• Syllabus
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Labs

• Lab 1 Introduction to Mathematica, Tuesday Aug. 27. Due Thursday Aug. 29 to GTA Tianyi Zhang or to Prof. Peckham.
  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.

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• Lab 2: Introduction to Differential Equations, Tuesday, Sept 4. Due Thursday, Sept 6. to Tianyi Zhang Link to Lab 2 assignment.

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• Lab 3: Comparing Qualitative, Numerical, and Analytic Solutions to the Logistic Differential Equation. Tuesday Sept 11 and 18. Due Thursday Sept. 21 to Tianyi Zhang. Link to Lab 3 assignment. Link to Lab 3 Separation of Variables Template.

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• Lab 4: Applications of First Order Differential Equations: Falling object. Tuesday Sept. 25 and Oct. 2. Due Thursday Oct. 4 to GTA Tianyi Zhang. Link to Lab 4-6 assignment.

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• Lab 5: Applications of First Order Differential Equations: Compartmental Analysis. Tuesday October 9 and 16. Due Thursday October 18 to Tianyi Zhang. Link to Lab 4-6 assignment. Link to First Order Linear DE template: Mathematica notebook, or pdf.

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• Lab 6: Applications of First Order Differential Equations: Parameter Matching. Tuesday October 23 and 30. Due Thursday November 1 to Tianyi Zhang. Link to Lab 4-6 assignment.

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• Lab 7: Resonant Forcing of a Spring-Mass System
  Tuesday Nov. 6 and 13. Due Thursday Nov. 15. to Tianyi Zhang. Link to Lab 7 assignment.

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• Lab 8: Differential Equations and Linear Algebra with Mathematica Tuesday Nov. 20. Do in lab or submit writeup. Due TUESDAY, Nov. 27 to Tianyi Zhang. Due TBA. Link to Lab 8 assignment.

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• Lab 9: Systems of Differential Equations: Phase plane analysis. Tuesday Nov. 27 and Dec. 4. Due THURSDAY Dec. 6 to Tianyi Zhang. Link to Lab 9 assignment.

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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 Aug. 30:
  • 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.

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• Quiz 1 on Chapter 1, Sections 1.1 - 1.4, including especially y'=ay Friday Sept. 7 : Solution

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• Set 2 Due Friday Sept. 7:
  • 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.

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• Quiz 2 on Chapters 1-2, through Sec. 2.1 Friday Sept. 14 : Solution

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• Set 3 Due Friday Sept. 14:
  • 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.

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• Set 4 Due Wednesday Sept. 19
  • 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 inbetween) 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

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• Quiz 3 on Chapters 1-2, y'=ay. Solve by inspection, separation of variables, first order linear, phase line (with solution sketch), Euler's method. Friday Sept. 21 : Solution

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• TEST 1: Chapters 1 and 2. Monday Sept. 24 6-7:30. SCC 120. (No class that day. Usual office hours 12:30-2, extra office hours 3-4pm.)
  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.
  

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• Set 5 Due Monday Oct. 1
  • 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

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• Quiz 4 Friday, Oct. 5. Ch 3: Secs 3.2, 3.4, 3.5 Solutions link: here.

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• Set 6 Due Friday, Oct. 5 - moved to Mon. Oct. 8
  • 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.

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• Quiz 5 Friday, Oct. 12. Secs 3.6, 4.1-4.4. Solutions link: here.

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• Set 7 Due Friday, Oct. 12
  • 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; EC: 28,29. (EC on separate sheet)
  • Section 4.4: 1, 2, 10, 12, 16, 17, 25
  • Section 4.7: 1, 3, 5, 6, 9, 10, 13, 14, 15, 19, 23.

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• Quiz 6 Friday, Oct. 19. Secs 4.4, 4.7, 5.1, 5.2. Solutions link: here.

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• Set 8 Due Friday, Oct. 19.
  • Read Sections 5.1, 5.2
  • Section 5.1: 2, 3, 10, 14, 17, 33, 35, 40, 43, 44, 45; EC: 27, 52.
  • Section 5.2: 1, 8, 13, 21; EC: 38.

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• TEST 2: Chapters 3 (secs 1-6), 4 (secs 1-4,7), 5 (secs 1,2) and Lab 4-6 material. Tuesday, Oct. 23, 6-7:30 Montague Hall 70. No class Wed. Oct. 24.
  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. Test 2 solutions here.

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• Fall Break. No Class Oct. 25-26. Class Oct. 29, 31. Prof. Peckham out of town: No class Nov. 1-2.

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• Set 9 Due Friday, Nov. 2.
  • Read Sections 5.3, 5.4, 5.5
  • 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.

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• Quiz 7 Friday, Nov. 9 . Selected sections from Ch's 5, 6 and 7. UPDATE: Sections 6.1, 7.1, 7.2, 7.3. Solutions link: here.

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• Set 10 Due Friday, Nov. 9:
  • Read Sections 5.6 (for Lab 7), 6.1, 7.1 (skip Examples 5,6,7), 7.2, 7.3, 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: 1,13,19,23,27; EC 36 (for 3x3 matrix only)
  • Section 7.1: 1,2,8
  • Section 7.2: 1,3,12,14,18,23
  • Section 7.3: 1,9, 11 (For 1,9,11 - no computer tasks are required.).
  • Section 7.7 :1a (in the 3rd edition Sec. 7.6: 1a)

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  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.

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• Quiz 8 Friday, Nov. 16. Secs 10.1, 10.2. Laplace Transform tables will be provided. Solutions link: here.

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• Set 11 Due Friday, Nov. 16:
  • Read Sections 10.1 - 10.2. A link to Reading Notes for Chapters 9 and 10 is here.
  • Section 10.1: 1,7,16,19,23,27,29,38.
  • Section 10.2: 1,8,9,11.

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• Set 12 Due Wed. Nov. 21 or Monday Nov. 26:
  • Read Sections 10.3 - 10.5. A link to Reading Notes for Chapters 9 and 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: 1,4,6,11,16,20; EC: 32 (turn in on separate sheet).

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• No class Wed. Nov. 21. Thanksgiving Break Nov. 22-23. No class.

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• Quiz 9 Mon. Nov. 26 Cancelled. Regular class instead.. Selected sections from Ch 10.

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• TEST 3: Thursday, Nov. 29, 6-7:30pm. MonH 80. Chapters 5,6,7,10, and labs on resonant forcing and phase planes.
  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 9 and 10 is here.

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• Quiz 9: Friday Dec. 7 Solutions link: here.

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  Extra Credit. Points will be added to your quiz 1-8 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 y''+ay'+by=0, first order linear (integrating factor) for y'+p(x)y=q(x). Method of annihilators 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.
  

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• Final Exam Fri. Dec. 14, 2:00-3:55am. SCC 120.. Cumulative: All sections covered in Chapters 1 - 10 and labs.
  Final Exam Review materials:
  Abreviated course summary: here.
  Solutions to semester tests:
  Test 1 solutions: here.
  Test 1 Spring 2018,2 Fall 2018 and 3 Fall 2018 solutions: here.
  Quizzes 1-5 solutions from Spring 2018 quizzes: here.
  Quiz 1-9 solutions for Fall 2018 semester are included with the quiz announcements above on this page.
  

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• Go to the Fall 2018 Math 3280 Syllabus
• Go to Bruce Peckham's Home Page
• Go to the Department of Mathematics and Statistics Home Page