## 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.

**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 |
1.1-1.4 & 1.6 |
Introduction. Standard examples of PDEs. Derivation of transport, wave and diffusion equation from simple physical principles. First order equations: coordinate method and geometric method of characteristics. Second order equation. Initial and boundary conditions. |

2 |
2.1-2.5 |
Wave and Diffusion equation on the whole real line The wave equation: Coordinate method and geometric method. Causality and energy. The Maximum Principle for the diffusion equation, Uniqueness and Stability of solutions. Derivation of the Solution of the diffusion equation. Comparison of wave and diffusion equation. |

3 |
3.1-3.3 |
Reflections and Sources Diffusion on the half-line with Dirichlet and Neumann boundary conditions. Method of reflection. Method of reflection on a finite interval with outlook to chapter 4. Inhomogeneous diffusion equation on the whole real line. |

4 |
4.1-4.2 |
Boundary Problems Wave and diffusion equation on a finite interval with Dirichlet boundary conditions. Wave and diffusion equation on a finite interval with Neumann and periodic boundary conditions. Sketch discussion on Robin boundary conditions. |

5 |
5.1-5.4 |
Fourier Series Fourier-sine, Fourier-cosine and full Fourier series, complex and real version. Orthogonally and Completeness of Fourier series, convergence theorems. |

**Additional Notes:**