## Course Information

Partial differential equations (PDE) are ubiquitous in mathematics, science, engineering and physics. A brief list of applications includes diffusion of heat, propagation of waves, optimal control theory, fluid dynamics, computer vision, and image processing. This course is a rigorous graduate level introduction to partial differential equations. The first part of this course will study the three classical linear PDE: Laplace's equation, the wave equation, and the heat equation. Then we will move on to nonlinear PDE, and we will cover the method of characteristics, Hamilton-Jacobi equations, and conservation laws. In the final part of the course we will study Sobolev spaces and general techniques for second-order elliptic equations. Other topics we may touch on include Fourier and Laplace transform techniques, and separation of variables.

The animation above is a simulation of a nonlinear diffusion partial differential equation (the Perona-Malik equation) applied to a color image. Note: The png animation may not play in some browsers. Click here for for a lower quality gif.

Instructor |
Jeff Calder (Office: 1053 Evans, Email: jcalder at berkeley dot edu) |

Lectures |
Mon, Wed, Fri, 10am-11am in 2 Evans |

Office Hours |
Mon, Wed, Fri, 11:30am-12:30pm in 1053 Evans |

Textbook |
Evans, L.C. Partial Differential Equations (1st or 2nd Edition) |

Grades |
Your grade will be based on homework (20%), a midterm exam (30%), and the final exam (50%). The exams will be take-home exams and dates will be announced in the first week of classes. Homework will be assigned on a weekly basis. |

Piazza |
We have a Piazza website for student discussions. To sign up for Piazza and join our class, click here . |