Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 118C: Partial Differential Equations

Approved: 2003-03-01, Spitzer & Shkoller
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
“Introduction to Partial Differential Equations, 1st Edition” by Walter Strauss. ($50.00)
Search by ISBN on Amazon: 471548685
Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

11.1-11.4 & 11.6

General Eigenvalue Problems.

Minimum Principle.

Minimax and Maxmin Principle.

Completeness of Eigenfunctions.

Extension to Symmetric Differential Operators.

Asymptotics of Eigenvalues, Neumann-Dirichlet bracketing

2

8.1-8.4 (8.5 optional)

Computation of Solutions

Finite Difference Method.

Diffusion Equation.

Wave Equation.

Laplace Equation.

Finite Element Method (optional)

3

12.1-12.3 & 12.5 plus Asymptotics, Stationary Phase Method (not in the textbook)

Distributions and Fourier Transform

Distributions.

Green’s functions, revisited.

Fourier Transform, revisited.

Laplace Transform Techniques

Asymptotics, Stationary Phase Method (not in textbook)

4

14.1-14.3

Non-linear PDEs

Burgers’ equation, shock waves, RH formula, entropy condition.

KdV equation, inverse scattering method, KP equation.

Calculus of variations.

Additional Notes:
Recommendation: Use matlab, mathematica, or maple for demonstration in class early on, and frequently.

In 118C (see chp 8), it should be required for students to adapt or write some simple codes.
Learning Goals:
AS A CAPSTONE: In the second and third courses of the MAT 118 sequence, students undertake an in depth study of advanced methods in partial differential equations. These methods include integral operators, spectral decomposition, energy methods, calculus of variations, and many other advanced techniques. Applications of these techniques to standard and specialized equations arising from mathematics and physics will be demonstrated. Students will gain mastery over technical aspects of the field, and develop their ability to communicate at a capstone level, commensurate with that expected of an undergraduate degree in mathematics.