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Course Description form
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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Partial Differential Equations
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math406
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ر406
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3
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-
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-
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Pre-requisites
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Math 305
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Brief contents, to be posted in university site and documents(4-5 lines):
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Basic concepts -Existence and uniqueness of solutions -Method of Lagrange for first order quasilinear equations -Method of separation of variables for solving partial differential equations such as wave equation, diffusion equation, steady state equation - Use of Fourier and Laplace transforms to solve initial-boundary value problems for partial differential equations -Green’s function and non-homogeneous problems - Integral equations and solution techniques.
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Faculties and departments requiring this course (if any): Faculty of Science/
Department of Mathematics.
Objectives: Prefer In points
1- Deriving PDEs that describe various phenomena in physics, mechanics, chemistry, biology, etc.
2- Learning various methods for solving a great variety of Partial differential equations.
3- Upgrading the skills of the student to understand more better the other branches physics, mechanics, chemistry, biology, etc.
Contents: Prefer In points
1- Basic concepts and occurrence of partial differential equations
2- Existence and uniqueness of solutions
3- Method of Lagrange for first order quasilinear equations
4- Classification of linear second order partial differential equations in two variables
5- Method of separation of variables for solving partial differential equations such as wave equation, diffusion equation, steady state equation
6- Use of Fourier and Laplace transforms to solve initial-boundary value problems for partial differential equations
7- Green’s function and non-homogeneous problems
8- Integral equations and solution techniques
Course Outcomes:
A- Knowledge:
(Specific facts and knowledge of concepts, theories, formula etc.)
Study the basics of Partial differential equations and solution techniques
B-Cognitive Skills:
(Thinking, problem solving )
formulate and solve initial and boundary value problems involving standard partial differential equations of mathematical physics: wave equation, diffusion equation, steady state equation, etc.
C- Interpersonal skills and responsibilities:
(group participation, leadership, personal responsibility , ethic and moral behavior, capacity for self directed learning)
· The student will recognize that the various sciences form an integrated system.
· It will enable him to better understand his field and its applications to other fields, and share his expertise with others working in different fields.
· Consequently, he will learn the importance of group activity.
D- Analysis and communication:
)communication, mathematical and IT skills)
· learn to develop the mathematical modeling of the physical problems
· choose the best available analytic and numerical methods for solving the problems
· analyze/interpret the solution and derive the useful conclusions from it
Text book: Only one
Introduction to Partial Differential equations Author :A.Tveito (Springer2003).
Supplementary references
Introduction to ordinary Differential Equations. Auther:A.L.Rabenstein Publisher: (Academic press)
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Details of Weekly Distributed Material
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Remarks
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Experiment
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weak
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Partial differential equations: Basic concepts and occurrence of partial differential equations.
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1
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Existence and uniqueness of solutions, First order quasilinear partial differential equations and method of Lagrange
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2
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Linear second order partial differential equations with constant coefficients in two variables, Classification, Solution by D-operator method.
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3
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Methods of separation of variables, Solution of wave equation.
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4
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Solution of diffusion equation and Laplace equation (steady state equation).
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5
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Review of Laplace transform, Laplace transform of special functions
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6
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Inverse Laplace Transform
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7
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Use Laplace Transform to solve problems involving partial differential equations.
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8
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Fourier series and Fourier integrals, Non-homogeneous problems and the finite Fourier series
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9
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Solutions of PDEs by using Fourier series
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10
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Fourier transform and its properties, Inverse Fourier transform.
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11
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Application of Fourier transform to solve problems involving partial differential equations.
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12
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Green’s function and its construction
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13
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Green’s function and non-homogeneous problems
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14
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15
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Final exam.
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