Classnotes For Applied Mathematics MATH 416
Laura K. Gross
Bridgewater State University
Bridgewater, MA
Text: Introduction to Applied Mathematics by Strang
Prerequisite: Multivariable Calculus
  1. Plan
  2. Definitions
  3. Statement of Laplaces Equation
  4. Some Methods
  5. Elastic Bar
  6. Heat Application
  7. Sturm Liouville
  8. Nonhomogeneous
  9. Derive Laplace
  10. Divergence and Stokes' Theorems
  11. Source Example
  12. Line Integration
  13. Potential Functions
  14. Line Integration Problems
  15. Conservative Vector Fields
  16. Divergence and Curl in 3-D
  17. Cross Product
  18. Surface Integrals
  19. Area Integrals
  20. Equation of a Plane
  21. Surface Integration Problems
  22. Surface Integrals of Vector Fields
  23. Divergence Theorem
  24. Stokes Theorem
  25. Orthogonality Groundwork
  26. Inner Product of Functions
  27. Orthogonal Sets
  28. Fourier Series
  29. Fourier Series Examples
  30. Fourier Sine and Cosine Series
  31. Properties of Fourier Series
  32. Application of Fourier Series to Laplace's Equation
  33. Laplace's Equation on a Disk
  34. More Orthogonal Functions
  35. Eigenfunctions
  36. Bessel Functions
  37. Bessel Function of Order Zero
  38. Fourier Integral
  39. Fourier Transform
  40. Partial Differential Equations
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last updated July 22, 2016