### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

### Prerequisites

Differential Equations (18.03 or 18.034). Complex Variables with Applications (18.04) or Functions of a Complex Variable (18.112) are useful, as well as previous acquaintance with the equations as they arise in scientific applications.

### Textbook

Either one of the following textbooks will do.

Guenther, R. B., and J. W. Lee. *Partial Differential Equations of Mathematical Physics and Integral Equations*. New York, NY: Dover Publications, 1996. ISBN: 0486688895.

Myint-U, Tyn, and Lokenath Debnath. *Linear Partial Differential Equations for Scientists and Engineers.* 4th ed. Boston, MA: Birkhauser, 2006. ISBN: 0817643931.

### Assignments and Exams

There will be 6 problem sets given throughout the term. There will be two in-class tests and a final exam.

### Grading

ACTIVITIES | PERCENTAGES |
---|---|

Assignments | 20% |

In-class Tests (2 tests each worth 20%) | 40% |

Final Exam | 40% |

### Outline

I. The Heat Equation in One Space Variable

- Separation of Variables, Fourier Series, Sturm-Liouville Eigenvalue Problems

II. The Wave Equation in One Space Variable

- Method of Characteristics

III. Method of Characteristics Solution to Quasilinear PDEs

IV. The Heat and Wave Equations with Two or Three Space Variables

- Bessel Functions, Laplace’s Equation

V. The Heat Equation and Laplace’s Equation on Unbounded Spacial Domains

- Fourier Transform

VI. Green’s Function Method for Solving ODEs, PDEs