### Lecture notes by Jonathan Goodman

- Section 1, The Linear Heat Equation. Last update: January 29.
- Section 2, The Fourier Transform and the Heat Equation. Last update: February 8.
- Section 3, Theory. Last update: February 10.
- Section 4, Solution techniques. Last update: February 25.
- Section 5, Probability flux. Last update: March 3.
- Section 6, Deterministic optimal control. Last update: March 28.
- Section 7, More on deterministic optimal control. Last update: April 5.
- Section 8, More on deterministic optimal control. very preliminary
- Section 9, More on deterministic optimal control. very preliminary
- Sample final exam,

### Lecture notes by Bob Kohn

### Books on PDE

- Fritz John,
**Partial Differential Equations**: A clear and concise reference for the linear heat equation with a down to earth treatment of qualitative properties such as existence, uniqueness, and regularity. It also covers Green's functions and Fourier transforms. - Lawrence C. Evans,
**Partial Differential Equations**: A deeper and longer discussion of partial differential equations. It discusses nonlinear Hamilton Jacobi equations of the kind that arise in deterministic and stochastic control.

### Books on finance

- Robert Merton,
**Continuous Time Finance**: A classic compilation of papers by Merton. - Silih Neftci,
**An Introduction to the Mathematics of Financial Derivatives**: An intuitive and well illustrated elementary introduction to the relation between PDE and stochastic processes.

### Books on stochastic calculus and PDE

- Steven Shreve,
**Stochastic Calculus for Finance, II**: A slow treatment of the relation between PDE and SDE. - J. Michael Steele,
**Stochastic Calculus and Financial Applications**: A more careful mathematical treatment.

### Deterministic and stochastic control

- Michael Athans and P. L. Falb,
**Optimal Control: An Introduction to the Theory and Its Applications**: A basic introduction to control theory that has derivations of the Hamilton Jacobi equations for optimal control problems. - Floyd Hanson Applied Optimal Control: A class page with helpful references and problems.

Page last updated: January 29, 2008