Differential Equations

Math 23 Spring 2019

Lecture Plan

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.

Lectures Sections in Text Description Practice Problems
Monday
March 25
1.1, 1.2 What are differential equations?
DirectionFields.nb
§1.1: #1, 2, 26
§1.2: # 1(a), 2(a)
KA - Differential equations intro
KA - Slope fields & equations
Plotting slope fields and trajectories
Wednesday
March 27
1.3, 2.1 Classification and linear first-order ODEs
DirectionFields2.nb
§2.1: #1, 9, 12
Friday
March 29
2.2, 2.4 Separable equations and existence-uniqueness theorems.
DirectionFields3.nb
§2.2: #9, 11
§2.4: #3, 7, 11
KA - Separable equations
KA - Exponential model equations
Monday April 1 2.3 Modeling with differential equations
MixingPlot.nb , WorksheetSlopeFields.nb
§2.3: Solve the IVPs in Examples 2 and 3
§2.3: #9, 10
KA-Write differential equations
Wednesday
April 3
2.5 Autonomous equations and population dynamics §2.5: #9, 23
Review multivariable chain rule
KA - Slope fields & solutions
Friday
April 5
2.6 Exact equations
LastExamplePlot.nb
§2.6: #23, 26, 30, 31
Monday
April 8
3.1, 3.2 Second order constant coefficient equations
with distinct roots; the Wronskian
§3.1: #2, 4
§3.2: #2, 4, 14
Wednesday
April 10
3.3 Complex conjugate roots
SolutionPlots.nb
§3.2: # 25
§3.3: # 2, 16, 24
Friday
April 12
3.4 Repeated roots and reduction of order §3.4: # 2, 16, 24
Monday
April 15
3.5, 3.6 Method of undetermined coefficients; Variation of parameters §3.5: #5, 19
§3.6: #9, 13
April 16 (Tue)
4:30 - 6:30
Wilder 104
1st Midterm 1st Midterm:material through 3.1. Past exams
Wednesday
April 17
7.1, 7.2 Review of matrices.
Demo
§7.1: #10, 14
Friday
April 19
7.3, 7.4 Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. §7.3: #17, 18
§7.4: #6
Monday
April 22
7.5 Constant coefficients systems with distinct real eigenvalues
Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb
§7.5: #3, 12
Wednesday
April 24
7.6 Constant coefficient systems with complex conjugate eigenvalues
ComplexEigenPlot.nb
§7.6: #2, 6
Friday
April 26
7.8 Repeated Eigenvalues §7.8: #1, 18
Monday
April 29
7.8 & 9.1 Repeated eigenvalues; Phase plane; linear systems §9.1: #1, 8
Wednesday
May 1
9.1; begin 7.9. Phase Plane; Linear Systems §9.1: # 1, 8
Friday
May 3
7.9 Nonhomogeneous Linear Systems §7.9: # 1, 3, 15
Monday
May 6
9.2 Autonomous Systems and Stability §9.2: # 1, 3, 5
Plotting slope fields and trajectories
Direction field plotter
May 7 (Tue)
4:30 - 6:30
Wilder 104
2nd Midterm 2nd Midterm
Material from 3.3 through 7.8.
Past exams
Wednesday
May 8
9.3 & 9.4 Locally Linear Systems §9.3: # 1, 3, 5
Friday
May 10
9.4 and 9.5 Competing Species and Predator-Prey Equations §9.4: # 1, 8 §9.5: # 1, 3, 11
Monday
May 13
6.1, 6.2 Laplace Transform and the IVP KA: Laplace transform intro
KA: Properties of the Laplace transform
KA: Laplace transform to solve a differential equation
Wednesday
May 15
6.3 IVPs and Step functions
(LAST DAY TO WITHDRAW)
KA: Laplace/step function differential equation
Friday
May 17
6.4, 6.5 Discontinuous forcing functions, Impulse Functions KA: The convolution integral
Monday
May 20
6.6 The convolution integral §6.6: # 9, 13 KA: The convolution integral
Wednesday May 22 Course wrap up
Friday
May 24
Course wrap up
Monday May 27 Memorial Day No Class
Wednesday
May 29
Course wrap up Course instruction ends.
Jun 1 (Sat)
Kemeny 008
11:30 am
-
2:30 pm
Final
The exam is cumulative and covers material from the whole term.
Past exams