Course

code	ME756
credit_hours	3
title	Advanced Mathematics
arbic title
prequisites	none
credit hours	3
Description/Outcomes	Linear PDEs and basic problems – Equations of parabolic type with one and two space variables – Hyperbolic equations with one and two space variables – Elliptic equations with two space variables – Higher order PDEs – Nonlinear modal equations – First order nonlinear equations and applications – Special s and their properties – Gama, Beta and Error s – Bessel and Airy s – Legendre and associated Legendre s – Laguerre and associated Laguerre s – Hermite Polynomials and Weber Hermite s.
arabic Description/Outcomes
objectives	After completing this course the student should be able to use mathematical methods to solve engineering problems. In particular, the student will be able to solve a variety of second order differential equations, selecting from several techniques covered in the syllabus. Apply mathematical methods to solve important Laplace, Poisson, wave and heat equations. Identify specific types of equations and decide on appropriate mathematical methods to find the solution. Use various theoretical mathematical ideas and results in this course to analyze certain physical problems.
arabic objectives
ref. books	Farlow, L. ` Partial differential equations for scientists and engineers` , Dover Books, 1993.rn. O`Neil, P.V. ` Advanced Engineering Mathematics` , Thompson Books/Cole, latest edition rn. Polianin, A.D. ` Handbook of linear partial differential equations for engineers and scientists`, Chapman & Hall/CRC, 2002.rn. Debnath, S.J. ` Nonlinear Partial differential equations for scientists and engineers` , Birkhauser, 2004.rn. Debnath, L. ` Linear Partial differential equations for scientists and engineers` , Birkhauser, 2006.rn. Stephenson, G. ` Partial differential equations for scientists and engineers ` Imperial College Press, 2007.rn. Kristensson, G. ` Second order differential equations, Special s and their classification` , Springer, 2010.rn. Reissig, M. and Ruzhansky, M. ` Progress in partial differential equations ` Springer, 2013.rn
arabic ref. books
textbook
arabic textbook
objective set
content set

Course Content

content serial	Description
1	Linear PDEs, basic definitions and problems
2	Equations of parabolic type with one space variable
3	Equations of parabolic type with two space variables
4	Hyperbolic equations with one space variable
5	Hyperbolic equations with two space variables
6	Elliptic equations with two space variables
7	Laplace, Poisson, Helmholtz equations
8	Higher order PDEs and applications
9	Nonlinear modal equations
10	First order nonlinear equations and applications
11	Special s and their properties
12	Gama, Beta and Error s
13	Bessel, Airy s and applications
14	Legendre and associated Legendre s and applications
15	Legendre and associated Legendre s and applications
16	Final Examination.