Math 3280 Differential Equations with Linear Algebra
Spring 2020
Prof. Peckham
Labs, Assignments and Tests
Labs
Lab Procedures and Guidelines.
- Lab 1 Introduction to Mathematica, Tuesday Jan. 21.
Due Thursday Jan. 23 to GTA Noah Wong via Canvas.
Link to Lab 1 assignment.
Link to Lab 1 Mathematica Notes/Hints.
Reading these notes carefully now will save much time on future labs.
Additional Mathematica resources:
Learn with guided examples tutorial from the "Welcome to Wolfram Mathematica" window which appears when Mathematica first launches.
- Lab 2: Introduction to Differential Equations,
Tuesday, Jan 28. Due Thursday, Jan 30. to Noah Wong via Canvas
Link to Lab 2 assignment.
Link to Lab 2 handout.
- Lab 3: Comparing Qualitative, Numerical, and Analytic Solutions to the Logistic Differential Equation.
Tuesday Feb. 4 and 11.
Due Thursday Feb. 13 to GTA Noah Wong via Canvas.
Link to Lab 3 assignment.
Link to Lab 3 Separation of Variables Template.
Link to Lab 3 Slope Field Handout for sketching solutions.
- Lab 4: Applications of First Order Differential Equations: Falling object.
Tuesday Feb. 18 and Feb. 25.
Due Thursday Feb 27 to GTA Noah Wong via Canvas.
Link to Lab 4-6 assignment.
Link to slope field handout from GTA Noah Wong.
- Lab 5: Applications of First Order Differential Equations: Compartmental
Analysis.
Tuesday March 3 and 17.
Due Thursday March 19 MOVED TO MONDAY MARCH 23 MOVED AGAIN TO THURSDAY MARCH 26 to GTA Noah Wong via Canvas.
Link to Lab 4-6 assignment.
Link to First Order Linear DE template:
Mathematica notebook, or
pdf.
- Lab 6: Applications of First Order Differential Equations: Parameter Matching.
Tuesday March 24 and 31.
Due Thursday April 2 MOVED TO MONDAY APRIL 6 to Noah Wong via Canvas.
Link to Lab 4-6 assignment.
- Lab 7: Resonant Forcing of a Spring-Mass System
Tuesday April 7 and 14.
Due Thursday April 16. to GTA Noah Wong via Canvas.
Link to Lab 7 assignment.
- Lab 8: Differential Equations and Linear Algebra with Mathematica
Tuesday April 21.
Due FRIDAY, April 24 to GTA Noah Wong via Canvas.
Link to Lab 8 assignment.
- Lab 9: Systems of Differential Equations: Epidemic models.
Optional - for extra credit only. Extend the SIR model posted in the Announcements on Canvas and covered in class.
Add or change any assumptions like including a hospitalized class, a death class, a different way of modeling social distancing
other than using the transmission parameter I used, ... .
Due THURSDAY April 30 to Prof. Peckham via Canvas. USE Section 003 to submit.
Assignments and TESTS
Assigned problems below refer to Differential Equations and Linear Algebra,
by Henry Edwards and David Penny, and David Calvis 4th edition, Pearson/Prentice Hall, 2018.
Use of the 3rd edition is acceptable, but page numbers will differ from the 4th edition.
EC=Extra Credit problems; hand EC problems in on a separate sheet to Prof. Peckham.
Problems labelled as "additional" are not to be turned in, but you are expected to know how to do such problems.
All assignments turned in should conform to
Departmental Minimum HW Standards.
Scratch work will not be accepted.
- Set 1 Due Friday Jan. 17:
- Read Chapter 1: Sections 1.1, 1.2
- Section 1.1: 5, 6, 11, 16, 22, 32, 36, 41.
Additional: 1, 8, 15, 17, 19, 27, 35, 37, 43, 45.
- Quiz 1 on Chapter 1, Sections 1.1 - 1.4 Friday Jan. 24 .
Solutions
- Set 2 Due Friday Jan. 24:
- Read Sections 1.2, 1.3, 1.4, 1.5.
- Section 1.2: 2,8,12,19,24. EC: 44 (Suggestion: use Mathematica. Hand in to Prof. Peckham on a separate sheet.) Additional: 1,31
- Section 1.3: 1-6 (photocopy provided in class or download here.), 13,14,17,18,21
- Section 1.4: 2,8,17,20,27. Additional 1,9.
- Quiz 2 on Chapters 1-2, through Sec. 2.1, esp. Secs 1.5, 1.6. Friday Jan. 31 .
Solutions.
- Set 3 Due Friday Jan. 31:
- Read Sections 1.5-1.6 (Homogeneous and Bernoulli sections only),
Chapter 1 summary (ignore reference to Exact Equations),
2.1. Instead of Sec 2.2, read the 6 pages at the following link.)
- Section 1.4: 34, 49, 51;
- Section 1.5: 2,4,10, 12,24,32,34,36; EC: 38 (turn in on separate sheet)
- Section 1.6: 2,22,23,46.
- Section 2.1: 9.
- Quiz 3 Friday Feb. 7 : on Chapters 1-2, y'=ay. Solve by inspection, separation of variables, first order linear, phase line (with solution sketch), Euler's method.
Solutions.
- Set 4 Due Friday Feb. 7
- Read Sec. 2.3 (Read the "Resistance Proportional to Velocity" section. Skim the rest - it will be covered in Labs.),
2.4 (Read through Example 2.)
- Section 2.2: 1,4,14. For all 3 problems, ignore the book instructions.
Instead, construct a phase line diagram (including dots at equilibrium points and arrows in between) and use it to
(i) describe the long term fate of solutions for ALL initial conditions, and
(ii) sketch several representative solution curves.
See this link for examples.
- Section 2.3: 10
- Section 2.4: 1,10
- Quiz 4 Wednesday Feb. 12 :Topics: similar to Quiz 3, but not all differential equations are guaranteed to be of the form y'=ay.
Solutions.
No class Friday Feb. 14. Study for Test 1 on Monday. Extra office hours 9-11am.
- TEST 1: Chapters 1 and 2. Monday Feb. 17 5-6:30. Room SCC 120. (No class that day. Extra office hours 9-11am.) Test 1 Solutions.
Sample test 1 link:
here.
Partial solutions link:
here.
Partial solutions to a second practice test: here.
Partial solutions to a third practice test: here.
Solutions to another practice test: here.
- Set 5 Due Friday Feb. 21
- Read Sections 3.1, 3.2, 3.3, 3.4
- Section 3.1: 1, 14, 18, 19, 27, 33
- Section 3.2: 1, 4, 10, 11, 24
- Section 3.3: 4, 14, 15, 20, 21 (for 11 in Sec 3.2), 33, 34 (compare with the echelon forms in the text in Sec. 3.2)
- Section 3.4: 2, 5, 9, 13, 17, 24, 26, 31, 40
- Quiz 5 Friday, Feb. 28. Ch 3: Secs 3.2, 3.4, 3.5, 3.6
Solutions.
- Set 6 Due Friday, Feb. 28
- Read Sections 3.5, 3.6, 3.7 (optional), 4.1
- Section 3.5: 1, 9, 12, 23, 32, 34, 39 (Hint: OK to use Theorem 7 for 32 and 34)
- Section 3.6: 1, 4, 11, 18, 21, 28, 33 (top row of A inverse only), 43; EC: 52 (Hint: Use Theorem 3)
- Section 3.7: EC: 4
- Section 4.1: 1, 4, 7, 8, 9, 16, 21, 22, 25, 32, 33; EC: 41.
- Turn in all EC on a separate sheet to Prof. Peckham.
- Quiz 6 Thursday, March 5. Secs 3.6, 4.1-4.4.
Solutions.
- Set 7 Due Thursday or Friday, March 6 or 7
- Read Sections 4.1, 4.2, 4.3, 4.4, 4.7
- Section 4.2: 4, 5, 9, 15, 20, 28.
- Section 4.3: 1, 2, 3, 6, 8, 12, 13, 19, 22.
- Section 4.4: 1, 2, 10, 12, 16, 17, 25
- Section 4.7: 1, 3, 5, 6, 9, 10, 13, 14, 15, 19, 23.
No Class Fri. March 6
Spring Break March 9-13
- NEW!! EXTRA CREDIT QUIZ 6EC. 9-10AM FRIDAY MARCH 20 VIA CANVAS. REPEAT OF QUIZ 6 WITH DIFFERENT NUMBERS. UP TO 4 POINTS EXTRA CREDIT.
Solutions link: here.
- Quiz 7 Thursday, March 19. MOVED TO MONDAY MARCH 23 9-10AM VIA CANVAS.. Secs 4.7, 5.1, 5.2.
Solutions link: here.
- Set 8 Due Thursday, March 19.
- Read Sections 5.1, 5.2
- Section 5.1: 2, 3, 10, 14, 17, 33, 35, 40, 43, 44, 45; EC: 27.
- Section 5.2: 1, 8, 13, 21.
- TEST 2: Chapters 3 (secs 1-6), 4 (secs 1-4,7), 5 (secs 1,2)
and Lab 4-6 material.
Monday, March 23, 5-6:30 Room LSBE 118. Extra office hours 9-11. MOVED TO WEDNESDAY MARCH 25, 4-6pm via CANVAS.
Test 2 Solutions: here.
Sample test 2 link
here.
Partial solutions are
here.
Partial solutions to a second practice test: here.
Link to an (incomplete) summary of topics for TEST 2
here.
Third practice test with solutions here.
- Set 9 Due Friday, March 27. MOVED TO MONDAY MARCH 30.
- Read Sections 5.3, 5.4, 5.5
- Section 5.2: 25, 26.
- Section 5.3: 2, 9, 21, 33, 39, 40, 42.
- Section 5.4: No problems assigned other than Lab 7.
- Section 5.5: 1, 2, 3, 16, 21, 22, 25, 30; EC: 57.
- Quiz 8 Friday, April 3 . Selected sections from Ch's 5, 6 and 7, including annihilators (see link to annihilator reference below)
Solutions link: here.
- Set 10 Due Friday, April 3:
- Read Sections 5.6 (for Lab 7), 6.1,
7.1 (read through Example 4 only),
7.2 (read through Example 2 only),
7.3 (read beginning through Example 1 and Complex Eigenvalues through Example 3 only),
7.7 through example 1 only (Sec. 7.6 in the 3rd edition). See "Annihilator Reference below.
- Section 5.6: No problems assigned other than Lab 7.
- Section 6.1: 1,13,23,27; EC 36 (for 3x3 matrix only)
- Section 7.1: 1,2,8
- Section 7.2: 1,3,12,14,18,23. For 14 and 18, verify and write general solution only. Do not compute the Wronskian.
- Section 7.3: 1,3,9,11 (For 1,3,9,11 - Do not graph direction field or solution curves.).
- Section 7.7 :1a (in the 3rd edition Sec. 7.6: 1a)
Annihilator reference: Prof. Laugeson, Univeristy of Illiniois (http://www.math.uiuc.edu/~laugesen/286/annihilators.pdf): here. The method of annihilators is what our text calls the method of undetermined coefficients for finding a particular solution to a linear nonhomogeneous differential equation. I called the method "lucky guess" in class. The method of annihilators takes the "lucky" out of the lucky guess. Remember that this method (under any of the three names) just gives you a form of a trial function for one particular solution. By plugging in this guess to the original nonhomogeneous linear differential equation, you ``determine'' the undetermined coefficients in the trial function. Then you add the general solution to the associated homogeneous differential equation (with the arbitrary constants) to get the general solution to the nonhomogeneous differential equation.
- Quiz 9 Friday, April 10. Secs 10.1, 10.2. See Course Canvas page for specifics on topics for the quiz.
Solutions link: here.
- Set 11 Due Friday, April 10:
- Read Sections 10.1 - 10.2. A link to Reading Notes for Chapter 10 is
here.
- Section 10.1: 1,7,16,19,23,27,29,38.
- Section 10.2: 1,8,9,11.
- Set 12 Due Friday, April 17:
- Read Sections 10.3 - 10.5. A link to Reading Notes for Chapters 10 is
here.
- Section 10.3: 1,5,11,12,18,27,30
- Section 10.4: 15, 18 [Hint: first use the trig identity sin^2(x)=(1-cos(2x))/2].
- Section 10.5: 1,4,6,11,20
- Quiz 10 Friday, April 17 . Selected sections from Ch 10.
See Course Canvas page for specifics on topics for the quiz.
Solutions link: here.
- TEST 3:
Thursday, April 23, 4-6pm via Canvas. Chapters 5,6,7,10, and lab on resonant forcing.
Test 3 Solutions: here.
See Canvas Announcement for list of possible proofs to be asked.
A copy of the Laplace Transforms on the inside cover of the Penny and Edwards text will be provided.
Link to practice exam is
here.
Partial answers are
here.
Link to a second practice exam is
here.
Partial answers to the second practice exam are
here.
Handwritten answers to a third practice exam here.
A link to Reading Notes for Chapters 10 is
here.
- Quiz 11: Friday May 1
Solutions link: here.
Extra Credit. Points will be added to your quiz 1-10 total.
Problems will be chosen from:
A. Differential equations: Solve y'=ay, y'+p(x)y=q(x) (first order linear), ay''+by'+c=0.
Methods: "Guess e^{rx}" for y'=ay; and 3 methods for y''+ay'+by=0, first order linear (integrating factor) for y'+p(x)y=q(x). Method of undetermined coefficients to find a ``form of a guess'' for y_p.
B. Linear Algebra: Find a basis for the solution to Ax=0 when the solution has free variables;
prove that the solution to Ax=0 is a vector subspace.
Prove that solutions to L[y]=0 form a vector subspace.
Prove that the span of any 2 vectors (in any vector space) is a vector subspace.
- Final Exam Tues. May 5, 8:00-9:55am via Canvas..
Cumulative: All sections covered in Chapters 1 - 10 and labs.
Final Exam Review materials:
Abreviated course summary:
here.
Solutions to semester tests and quizzes are provided above. Same for practice tests.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Friday, 01-May-2020 11:15:54 CDT.