation, Fourier sine and cosine representation, Fourier transform pair, transform of elementary functions and Dirac delta function, finite Fourier transforms, solutions of heat, wave and Laplace equations by Fourier transforms.

PROJECT

N/A

ASSESSMENT CRITERIA

Mid exam:       30

Sessional:        20

Project:            --

Assignments:   10

Presentation:   10

Final exam:      50

Total:               100

RULES AND REGULATIONS

75% attendance is compulsory to appear in Final Term exam.