Date |
Topic |
Reading Assignment |
Written Assignment |
| |
Monday, January 13 |
Discuss Syllabus, briefly
Modeling using Differential Equations
Introducing: "Shakespeare and Love"
Numerical technique:
(Review of) Euler's Method.
|
Euler's method reference: Section 1.4 in BDH. |
|
| Wednesday, January 15 |
Work on your "Shakespeare and Love" Model:
Goals:
descriptive name and conjectures about long-term behavior. |
Sections 1.1 and 1.2 in BDH |
|
| Friday, January 17 |
Continue work on S&L exploration
Goal: get to the point where you have planned out the report you will give on Monday. |
|
| * |
| Monday, January 20 |
5 minute reports on S&L Exploration I.
Qualitative and Quantitative observations about Modeling using Differential Equations |
Read Section 1.1 (again!) |
Section 1.2; 1, 3, 5, 7, 15, 17, 23, 35.
Note: MLK day. Class meets from 11:30-12:10. |
| Wednesday, January 22 |
More on Modeling: Slope fields |
Section 1.3 in BDH |
|
| Friday, January 24 |
Equilibria and the Phase line |
Section 1.6 in BDH |
Section 1.1; 4, 5, 13, 14, 15, 17, 23. |
| * |
| Monday, January 27 |
Quiz # 1
Equilibria and the phase line---cont. |
|
Section 1.3; 7, 11, 13, 15, 16, 17. (For problem 7, use HPGSolver to reproduce the slope field, print it out, and write your solution on the printout.) |
| Wednesday, January 29 |
Bifurcations |
Section 1.7 |
Section 1.6; 2, 8, 20, 22, 23, 26, 32, 36, 37, 39. |
| Friday, January 31 |
Bifurcations in applications
Introducing the Phisheries Project. |
|
Section 1.7; 2, 3, 4, 6, 7, 8, 13, 18, 22. |
| * |
| Monday, February 3 |
Improving Euler's Method--- laboratory exercise. |
|
|
| Wednesday, February 5 |
Test #1
|
| Friday, February 7 |
Introducing Linear Equations |
Section 1.8 |
|
| * |
| Monday, February 10 |
Integrating Factors for Linear Equations |
Section 1.9 |
(By this point, you should have the bulk of the mathematical work done on the Phisheries Project.) |
| Wednesday, February 12 |
Existence and Uniqueness of Solutions--Big Picture Discussion.
Quiz # 2 ---Linear eqns and Integrating factors. |
Section 1.5 |
Section 1.9; 4, 5, 6, 8, 9, 10, 20, plus problem on handout. |
| Friday, February 14 |
More on linear equations: applications and interpretation---a work day. |
|
Phisheries Project Due |
| * |
| Monday, February 17 |
Modeling via Systems |
Section 2.1 |
Section 1.5; 4, 9, 10, 12, 16. |
| Wednesday, February 19 |
The Geometry of Systems |
Section 2.2 |
What about Cold Meds? worksheet. |
| Friday, February 21 |
Geometry of Systems, continued. |
|
Section 2.1; 1, 2, 5, 6, 8, 9, 11, 12, 16a. |
| * |
| Monday, February 24 |
Quiz #3---Geometry of systems.
Finish Bees and Clover Handout
|
|
|
| Wednesday, February 26 |
Existence and Uniqueness of Solutions for Systems |
Section 2.6 |
Homework Handout plus Section 2.2 18, 19, 21cd, 26. |
| Friday, February 28 |
Shakespeare and Love, Part II |
|
|
Spring Break |
| Monday, March 17 |
Introduction to Linear Systems and the Linearity Principle. Linear Independence of Solutions |
Section 3.1. |
|
| Wednesday, March 19 |
Class cancelled due to power outage |
|
Work on homework from Section 3.1; 10, 12, 14, 15, 17, 18, 24, 26-29, 30, 31, 33. |
| Friday, March 21 |
Linear Algebra in Diff Eqs
Introducing straight Line Solutions |
Section 3.2 |
Section 3.1 homework due. |
| * |
| Monday, March 24 |
Straight Line Solutions, cont. |
Linear Alg Handout (read & make connections to book!)
Section 3.2 (again!) |
|
| Wednesday, March 26 |
Phase portraits and distinct, real Eigenvalues. |
Section 3.3
|
Section 3.2; 1, 3, 6, 8, 10, 12, 13, 16, 17, 19.
|
| Friday, March 28 |
Test # 2
covers through Section 3.2 |
| * |
| Monday, March 31 |
Complex Eigenvalues |
Section 3.4 |
Section 3.3; 1, 3, 8, 12, 14, 19, 20, 24, 27. |
| Wednesday, April 2 |
Special Cases: Zero and Repeated Eigenvalues |
Section 3.5 |
Section 3.4; 2, 6(abde), 10, 12, 14, 15, 16, 23. |
| Friday, April 4 |
Finish Linear Systems |
|
|
| * |
| Monday, April 7 |
Quiz #4---Analyzing Linear Systems. |
|
|
| Wednesday, April 9 |
The Trace Determinant Plane
|
Section 3.7 |
Section 3.5; 4, 6, 8, 11, 13, 14, 18, 21, 22, 23. |
| Friday, April 11 |
Two-parameter families |
|
|
| * |
| Monday, April 14 |
Shakespeare and Love---the final encounter. |
|
Section 3.7; 2, 5, 8, 10. |
| Wednesday, April 16 |
Equilibrium Point Analysis |
Section 5.1 |
Work on Shakespeare and Love! |
| Friday, April 18 |
Project # 3: Bifurcations Project |
|
|
| * |
| Monday, April 21 |
Linearization and bifurcations |
|
"Shakespeare and Love" Project Due. |
| Wednesday, April 23 |
Test # 3 |
Section 5.1: 1, 2, 3abd, 4, 8a, 11a, plus handout problems. |
| Friday, April 25 |
Linear and Affine Difference Equations.
Introducing Iteration |
Handout: A Short Introduction to Difference Equations. |
|
| * |
| Monday, April 28 |
Iteration and fixed points. |
|
Handout: Problems on Affine and Linear Difference Equations.
Preliminary check-up on bifurcations project, by appointment, no later than Tuesday, April 29. |
| Wednesday, April 30 |
Systems of Difference Equations: The Leslie Matrix Model. |
|
|
| Friday, May 2 |
Leslie Matrices, cont. |
|
Handout on Leslie Matrices
Bifurcations Project Due at 3 p.m. |
| |
| |
Final Examination
6:30 p.m. on Wednesday, May 7, 2014
(Note: This is the scheduled time for the Period 3 courses) |