Math 450

Applied Mathematics 1
MWF 10-10:50AM in Wilson Hall 1-124

Announcements

  • For a general overview of the course, download the Course Policies .
  • The FINAL EXAM is 8:00-9:50AM on Monday, December 10.

Course Policies (pdf file format)
Textbook:Applied Mathematics, by J. David Logan (3rd edition)

Topics for the Course

  1. Review of Ordinary Differential Equations
    • Separation of Variables
    • Integrating Factors
    • Variable Substitution - Bernoulli
    • Characteristic Equations
    • Variation of Parameters
    • Eigenvalue-Eigenvector Methods for Linear Systems
    • Phase Line and Plane Analysis
    • Bifurcation Analysis
  2. Chapter 1: Dimensional Analysis and Scaling
    • Buckingham Pi Theorem
    • Characteristic Scales
  3. Chapter 2: Perturbation Methods
    • Regular Perturbation
    • Poincare-Linstedt Method
    • Asymptotic Analysis - Pointwise and Uniform Convergence
    • Singular Perturbation
    • Boundary Layer Analysis
  4. Chapter 3: Calculus of Variations

Homework Assignments

Some Class Notes

These Links are no longer active. Email me if you would like a copy of any of them.

Chapter 1

  • 1st-order ODEs
  • 2nd-order ODEs
  • nth-order ODEs
  • Homogeneous Linear Systems
  • Nonhomogeneous Linear Systems
  • Dimensional Analysis
  • Stability for Linear Autonomous Systems
  • Stability for Non-Linear Autonomous Systems

Chapter2

  • Non-Linear Resistive Medium
  • Polynomial Roots
  • Duffing Equation
  • Poincare Lindstedt
  • Asymptotic Analysis
  • Singular Perturbation - 1
  • Singular Perturbation - 2
  • WKB Approximation
  • Boundary Layers - 1
  • Initial Layers

Supplementary Texts:

  1. Elementary Differential Equations texts (pick your favorite).

Students are NOT required to buy the supplementary texts. Occasionally, I will cover topics and include material from these texts that are not covered to my satisfaction in the required text.