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MATH 560
Methods of Applied Mathematics I
TR 12:45-2PM in Wilson Hall 1-139


Announcements
Course Syllabus and Policies: PDF
Textbook: Principles of Applied Mathematics, by James P. Keener (2nd edition)

Topics for the Course
  1. Chapter 1: Finite Dimensional Vector Spaces
    • Linear Vector Spaces
    • Spectral Theory for Matrices
    • Geometrical Significance of Eigenvalues
    • Fredholm Alternative Theorem
    • Least Squares Solutions - Pseudo Inverses
    • Applications of Eigenvalues and Eigenfunctions

  2. Chapter 2: Function Spaces
    • Complete Vector Spaces
    • Sobolev Spaces
    • Approximation in Hilbert Spaces
    • Fourier Series and Completeness
      Nifty Online Plots
    • Finite Elements

  3. Chapter 3: Integral Equations
    • Introduction
    • Bounded Linear Operators in Hilbert Space
    • Compact Operators
Assignments
Homework 1: Pages 49-50 Problems 2, 4, 6, 9a, 9b
Due Tuesday, 9-16-08

Homework 2: Pages 50-52 Section 1.2, Problems 1, 9
Due Tuesday, 9-23-08

Homework 3: Click Here
Due Friday, 10-3-08

Homework 4: Pages 54-56 Section 1.5, Problems 1a, 1c, 2, 5, 10
Due Thursday, 10-23-08

Homework 5:
Section 1.3, p.53 Probs 2, 3
Section 2.1, p.93-94 Probs 1, 5, 7, 8
Due Thursday, 11-13-08



Midterm: Click Here
Due Tuesday, 12-2-08

Final: Click Here
Due Wednesday, 12-17-08
Class Notes

Chapter 1

Chapter 2

Chapter 3

Supplementary Texts:
  1. Green's Functions and Boundary Value Problems by Ivar Stakgold
  2. Applied Partial Differential Equations, J. David Logan
  3. Partial Differential Equations of Mathematical Physics and Integral Eqautions by R.B. Guenther and J.W. Lee
  4. Partial Differential Equations, a Schaum's Outlines text by McGraw Hill

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.