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Chapters 1-6 from *Differential Equations: an Applied Approach*
by J. M. Cushing

Pearson Prentice-Hall,Upper Saddle River , New Jersey , 2004
(ISBN: 0-13-044930-X)

Subject to change

Pearson Prentice-Hall,

Subject to change

Model derivation (variable identification/classification/symbolization/inter-relationships, laws/assumptions/hypotheses)

Mathematical analysis (solution formulas, analytic/numeric/graphic approximations, qualitative methods)

Solution interpretation/utilization (evaluation/critique/data)

Model modification (re-evaluation of assumptions, added phenomena & mechanisms)

1. Thursday, January 17

2. Tuesday, January 22

3. Thursday, January 24

Solutions, the Fundamental Existence & Uniqueness Theorem, graphic approximations, numeric approximations

4. Tuesday, January 29

5. Thursday, January 31

2. Linear First Order Equations : Chapter 2

General solution & initial value problems, Variation of Constant formula, homogeneous & non-homogeneous equations, method of undetermined coefficients, autonomous equations (equilibria, stability, phase line portraits)

6. Tuesday, February 5

7. Thursday, February 7

3. Nonlinear First Order - Autonomous equations (qualitative theory & methods) : Chapter 3.1

Phase line portraits, equilibria, attractors/repellers/sinks, linearization, qualitative equivalence, dependence on parameters & bifurcations, bifurcation diagrams

8. Tuesday, February 12

9. Thursday, February 14

10. Tuesday, February 19

11. Thursday, February 21

4. Nonlinear first Order - Non-autonomous equations (analytic methods) : Chapter 3.2 - 3.4

Solution formulas (separable equations, change of variables), approximation formulas (

12. Tuesday, February 26

13. Thursday, February 28

14. Tuesday, March 4

15. Thursday, March 6 (TEST #1)

Conversion of higher order equations to systems, Fundamental Existence & Uniqueness Theorem,

graphic & numeric approximations, phase plane

16. Tuesday, March 11

2. Linear Systems - Basics : Chapter 4.2

Structure of general solution, initial value problems

17. Thursday, March 13

SPRING BREAK: March 15-23

3. Linear Systems – Autonomous Homogeneous : Chapter 5.1 - 5.5

Solution formulas (using eigenvalues), short cuts for 2

18. Tuesday, March 25

19. Thursday, March 27

20. Tuesday, April 1

21. Thursday, April 3

22. Tuesday, April 8

23. Thursday, April 10

4. Linear Systems – Autonomous Non-homogeneous : Chapter 6.1 - 6.2

Variation of Constants formula, method of undetermined coefficients for 2

24. Tuesday, April 15

5. Autonomous Nonlinear Systems – Equilibria : Chapter 8.1 - 8.3

Equilibria, stability, linearization, Fundamental Theorem of Stability, geometry of local phase portraits

25. Thursday, April 17

26. Tuesday, April 22

27. Thursday, April 24 (TEST #2)

6. Autonomous Nonlinear Systems – Oscillations : Chapter 8.5

Periodic solutions, limit cycles, bifurcations & Hopf criteria

28. Tuesday, April 29

29. Thursday, May 1

Review

30. Tuesday, May 6

J.
M.
Cushing / Department
of Mathematics
/ Program
in Applied Mathematics / University
of Arizona / Tucson, AZ, 85721-0089

(last revised 28 January 2008)

Copyright © 2007