**URL: ** http://www.math.utah.edu/~cherk/teach/5720-04/appl-2-2004.html

Instructor: Professor Andrej
Cherkaev
Office: JWB 225 Telephone: 581-6822 E-mail: cherk@math.utah.edu |
Three credit hours.
10:45-11:35AM JWB 333 office hours: WF after class |

**Addressed** to graduate and senior undergraduate students in math,
science, and engineering.

Grade is based on regular homework assignments and a course project.

Gilbert Strang. Introduction to Applied Mathematics. Instructors notes.

Strang: Chapters 4, 6, 7, 8. Notes: Extremal problems .

4. Analytical Methods4.1 Fourier Series and Orthogonal Expansions

4.2 Discrete Fourier Series and Convolution

4.3 Fourier Integrals

4.4 Complex Variables and Conformal Mapping

4.5 Complex Integration6. Initial-Value Problems

6.1 Ordinary Differential Equations

6.2 Stability and the Phase Plane and Chaos

6.3 The Laplace Transform and the z-Transform

6.4 The Heat Equation vs. the Wave Equation

6.5 Difference Methods for Initial-Value Problems

6.6 Nonlinear Conservation Laws7. Network Flows and Combinatorics

7.1 Spanning Trees and Shortest Paths

7.2 The Marriage Problem

7.3 Matching Algorithms

7.4 Maximal Flow in a Network8. Optimization

8.1 Introduction to Linear Programming

8.2 The Simplex Method and Karmarkar's Method

8.3 Duality in Linear Programming

8.4 Saddle Points (Minimax) and Game Theory

8.5 Nonlinear Optimization

The grade will be based on homework scores and course project.

As a rule, the homework will be assigned each week.

List of projects.

Preliminary presentations.

Presentations