5720   Introduction to Applied Math 2

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

    Contents of the Chapters
          4. Analytical Methods

    4.1  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 Integration

              6. 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 Laws

          7. 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 Network

          8. 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.
    Course projects
    List of projects.
    Preliminary presentations.