Proposed update of lecture syllabus and matlabs using Conrad (Holst/Lindblad 6/15/04)

---------------------------- Proposed Update of 20D MATLAB Assignments: ----------------------------
1. Introduction to MATLAB using Sequences and Series
2. Taylor Series
3. Direction fields and ODE solution curves using DFIELd
4. Modeling with ODEs
5. Phase plane and solution curves for systems of ODE using PPLANE
6. Solution of linear systems using eigenvalues and eigenvectors
7. Numerical methods for ODE and systems of ODE
8. Second order ODEs
9. Laplace Transform

------------------------- Proposed Lecture Syllabus for 20D -------------------------
Lec. Sec. Topics
  1. 11.1 Sequences: Concepts, Squeeze Thm, Monotonic Seq Thm
  2. 11.2-3 Geometric and Harmonic Series, Integral Test
  3. 11.4-5 Comparison and Alternating Series Tests
  4. 11.6 Absolute convergence, Ratio and Root Tests
  5. 11.8-9 Power series, radius of convergence, examples
  6. 11.10 Taylor series and remainder estimate
  7. 11.10,12 Applications of Taylor series and remainder estimate
  8. 1.1-2 Introduction to ODE and linear growth/decay models
  9. 1.3 (1.4) Linear first-order ODE and mixture problems
10. 2.1 (2.2) Separate ODE, exact form, and integrating factors
11. 2.3 (2.4) Graphical analysis of ODE and initial value problems (IVP)
12. 2.5 Nonlinear growth models and asymptotic behavior
13. 3.1-2(3.3) Systems of ODE, the phase plane, and IVP solvers
14. 3.4-5 Autonomous systems and interacting population models
15. 4.1 IVP for linear systems of ODE
16. 4.2 Systems with constant coefficients
17. 4.3 Systems with oscillating solutions
18. 4.4 General solution of a linear system
19. 5.1-2 IVP for second order homogeneous equations
20. 5.3 Homogeneous eqns with constant coefficients, examples
21. 5.4 Inhomogeneous eqns with constant coefficients, examples
22. 5.5 Variation of constants/parameters
23. 6.1, 6.3 Definition and properties of the Laplace transform
24. 6.4 Inverse transforms of rational functions
25. 7.1-2 Series solutions of ODE at a regular point.
11.* - Refers to Stewart; remaining sections refer to Conrad. (*) - Means cover only the relevant material from the section. The remaining lectures if any can be filled with either of the following:
    6.5-7 Transform of step and delta functions, convolutions
    7.3-5 Cauchy-Eulers eqs, Regular Singular Points, Bessel func.