Math 256 - Differential Equations - Schedule

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Week 1

• Syllabus discussion.
• 1.1 Modeling via Differential Equations
  1.1 HW: 1, 4*, 6, 8*, 15, 16*, 19, 20*
  (starred problems graded for accuracy)

Week 2 (Monday Sept 5, Labor Day, no classes)

• 1.2 Analytic Technique: Separation of Variables
  1.2 HW: 2, 6, 10, 18*, 28*, 36*
• 1.3 Qualitative Technique: Slope Fields
  1.3 HW: 6*, 7, 12*, 15, 24*
• 1.4 Numerical Technique: Euler's Method
  1.4 HW: 2*, 6*, 10, 13*

Week 3 (Last day to add/drop, Sept 12)

• 7.1 Numerical Error in Euler's Method
  Homework Assignment 3
• 1.5 Existence and Uniqueness of Solutions
  1.5 HW: 12*, 16(due with HW 4)
• 1.6 Equilibria and Phase Line
  1.6 HW: 2*, 9, 32*, 37 (due with HW 4)

Week 4

• 1.8 Linear Equations
  1.8 HW: 2*, 10 (due with HW 4)
  more from 1.8 HW: 12, 19*, 20*, 21*(due with HW 5)
• Lab 1: Memorization Model (page 144)
• 1.9 Integrating Factors for Linear Equations
  1.9 HW: 4*, 8, 12*, 25 (due with HW 5)
• Chapter 1 Review Exercises: 11-20

Week 5

• 2.1 Modeling via Systems
  2.1 HW: 7a, 9, 10*, 16a* (due with HW 5)
• 2.2 The Geometry of Systems
  2.2 HW: 7*, 10*, 11*, 14* (due with HW 5)
• 2.3 Analytic Methods for Special Systems
  2.3 HW: 19* (due with HW 5)
• 2.4 Euler's Methods for Special Systems
  2.4 HW: 3, 6*, 7*, 8*, 9* (due with HW 6)
  Chapter 2 review problems: 27*, 30 (due with HW 6)

Week 6

• Midterm Exam 1: Friday, October 6.
• 2.5 The Lorenz Equations
• 3.1 Properties of Linear Systems and the Linearity Principle
  3.1 HW: 6*, 14*, 16*, 18* (due with HW 6)

Week 7

• 3.2 Straight Line Solutions
• 3.3 Phase Planes for Linear Systems with Real Eigenvalues

Week 8 (Mid-semester day, Oct 20, no classes)

• 3.3 Phase Planes for Linear Systems with Real Eigenvalues
• 3.4 Complex Eigenvalues
• Lab #2, due Friday, October 27 (Lab 2 is HW 7)

Week 9

• 3.5 Special Cases and Zero Eigenvalues
  3.5 HW: 2*, 6*, 11, 12*, 18*, 24* (HW 8, due Wednesday, Nov 1)
  3.2 HW: 6*, 8* (due with HW 8)
• 3.6 Second Order Linear Equations
  3.6 HW: 2, 6*, 12* (due with HW 8)
• 3.7 The Trace Determinant Plane
  3.7 HW: 3, 12* (due with HW 9, due Nov 10)

Week 10 (Last day to withdraw Nov 3)

• 4.1 Forced Harmonic Oscillators
  4.1 HW: 8*, 10, 14*, 16*, 19, (due with HW 9, due Nov 10)
• 4.2 Sinusoidal Forcing
  4.2 HW: 4, 8*, 14*, 17* (due with HW 9, due Nov 10)
• 4.3 Undamped Forcing and Resonance
  4.3 HW: 6*, 10, 12, 18* (due with HW 9, due Nov 10)

Week 11

• Lab #3: Pick your own lab. Pick from Lab 3.1, 2.1, 4.1, 3.2, 4.2, 3.4, 2.4, OR 4.3.
  Lab #3 due Monday, November 20.
• 4.4 Amplitude and Phase of the Steady State
  4.4 HW: 6*(due with HW 10, due Nov 15)
• 5.1 Nonlinear Systems: Equilibrium Point Analysis
  5.1 HW: 2*, 4, 8*, 14*, 18*, 27, 30(due with HW 10, due Nov 15)
• Midterm Exam 2, Wednesday, November 8
  Midterm 2 will emphasize material from Chapter 3 (except 3.8) and 4.1 - 4.3. (assuming we get through all of 4.3 by Nov 3.)

Week 12

• 5.2 Nonlinear Systems: Qualitative Analysis
  5.2 HW: 2*, 8*, 10, 12*(due with HW 11, due Nov 29)
• 5.3 Nonlinear Systems: Hamiltonian Systems
  5.3 HW: 14, 15, 16* (due with HW 11, due Nov 29)
• Lab #4: Pick your own lab. Pick from Labs 5.3, 5.4, OR 6.2
  Lab #4 due Friday, December 8.

Week 13 (Thurs & Friday Nov 23-24, Thanksgiving break, no classes)

• 6.1 Laplace Transforms
  6.1 HW: 2, 10*, 12, 16*(due with HW 11, due Nov 29)
• 6.3 Second-Order Equations
  6.3 HW: 2*, 12, 14, 16*, 28*(due with HW 11, due Nov 29)
  

Week 14

• Laplace transform worksheet
• 6.2 Discontinuous Functions
  6.2 HW: 1, 2*, 6*, 7, 12*(due with HW 12, due Dec 8)
• 6.5 Convolutions
  6.5 HW: 3, 4*, 10*(due with HW 12, due Dec 8)
  6.3 HW: 6*, 30*, 34 (do the problems from 6.2 first) (due with HW 12, due Dec 8)
  6.1 HW: 5*(due with HW 12, due Dec 8)

Week 15

• Series Solutiuons (Appendix B)
  Appendix B HW: 6*, 12*, 14 (due with HW 12, due Dec 8)
• review