## 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 |
6.1-6.4 |
Second order Linear Differential equations in 2D and 3D. Harmonic Functions Laplace equation; examples, Maximum Principle, Uniqueness of solutions, and Symmetries. Extension to elliptic differential equations. Laplace equation on Rectangles and Cubes. Poisson’s Formula, Mean Value Property, and Maximum Principle. Laplace equation on Circles, Wedges, and Annuli. |

2 |
7.1-7.4 |
Green’s Identities and Green’s Functions Green’s First Identity, Maximum Principle, Dirichlet’s Principle. Green’s Second Identity. Green’s Functions in general. Green’s Function for Half-Space and Sphere. |

3 |
9.1-9.4 |
Diffusion and Wave Equation in unrestricted 2D and 3D. Energy and Causality. Kirchhoff’s Formula in 3D, and the solution in 2D. Inhomogeneous wave equation in 3D. Diffusion equation in 2D and 3D. |

4 |
10.1-10.3 |
Boundary Problems in 2D and 3D. Separation of Variables, revisited. Vibrations of a Drumhead, Bressel functions (see also 10.5) Sketch of 3D Wave Equation in a ball. |

5 |
11.1 & 11.6 |
General Eigenvalue Problems: An Introduction Minimum Principle Asymptotics of Eigenvalue |

**Additional Notes:**