# 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)

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:**

In 118C (see chp 8), it should be required for students to adapt or write some simple codes.

**Learning Goals:**