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 |