Spring 2009 Math 20 Differential Equations (Syllabus)

Prof. Tanya Leise

MWF 9am  Mudd206, Tues 9am Mudd014 (basement computer lab)

Date
Topic
Practice
To Hand In
Due Date
1/26-1/30




M 1 Overview Read Chapter 1    
T
Lab #1 Introduction to Mathematica      
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2.1-2 Flows on the line 2.1.1, 2.2.1, 2.2.10 2.1.2, 2.1.3, 2.2.3, 2.2.4
Mon
F

2.3 Population growth
2.4 Linear stability analysis

2.3.1, 2.4.1, 2.4.2 2.3.2, 2.3.4, 2.4.4, 2.4.7 Wed
2/2-2/6
       
M

2.5 Existence and uniqueness
Slope fields
2.8 Numerical methods

2.5.2 2.5.1, 2.5.4, 2.5.6 Fri
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Lab #2 Euler's Method      
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2.6-7 Potentials 2.6.1, 2.7.1, 2.7.2 2.7.3, 2.7.4, 2.7.6 , 2.7.7 Mon
F
3.1 Saddle-node bifurcation 3.1.1 3.1.2, 3.1.4, 3.1.5 Wed
2/9-2/13
       
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3.2 Transcritical bifurcation 3.2.1 3.2.3, 3.2.5, 3.2.6 Fri
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Lab #3 Bifurcation diagrams      
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3.3 Laser threshold   3.3.1, 3.3.2 Mon
F
3.4 Pitchfork bifurcation 3.4.1, 3.4.3 3.4.4, 3.4.5, 3.4.6, 3.4.7, 3.4.10 Wed
2/16-2/20
     
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3.4 cont'd   3.4.11, 3.4.16 Fri
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Lab #4 Bifurcation diagrams 3.4.13      
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3.5 Overdamped bead on a rotating hoop 3.5.1, 3.5.2 3.5.7, 3.5.8 Mon
F
3.6 Imperfect Bifurcations 3.6.1 3.6.2, 3.6.3, 3.6.4 Wed
2/23-2/27
       
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3.7 Insect Outbreak 3.7.1 3.7.6
Fri
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Lab#5 Tricritical bifurcation
Original article

     
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4.1 Flows on the circle
4.2 Uniform oscillator
4.1.2,4.1.4 4.1.3, 4.1.7, 4.1.8 Wed
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4.3 Nonuniform oscillator 4.3.1 4.3.3, 4.3.6, 4.3.9 Fri
3/2-3/6
       
M Exam 1 (take-home)   Review and practice exam  
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Lab #6 Biochemical switch 3.7.5      
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4.5 Fireflies   4.5.1 Mon
F
5.1 Linear systems 5.1.2-4 5.1.10, 5.1.11 Wed
3/9-3/13
       
M
5.2 Classification (eigenvalue analysis) 5.2.1, 5.2.2 5.2.3, 5.2.5, 5.2.7, 5.2.9 Fri
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Lab #7 Eigenvalues and stability of dynamical systems      
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5.2 cont'd      
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5.3 Love affairs 5.3.6 5.3.3, 5.3.4, 5.3.5 Mon
3/14-3/22
Spring recess      
3/23-3/27        
M
6.1-2 Phase portraits 6.1.1 6.1.2, 6.1.3, 6.1.6, 6.2.2 Fri
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Lab #8 Nonlinear systems      
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6.3 Fixed points and linearization 6.3.1 6.3.2, 6.3.3, 6.3.6, 6.3.11 Mon
F
6.4 Rabbits vs sheep
6.4.1
6.4.6
Wed
3/30-4/3
       
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6.5 Conservative systems   Lab #9 Conservative systems
6.5.19
Fri
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No class      
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6.6 Reversible systems Read 6.7 6.6.3 Mon
F
7.1 Limit cycles 7.1.1 7.1.5, 7.1.8 Wed
4/6-4/10
       
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7.2 Liapunov functions 7.2.4, 7.2.5 7.2.6, 7.2.7, 7.2.10, 7.2.13 Mon
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Lab #10 Limit cycles      
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7.3 Poincare-Bendixson theorem Read 7.4
7.3.1, 7.3.4
Wed
F
7.5 Relaxation oscillators   7.5.5 Mon
4/13-4/17
       
M
7.6 Weakly nonlinear systems
  Project proposal due today
 
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Lab #11 Scroll circuit      
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7.6, cont'd   7.6.5, 7.6.7, 7.6.17 Mon
F
Exam 2   Review problems and practice exam  
4/20-4/24
       
M
8.1 Bifurcations revisited 8.1.1-4 8.1.6, 8.1.13 Wed
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Lab #12 Chemical oscillator      
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8.2 Hopf bifurcations
  8.2.2, 8.2.3, 8.2.5 Mon
F
8.3 Oscillating chemical reactions   8.3.1
Project outline due today
Wed
4/27-5/1
       
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9.0 Lorenz equations
9.1 Chaotic water wheel
  9.1.3 Fri
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Lab #13 Lorenz equations      
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9.2 Properties of Lorenz eqs   9.2.2 Fri
F
9.3,5 Chaos on a strange attractor      
5/4-5/8




M
Exam 3: take home, due 4pm Wed May 13  

 
T

Watch Strogatz's demos of chaos
(go to this website, then open Quicktime video at bottom)

     
W Work on project      
F Work on project (due 4pm Mon May 11)      
    No final exam