# Differential Equations---Math 333

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### Suggested Problems

Homework Problems are in red bold

Tuesday, January 15

Discuss Syllabus

Modeling via Differential Equations
Section 1.1
Thursday, January 17 Analytic Technique: Separation of variables (review)
Qualitative technique: Slope Fields
Sections 1.2 and 1.3 Section 1.1; 4, 5, 13, 14, 15, 17, 23.
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Tuesday, January 22 Numerical technique: Euler's method Section 1.4 Section 1.2; 1, 3, 5, 7, 15, 17, 23, 35.
Section 1.3; 7, 11, 13, 15, 16, 17.
Thursday, January 24 Quiz #1
Equilibria and the Phase Line
Section 1.6 Homework handouts: The Pendulum; the SIR model.
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Tuesday, January 29 Bifurcations Section 1.7 Section 1.6; 2, 8, 20, 22, 23, 26, 32, 36, 37, 39.
Thursday, January 31 Bifurcations in applications
Introducing the Phisheries Project.
Section 1.7; 2, 3, 4, 6, 7, 8, 13.
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Tuesday, February 5

## Test #1

Thursday, February 7 Linear Equations Section 1.8 (By this point, you should have the bulk of the mathematical work done on the Phisheries Project.)
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Tuesday, February 12 Integrating Factors for Linear Equations Section 1.9 Section 1.8; 2, 4, 8, 10, 17, 18, 19, 23, 31.
Thursday, February 14 Quiz #2
Existence and Uniqueness of Solutions
Section 1.5 Section 1.9; 4, 5, 6, 8, 9, 10, 20, 25.
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Tuesday, February 19
No Class Professor Schumacher is out of Town
Phisheries Project Due---turn in to Professor Milnikel before 4 p.m.
Thursday, February 21 Modeling via Systems Section 2.1 Section 1.5; 4, 5-8, 10abc, 12, 14, 16.
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Tuesday, February 26 The Geometry of Systems Section 2.2 Section 2.1; 1, 2, 5, 6,11, 12, 13, 16a, 20.
Thursday, February 28 Quiz #3
Existence and Uniqueness of Solutions for Systems
Section 2.6 Section 2.2; 8, 10, 11ac, 14, 15. (Use Maple instead of HPGSystemSolver. In other assignments, too!)

## Spring Break

Tuesday, March 19 No class---too many students gone.   Section 2.2 (again!); 18, 19, 21cd, 26.

Thursday, March 21 Introduction to Linear Systems and the Linearity Principle. Linear Independence of Solutions Section 3.1.
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Tuesday, March 26 Linear Algebra in Diff Eqs
Introducing straight Line Solutions
Section 3.2
Section 3.1; 10, 12, 14, 15, 17, 18, 24, 26-29, 30, 31, 33.
Thursday, March 28

## Test # 2covers through Section 3.1

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Tuesday, April 2 Straight Line Solutions, cont.
Phase portraits and distinct, Real Eigenvalues.
Linear Alg Handout (read make connections to book!)
Section 3.3
Section 3.2; 1, 3, 6, 8, 10, 12, 13, 16, 17, 19.
Thursday, April 4 Quiz #4
Complex Eigenvalues
Section 3.4 Section 3.3; 1, 3, 8, 12, 19, 20, 24, 27.
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Tuesday, April 9 Special Cases: Zero and Repeated Eigenvalues Section 3.5

Section 3.4; 2, 6, 10, 12, 14, 15, 16, 23.

Thursday, April 11 Finish Linear Systems
Project # 2
: Shakespeare and Love

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Tuesday, April 16 The Trace Determinant Plane
Section 3.7 Section 3.5; 4, 6, 8, 11, 13, 14, 18, 21, 23.
Thursday, April 18 Introducing the Bifurcations Project.   Section 3.7; 2, 5, 9, 10.
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Tuesday, April 23 Power Series Solutions

"Shakespeare and Love" Project Due at 7 p.m.

Thursday, April 25

## Test # 3

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Tuesday, April 30 Equilibrium Point Analysis Section 5.1 Handout: Power series solutions.
Thursday, May 2 Linearization and bifurcations   Section 5.1: 1, 2, 3abd, 4, 8a, 11a.
Bifurcations Project Due at 3 p.m. on Friday, May 3.

### Final Examination

8:30 a.m. on Thursday, May 9, 2013