Differential Equations

Math 23 Winter 2018

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
Wednesday
January 3
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
Friday
January 5
1.3, 2.1 Classification and linear first-order ODEs
DirectionFields2.nb
§2.1: #1, 9, 12
Sunday
January 7
There will be MATLAB demonstration during tutorial on direction fields.
Monday
January 8
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
Wednesday
January 10
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
Friday
January 12
2.5 Autonomous equations and population dynamics §2.5: #9, 23
Review multivariable chain rule
KA - Slope fields & solutions
Monday
January 15 (class moved to x-hour)
2.6 Exact equations
LastExamplePlot.nb
§2.6: #23, 26, 30, 31
Wednesday
January 17
2.7, 8.1 Numerical Approximations: Euler's Method §2.7: #4, 9, 16
§8.1: #10, 19
Thursday
January 18
There will be a MATLAB demonstration in tutorial on the Euler Method.
Friday
January 19
8.2, 8.3 Improvements on Euler's Method; Runge-Kutta Method §8.2: #10
§8.3: # 10
Sunday
January 21
There will be a MATLAB demonstration in tutorial on the Runge Kutta method.
Monday
January 22
3.1, 3.2 Second order constant coefficient with distinct real roots; the Wronskian §3.1: #2, 4
§3.2: #2, 4, 14
Wednesday
January 24
3.3 Complex conjugate roots
SolutionPlots.nb
§3.2: #25
§3.3: #8, 27
Thursday
January 25 4 - 6 pm, Location Silsby 028
1st Midterm 1st Midterm:material through 8.3. Past exams
Friday
January 26
3.4 Repeated roots and reduction of order §3.4: #2, 16, 24
Monday
January 29
3.5, 3.6 Method of undetermined coefficients; Variation of parameters §3.5: #5, 19
§3.6: #9, 13
Wednesday
January 31
7.1, 7.2 Review of matrices.
Demo
§7.1: #10, 14
Thursday
Feruary 1
Matrices will be reviewed in tutorial.
Friday
February 2
2.8, 7.3, 7.4 Theorem 2.8.1; Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. §7.3: #17, 18
§7.4: #6
Monday
February 5
7.5 Constant coefficients systems with distinct real eigenvalues
Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb
§7.5: #3, 12
Wednesday
February 7
7.6 Constant coefficient systems with complex conjugate eigenvalues
ComplexEigenPlot.nb
§7.6: #2, 6
Friday
February 9
7.8 Repeated eigenvalues §7.8: #1, 18
Monday
February 12
7.9 Nonhomogeneous Linear Systems §7.9: # 1, 3, 15
Wednesday
February 14
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
Thursday
February 15 4 - 6 pm, Room Silsby 028
2nd Midterm 2nd Midterm
Topics TBD
Past exams
Thursday
February 15
There will be a review on integration methods using partial fractions during tutorial.
Friday
February 16
6.3, 6.4 IVPs with discontinuous forcing functions KA: Laplace/step function differential equation
Monday
February 19
6.5, 6.6 Impulse Functions and the convolution integral KA: The convolution integral
Wednesday
February 21
9.1 The Phase Plane: Linear Systems §9.1: # 1, 13
Friday
February 23
9.2 Autonomous Systems and Stability §9.2: # 1, 3, 5
Plotting slope fields and trajectories
Monday
February 26
9.3 Locally Linear Systems §9.3: # 1, 3, 5
Wedensday
February 28
9.4 Competing-Species equations §9.4: # 1
Friday
March 2
9.5 Predator-Prey equations §9.5: # 1, 3
Monday
March 5
Course wrap up
Tuesday
March 6
Course instruction ends.
Friday
March 9
Room TBD
3:00 pm Final
Exam topics TBD
Past exams