Math 211: Ordinary Differential Equations (Section 002)

Meeting times:
MWF 11:00 AM - 11:50 AM
Class room:
 GRB W212
Office Hours:
 HBH 36, 1-2pm MR and 3-4pm TF

The syllabus can be found here. The class schedule is produced below.

 

 
Date
Section(s) covered
Topics discussed
Notes
Assignment
 
M 1/07

2.1

  

Lecture 01: Introduction to ODE, Slope fields

W 1/09
2.1
  

2.2

Lecture 02: Equilibria, Separable equations
F 1/11
2.3
  
2.4

Lecture 03:Examples of separable DE: simple physical systems; Linear DE: homogeneous and inhomogeneous, Integrating Factor for first-order inhomogeneous linear ODE
M 1/14
2.4
  
Lecture 04: Linear DE, Variation of Parameter
W 1/16

2.5

  

Lecture 05: Review Linear DE, Example: Mixing problems
F 1/18

2.6

  

Lecture 06: Exact DE, Integrating Factor for exact DE (CHANGE: Partial derivatives, utility of exactness condition, and checking exactness via Theorem 6.20)
M 1/21

 

  

Martin Luther King, Jr. Day
W 1/23

2.7

  
2.8

Lecture 07: (Geometric interpretation of) Uniqueness of solutions to DE (CHANGE: Derivation of solutions to exact ODE)
F 1/25
2.8
  
2.9

Lecture 08: Continuity of solutions with respect to initial data for DE (CHANGE: Finish up non-exact ODE via IF and solve the homogeneous ODEs)
M 1/28
4.1
  

Lecture 09: Second-order DE, homogeneous versus inhomogeneous equations, fundamental sets of solutions, the Wronskian (CHANGE: 2.7-2.9 will be consolidated)
W 1/30
4.2
  

Lecture 10: (Reduction of second-order DE to) Planar systems, Phase plane analysis (CHANGE: Skipped - will handle in greater generality in chapter 9; instead, cover 4.1)
F 2/1
4.3
  

Lecture 11: Linear homogeneous equations with constant coefficients
M 2/4
4.4
  
4.5

Lecture 12: Harmonic motion, Undetermined Coefficients (CHANGE: Complete Linear homogeneous equations with constant coefficients)
W 2/6
4.5
  

Lecture 13: (Complex) forcing, the case of a linear combination of simple forcing terms
F 2/8
4.6
  
4.7

Lecture 14: Variation of Parameters, Example: Forced harmonic oscillator (CHANGE: Method of Undetermined Coefficients)
M 2/11
4.7
  

Lecture 15: Forced harmonic oscillator analysis, Review
Review
 
T 2/12
 

Midterm 1 - Write up your own first-order ODE and second-order ODE field guides as a study guide!
 
W 2/13
7.1
  

Lecture 16: Vectors, Matrices (multiplication, transpose)
F 2/15
7.1
  
7.2

Lecture 17: Lines, planes, and their parametrizations
 
M 2/18
7.2
  
7.3

Lecture 18: Pivots Row Echelon Form (REF), Theorem 3.12, Backsolving systems of linear equations (CHANGE: finish 7.1)
 
W 2/20
7.3
  

Lecture 19: Compute a few examples, pivot/free variables, consistency of a system of linear equations (CHANGE: cover 7.2 and begin 7.3)
 
F 2/22
7.4
  
Lecture 20: Homogeneous and inhomogeneous systems, Nullspace
Enjoy SB
 
M 2/25
 

Spring Break

 
W 2/27
 

Spring Break
 
F 3/01
 

Spring Break
 
M 3/04
7.5
  

Lecture 21: Span, subspaces, linear dependence and independence
 
W 3/06
7.5
  

Lecture 22: Finding a basis for the nullspace, span, examples
 
F 3/08
7.6
  

Lecture 23: Square matrices (singular and invertible) (CHANGE: finish 7.5)
 
M 3/11
7.7
  

Lecture 24: Determinants and row operations (CHANGE: 7.6)
 
W 3/13
7.7
  
8.1

Lecture 25: Example computations of determinants, describe the SIR model (CHANGE: finish 7.6)
 
F 3/15
8.1
  

Lecture 26: SIR model analysis, IVPs, planar systems (CHANGE: 7.7)
 
M 3/18
8.2
  

Lecture 27: Phase plane/phase plot of planar system
 
W 3/20
8.3
  
8.4

Lecture 28: Qualitative analysis via nullclines; linear systems (CHANGE: 8.1-8.2)
 
F 3/22
8.5
  

Lecture 29: Linearly independent solutions, fundamental set of solutions, the Wronskian (CHANGE: 8.3)
 
M 3/25
9.1
  

Lecture 30: Eigenvalues, eigenvectors, characteristic polynomials and characteristic equations (for linear algebra's sake) (CHANGE: nullcline examples, review)
Review
 
 
 
T 3/26
 
Midterm 2 - Review your linear algebra!
 
 
 
W 3/27
9.1
  
9.2

Lecture 31: Stuff from 9.1 above (applied to ODE), Review technique of the planar system; the cases of distinct real roots, repeated real roots (with dimension of eigenspace being 2), complex roots (CHANGE 8.4-8.5)
 
F 3/29
 
Midterm Recess
 
M 4/01
9.2
  

Lecture 32: Repeated real roots in the case the dimension of the eigenspace is 1 (CHANGE 9.1 and 9.2)
Revert to study mode
 
W 4/03
9.3
  

Lecture 33: Stable/unstable solutions, saddle points, nodal/spiral sink/sources (CHANGE: 9.2)
 
F 4/05
9.3
  
9.4

Lecture 34: Overview of each case from 9.3, the Trace-Determinant plane (CHANGE: finished 9.2)
 
M 4/08
9.5
  

Lecture 35: Higher dimensional systems (CHANGE: 9.3)
 
W 4/10
9.6
  

Lecture 36: Behavior of matrix exponentiation and its utility, generalized eigenvectors (CHANGE: covered 9.4)
 
F 4/12
9.6
  
9.8

Lecture 37: Examples of generalized eigenvectors; higher-order linear equations and reduction of second order linear ODE (CHANGE: 9.6)
 
M 4/15
9.8
    

Lecture 38: Examples of reduction of second order ODE to a planar system
 
W 4/17
9.9
  

Lecture 39: Inhomogeneous linear systems
(Examples)
 
F 4/19
 

Buffer day (if necessary, day can be used up earlier if we'd like to spend more time on anything); otherwise, expect a very involved example problem