|NAME OF COURSE/MODULE:||PARTIAL DIFFERENTIAL EQUATIONS|
|COURSE CODE:||SFC 4013|
|NAME(S) OF ACADEMIC STAFF:|
|RATIONALE FOR THE INCLUSION OF THE COURSE/MODULE IN THE PROGRAMME:||This subject is an advance mathematical course to develop the understanding on computational physics.|
|SEMESTER AND YEAR OFFERED:||SEM 6 / YEAR 3|
|TOTAL STUDENT LEARNING TIME (SLT)||FACE TO FACE||TOTAL GUIDED AND INDEPENDENT LEARNING|
|L = Lecture
T = Tutorial
P = Practical
L + T + P + O = 120 HOURS
|PREREQUISITE (IF ANY):||NONE|
|OBJECTIVES:||1. Describe real-world systems using PDEs.
2. Solve ﬁrst order PDEs using the method of characteristics.
3. Determine the existence, uniqueness, and well-posedness of solution of PDEs.
4. Solve linear second order PDEs using canonical variables for initial-value problems, Separation of
5. Variables and Fourier series for boundary value problems.
|LEARNING OUTCOMES:||Upon successful completion of this course students should have the ability to:
|TRANSFERABLE SKILLS:||Students should be able to develop problem solving skills through a process of lectures and tutorials.|
|TEACHING-LEARNING AND ASSESSMENT STRATEGY:||Teaching-learning strategy:
|SYNOPSIS:||Partial diﬀerential equations are often used to construct models of the most basic theories underlying physics and engineering. For example, the system of partial diﬀerential equations known as Maxwell’s equations can be written on the back of a post card, yet from these equations one can derive the entire theory of electricity and magnetism, including light. Our goal here is to develop the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. We will see that the frequencies of a circular drum are essentially the eigenvalues from an eigenvector-eigenvalue problem for Bessel’s equation, an ordinary diﬀerential equation which can be solved quite nicely using the technique of power series expansions. Thus we start our presentation with a review of power series, which the student should have seen in a previous calculus course.|
|MODE OF DELIVERY:||Lecture, Lab Practical, Group Work, Online assignment etc|
|ASSESSMENT METHODS AND TYPES:|
|A. Continuous Assessment (60%)|
· One Assignment Based on Aqli-Naqli Integration
· Mid-Term Test
|B. Final Examination (40%)|
|Examination||40 %||Structured and essay type questions|
|MAIN REFERENCES SUPPORTING THE COURSE||1. Partial Differential Equations: An Introduction (2nd Edition), W. A. Strauss|
|ADDITIONAL REFERENCES SUPPORTING THE COURSE||
1. An Introduction to Partial Differential Equations, Y. Pinchover and J. Rubinstein.
2. Partial Differential Equations of Applied Mathematics, E. Zauderer
3. Partial Differential Equations of Mathematical Physics and Integral Equations, R. B. Guenther and J. W. Lee
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