Friday, August 22. Using an Initial Value Problem to model fish population. Section 1.1.

Monday, August 25. First-order ODEs: existence and uniquness theorem, direction fields. Section 1.2.

Tuesday, August 26. First-order Linear ODEs: integrating factors and solution formulas. Section 1.3.

Wednesday, August 27. First-order Linear ODEs: existence and uniqueness of solution to IVPs, modeling. Sections 1.3 and 1.4.

Friday, August 29. Modeling with first-order linear ODEs, method of undetermined coefficients. Section 1.4.

Tuesday, September 2. Introduction to systems, radioactive decay, vertical motion. Section 1.5.

Wednesday, September 3. Vertical motion with viscous damping, separable first-order ODE. Sections 1.5 and 1.6.

Friday, September 5. Separable first-order ODE: theory, solution method, examples. Section 1.6.

Monday, September 8. System methods for first-order equations, reducing a second-order equation to a first-order system. Using pplane to plot orbits of first-order systems. Section 1.7.

Tuesday, September 9. Applications of system methods: escape velocity, combat. Section 1.7.

Wednesday, September 10. Modeling the level of a drug in the body. Section 1.8.

Friday, September 12. Change of variables method for homogeneous rate functions of order zero. Modeling pursuit. Section 1.9.

Monday, September 15. The existence and uniquness theorem for first-order IVP's. Section 2.1 and Appendices A.1 and A.2.

Tuesday, September 16. The existence and uniquness theorem for first-order IVP's (cont.). Section 2.1 and Appendix A.2.

Wednesday, September 17. The existence and uniquness theorem for first-order IVP's (cont.). Section 2.1 and Appendix A.2.

Friday, September 19. Extension and long-term behavior of solutions. Autonomous equations. Section 2.2.

Monday, September 22. Long-term behavior of solutions to first-order IVPS for autonomous equations. Sections 2.2.

Tuesday, September 23. Long-term behavior of solutions to first-order IVPS for linear equations. Sensitivity of solutions to the data. Sections 2.2 and 2.3 and Appendix A.4.

Wednesday, September 24. Sensitivity of solutions to the data, the general case and the specific case of linear equations. Section 2.3 and Appendix A.4.

Friday, September 26. Introduction to Bifurcation. Section 2.4.

Monday, September 29. Approximate solutions. Section 2.5.

Tuesday, September 30. Approximate solutions (cont), computational issues and computer implementation. Sections 2.5 and 2.6.

Wednesday, October 1. Chaos, the logistic equation and Euler's method. Section 2.7.

Monday, October 6. Test 1 returned.

Tuesday, October 7. Second-order ODEs. Linear and nonlinear models for the oscillations of a spring. Section 3.1.

Wednesday, October 8. Linearizing nonlinear equations. Theory of second order IVPs. Graphical representations of solutions. Sections 3.1 and 3.2.

Friday, October 10. Autonomous second-order ODEs. Linear second-order ODEs with constant coefficients. Sections 3.2 and 3.3.

Monday, October 13. Linear second-order ODEs with constant coefficients. Sections 3.3 and 3.4.

Tuesday, October 14. Linear second-order ODEs with constant coefficients. Section 3.4.

Wednesday, October 15. Periodic functions, simple harmonic motion, driven constant coefficient linear ODEs. Sections 3.5 and 3.6.

Friday, October 17. Driven constant coefficient linear ODEs: method of undetermined coefficients, real vs. complex solutions. Section 3.6.

Monday, October 20. Driven constant coefficient linear equations: method of undetermined coefficients and general theory of linear ODEs. Sections 3.6 and 3.7.

Tuesday, October 21. General theory of linear ODEs. Section 3.7.

Wednesday, October 22. Simple pendulum. Section 4.1.

Friday, October 24. Simple pendulum (cont.). Sections 4.1.

Monday, October 27. Simple pendulum (cont.). Section 4.1.

Tuesday, October 28. Resonance and beats. Section 4.2.

Wednesday, October 29. First-order systems. Section 5.1.

Friday, October 31. Fundamental Theorem of first-order systems, autonomous systems generally and in the plane. Section 5.1.

Monday, November 3. Planar autonomous systems:graphical analysis and polar coordinates. Section 5.2.

Tuesday, November 4. Application of planar autonomous systems to modeling the populations of interacting species. Section 5.3.

Wednesday, November 5. Test 2 returned. Lotka-Volterra model for predator-prey interactions. Section 5.4.

Friday, November 7. Project guidelines. Using matlab to solve non-autonomous systems or systems of more than two equations.

Monday, November 10. The Laplace transform: Definition and examples. Functions of exponential order. Section 6.1

Tuesday, November 11. The Laplace transform: Existence and differentiability for transforms of functions in E. Sections 6.1 and 6.2.

Wednesday, November 12. The Laplace transform: More examples, step functions. Section 6.2.

Friday, November 14. Laplace transform: shifting, solving linear IVPs. Section 6.2.

Monday, November 17. Laplace transform: of periodic functions, application to delay equations and models of traffic flow. Sections 6.1-3.

Tuesday, November 18. Laplace transform and traffic flow (cont.). Section 6.3.

Wednesday, November 19. Convolution: Definition, Properties, and the Laplace transform, and relation to IVPs. Section 6.4.

Friday, November 21. The Delta Function, Convolution, IVPs. Section 6.5.

Monday, November 24. Linear systems with constant coefficients in the plane.

Tuesday, November 25. Linear systems with constant coefficients in the plane (cont.).

Wednesday, November 26. Linear systems with constant coefficients in the plane (cont.).