Outline of First Part of Lecture Notes

• Page 1: Intro to first order differential equations
• Page 2: Separable Equations (Section 2.2 of textbook)
  • Page 5: Initial Value Problems
  • Pages 6 & 7: Applications (Section 1.2 of textbook)
  • Page 8: Example using Maple
  • Page 9: Example using Matlab
  • Page 10: Existance and Uniqueness (Theorem 2.4.2)
  • Page 14: Homogeneous Equations (pages 49-50 in textbook)
• Page 19: Linear First Order Differential Eqations (2.1)
  • Page 25: Existance and Uniqueness (Theome 2.4.1)
  • Page 27: Example with jump discontinity
  • Page 30: Bernoulli Equations (page 77)
• Page 33: Analysis o solutions: slope fields (1.1)
  • Page 33: By hand.
  • Page 34: With Maple.
  • Page 37: With Matlab.
• Pages 39-56: Applications (2.3)
  • Pages 39-44: I. Mixing Problmes.
  • Pages 44-49: II. Radioactive Decay Example (coupled systems)
  • Pages 50-56: III. Motion Problems with Resistance.
• Pages 56(oops)-63: More Applications, Population, Autonomus Systems (2.5)
• Exact Equations (2.6) [15 pages]
• Numerical Methiods, Breif intro. (2.7) [4 pages]