Schedule

Notes

• The schedule is tentative and may change as the course progresses.

• For information about add/drop dates and other matters related to course registration, please consult the Registrar's Website.

• All dates and times are in ET (Eastern Time).

• Section numbers are as in Differential Equations and Boundary Value Problems (6th Edition) by C. Henry Edwards, David E. Penney, and David Calvis.

• Please see the Homework tab for information about homework frequency. Below, O\(N\) refers to the \(N\)th online assignment (i.e., MyLab homework) and H\(N\) refers to the \(N\)th written assignment (i.e., Gradescope homework).

Week of August 25th (Week 1)

• Classes begin on Monday, August 25th.

• No HW due this week.

• No Office Hours this week (in view of no HW).

Monday, August 25th

• Topics: Course Logistics; review of differential equations and linear algebra; systems of ordinary differential equations; review of matrix algebra; index formula for matrix multiplication; vector formulation of systems of ODEs; ansatz for solution; reducing to the eigenvalue-eigenvector problem.

• Reading: §5.2 The Eigenvalue Method for Homogeneous Systems.

• Video: (Kaltura01)

Wednesday, August 27th

• Topics: General formulation of constant-coefficient, homogenous systems of ODEs; finding eigenvalues via characteristic polynomials; finding eigenvectors via row-reduction; finding solutions of a system from an eigenpair; the principle of superposition; general solution of a system with nondefective matrix; issues with the algorithm.

• Reading: §5.2 The Eigenvalue Method for Homogeneous Systems.

• Video: (Kaltura02)

Friday, August 29th

• Topics: General solution to a system with a diagonalizable matrix; sketch of a \(3\times 3\) example; solving IVPs; systems with complex eigenvectors and eigenvalues; complex eigenpairs of real matrices come in complex conjugate pairs; Euler's formula; modified ansatz for complex eigenpairs; systems with defective matrices; review of defective matrices; algebraic multiplicity (\(k\)); geometric multiplicity (\(p\)); defect of an eigenvalue (\(d = k - p\)); analogy with \(n\)th order constant coefficient linear ODEs with repeated roots; rank-\(r\) generalized eigenvector; generalized eigenvectors come in sequences of decreasing rank with the same eigenvalue; modified ansatz for rank-\(2\) generalized eigenvectors.

• Reading: §5.2 The Eigenvalue Method for Homogeneous Systems; §5.5 Multiple Eigenvalue Solutions.

• Video: (Kaltura03)

Week of September 1st (Week 2)

• O1 is due Wednesday, September 3rd at 11:00 PM.

• O2 is due Friday, September 5th at 11:00 PM.

• H1 is due Saturday, September 6th at 11:00 PM.

• Office Hours will be on W, 11:00 AM to 12:30 PM (in-person) and F, 11:00 AM to 1:15 PM (via Zoom) this week (in view of Labor day and a personal exigency).

Monday, September 1st

• No Class (Labor Day).

Wednesday, September 3rd

• Topics: Review of rank-\(r\) generalized eigenvector; an example of an eigenvalue with defect \(2\); brief description of the step-up algorithm for finding generalized eigenvectors; general ansatz for rank-\(r\) generalized eigenvectors; asymptotics of the function \(t \mapsto e^{\lambda t}\); phase planes for various systems \(2\times 2\) matrices.

• Reading: §5.5 Multiple Eigenvalue Solutions; §5.3 Solution Curves of Linear Systems.

• Video: (Kaltura04)

Friday, September 5th

• Topics: Review of previous examples; table of behaviour according to eigenvalues; saddle point; (improper) nodal source; principle of time reversal; source versus sink; proper source and sink; example with many equilibrium solutions; spiral sink and source; determining directions by looking at the matrix action; center of ellipses.

• Reading: §5.3 Solution Curves of Linear Systems.

• Video: (Kaltura05)

Week of September 8th (Week 3)

• O3 is due Wednesday, September 10th at 11:00 PM.

• O4 is due Friday, September 12th at 11:00 PM.

Monday, September 8th

• Reading: §6.1 Stability and the Phase Planes.

Wednesday, September 10th

• Reading: §6.2 Linear and Almost Linear Systems.

Friday, September 12th

• Reading: §6.2 Linear and Almost Linear Systems.

Week of September 15th (Week 4)

• O5 is due Monday, September 15th at 11:00 PM.

• O6 is due Friday, September 19th at 11:00 PM.

Monday, September 15th

• Reading: §6.3 Predator-Prey and Competitions.

Wednesday, September 17th

• Reading: §6.3 Predator-Prey and Competitions.

Friday, September 19th

• Reading: §7.1 Laplace Transforms and Inverse Transforms.

Week of September 22nd (Week 5)

• I will be out of town for part of this week; see below for necessary adjustments.

• Office Hours will be on M, 11:00 AM to 12:30 PM (no Office Hours on F) this week (in view of my travel).

• O7 is due Monday, September 22nd at 11:00 PM.

Monday, September 22nd

• Reading: §7.2 Transformation of Initial Value Problems.

Wednesday, September 24th

• No Class (compensation for evening exam).

Friday, September 26th

• Online Class (via Zoom).

• Reading: §7.2 Transformation of Initial Value Problems.

Week of September 29th (Week 6)

• O8 is due Monday, September 29th at 11:00 PM.

• O9 is due Friday, October 3rd at 11:00 PM.

Monday, September 29th

• Reading: §7.3 Translation of Laplace Transforms.

Wednesday, October 1st

• Reading: §7.4 Derivative, Integral, and Multiplication of Laplace Transforms.

Friday, October 3rd

• Review for Midterm 1.

Week of October 6th (Week 7)

• Midterm 1 is on Monday, October 6th from 6:30 PM to 7:30 PM in MSEE B012.

• O10 is due Wednesday, October 8th at 11:00 PM.

• O11 is due Friday, October 10th at 11:00 PM.

Monday, October 6th

• Reading: §7.5 Discontinuous Input Functions.

Wednesday, October 8th

• Reading: §7.6 Impulse Functions.

Friday, October 10th

• Reading: §2.4 Euler's Method.

Week of October 13th (Week 8)

• O12 is due Wednesday, October 15th at 11:00 PM.

• O13 is due Friday, October 17th at 11:00 PM.

• Office Hours will be on WF, 11:00 AM to 12:30 PM this week (in view of Fall Break).

Monday, October 13th

• No Class (Fall Break).

Wednesday, October 15th

• Reading: §2.5 Improved Euler Method.

Friday, October 17th

• Reading: §2.6 The Runge-Kutta Method.

Week of October 20th (Week 9)

• O14 is due Monday, October 20th at 11:00 PM.

• O15 is due Friday, October 24th at 11:00 PM.

Monday, October 20th

• Reading: §9.1 Periodic Functions and Fourier Series.

Wednesday, October 22nd

• Reading: §9.1 Periodic Functions and Fourier Series.

Friday, October 24th

• Reading: §9.2 General Fourier Series and Convergence.

Week of October 27th (Week 10)

• O16 is due Monday, October 27th at 11:00 PM.

• O17 is due Friday, October 31st at 11:00 PM.

Monday, October 27th

• Reading: §9.2 General Fourier Series and Convergence.

Wednesday, October 29th

• Reading: §9.3 Fourier Cosine and Sine Series.

Friday, October 31st

• Reading: §9.3 Fourier Cosine and Sine Series.

Week of November 3rd (Week 11)

• O18 is due Monday, November 3rd at 11:00 PM.

• O19 is due Friday, November 7th at 11:00 PM.

Monday, November 3rd

• Reading: §9.4 Application of Fourier Series.

Wednesday, November 5th

• Reading: §9.4 Application of Fourier Series.

Friday, November 7th

• Review for Midterm 2.

Week of November 10th (Week 12)

• Midterm 2 is on Monday, November 10th from 6:30 PM to 7:30 PM in MSEE B012.

• O20 is due Friday, November 14th at 11:00 PM.

Monday, November 10th

• Reading: §9.5 Heat Equation.

Wednesday, November 12th

• Reading: §9.5 Heat Equation.

Friday, November 14th

• Reading: §9.6 Wave Equation.

Week of November 17th (Week 13)

• O21 is due Friday, November 21st at 11:00 PM.

Monday, November 17th

• Reading: §9.6 Wave Equation.

Wednesday, November 19th

• Reading: §9.7 Laplace's Equation.

Friday, November 21st

• Reading: §9.7 Laplace's Equation.

Week of November 24th (Week 14)

• No HW due this week.

• No Office Hours this week (in view of no classes and HW).

Monday, November 24th

• No Class (compensation for evening exam).

Wednesday, November 26th

• No Class (Thanksgiving Break).

Friday, November 28th

• No Class (Thanksgiving Break).

Week of December 1st (Week 15)

• I will be out of town this week; see below for necessary adjustments.

• There will be a substitute professor teaching all classes in-person in the usual time and place.

• Office Hours details TBA.

• O22 is due Monday, December 1st at 11:00 PM.

• O23 is due Friday, December 5th at 11:00 PM.

Monday, December 1st

• Substitute Class.

• Reading: §10.1 Sturm-Liouville Problem.

Wednesday, December 3rd

• Substitute Class.

• Reading: §10.1 Sturm-Liouville Problem.

Friday, December 5th

• Substitute Class.

• Reading: §10.1 Sturm-Liouville Problem.

Week of December 8th (Week 16)

• No HW due this week (in view of Quiet Period).

Monday, December 8th

• Review for Final Exam.

Wednesday, December 10th

• Review for Final Exam.

Friday, December 12th

• Review for Final Exam.

Week of December 15th (Final Exam Week)

• Final Exam schedule TBA by Registrar.