## Math 3280 Differential Equations with Linear Algebra

### Labs, Assignments and Tests

#### Labs

• Lab Procedures and Guidelines.

• #### Assignments and TESTS

Assigned problems below refer to Differential Equations and Linear Algebra, by Henry Edwards and David Penny, third edition, Pearson/Prentice Hall, 2010. EC=Extra Credit problems; you may arrange with me to work on EC problems after the HW Set due date. 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 Sept. 5:
• Read Chapter 1: Sections 1.1, 1.2
• Section 1.1: 5, 6, 11, 16, 22, 32, 36, 41. EC: 45 (Hint: use 43.). Additional: 1, 8, 15, 17, 19, 27, 35, 37, 43

• Set 2 Due Friday Sept. 12:
• Read Sections 1.2, 1.3, 1.4, 1.5.
• Section 1.2: 2,8,12,19,24. EC: 44 (suggestion: use Mathematica.). 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 1 on Chapter 1 Friday Sept. 19:
• Set 3 Due Friday Sept. 19:
• Read Sections 1.5-1.6 (except for Flight Trajectories and Exact Differential Equations sections), Chapter 1 summary, 2.1, 2.2. (Instead of 2.2, read the 6 pages at the following link.)
• Section 1.4: 36, 49, 51; EC: 69
• Section 1.5: 2,4,10, 12,24,32,34,36; EC: 38
• Section 1.6: 2,22,23,46; EC: 32.
• Section 2.1: 9. Additional: 13.

• Set 4 Due Friday Sept. 26
• Read Sec. 2.3 (skim Resistance Proportional to Square of Velocity and Variable Gravitational Acceleration sections), 2.4 (through Example 2)
• Section 2.1 18 (assume a>0 and b>0) and 2.2: 1,4,14. For all 4 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

• TEST 1: Chapters 1 and 2. Friday Oct. 3 in MonH 70.

• Set 5 Due Friday, Oct. 10
• 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 p. 158 in 2nd edition, p. 161 in 3rd edition)
• Section 3.4: 2, 5, 9. 13, 17, 24, 26, 31, 40

• Set 6 Due Friday, Oct. 17
• Read Sections 3.4 ,3.5, 3.6
• Section 3.5: 1, 9, 12, 23, 34, 39 EC: 32
• Section 3.6: 1, 4, 11, 18, 21, 28, 33 (top row of A inverse only), 43, 52
• Section 3.7: EC: 4
• Section 4.1: 1, 4, 7, 8, 9, 16, 21, 22, 25, 32, 33; EC: 41.

5.2 & 26 & 1\\ 5.3 & 33 & 2\\ & 40 & 2\\ 5.5 & 25 & 2\\ Rest&&7\\
• Set 7 Due Friday, Oct. 24
• 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: 32.
• Section 4.4: 1, 2, 10, 12, 16, 17, 25
• Section 4.7: 1, 3, 5, 6, 9, 10, 13, 14, 15, 19, 23

Quiz 2 Monday Oct. 27. Ch's 3-4.

• Set 8 Due Tuesday, Oct. 28. Moved to part of Set 9. Due with set 9.
• 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.

• TEST 2: Chapters 3 (secs 1-6), 4 (secs 1-4,7), 5 (secs 1,2) and Lab 4-6 material. Update: Friday Oct. 24: Chapter 5 will not be on Test 2. Friday Oct. 31,in MonH 70.
Sample test 2 link (available later) here. Note that the differential equations questions: 1, 2, 4, and the extra credit are on Chapter 5 topics which will not be on Test 2. Partial solutions are here. Link to an (incomplete) summary of topics for TEST 2 here. The differential equations topics listed will not be covered on Test 2.

• Set 8/9 Due Friday, Nov. 7 (Due date moved to Monday Nov. 10).
• Read Sections 5.1, 5.2, 5.3, 5.4, 5.5
• Section 5.1: 2, 3, 10, 14, 17, 33, 35, 40, 43, 44, 45; EC: 27, 52.
• Section 5.2: 1, 8, 13, 21, 25, 26; EC: 38.
• Section 5.3: 2, 9, 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 3 Wednesday Nov. 12 (Moved to Thursday Nov. 13). Selected sections from Ch's 5: 5.1, 5.2, 5.3, 5.5.

• Set 10 Due Friday Nov. 14:
• Read Sections 5.6, 6.1, 7.1 (skip Examples 5,6,7), 7.2, 7.3, 7.6 (through example 1 only)
• Section 5.5: EC: 47
• Section 5.6: No problems assigned other than Lab 7.
• Section 6.1: 1,13,23,27,36 (for 3x3 matrix only); EC 19
• Section 7.1: 1,2,8,24 (Hint: use F=ma)
• Section 7.2: 1,3,12,14,18,23
• Section 7.3: 1,9, 11 (For 1,9,11 - no computer tasks are required.), 17; EC 27.
• Section 7.6: 1a

• Set 11 Due Friday Nov. 21.:
• Read Sections 10.1 - 10.5
• Section 10.1: 1,7,16,19,23,27,29,38; EC 40.
• Section 10.2: 1,8.9.11
• 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]; EC: 29.

• Quiz 4 Monday Nov. 24. Selected sections from Ch's 6,7,9,10. Update: No topics from Ch 9. There will be 2 second order constant coefficient linear homogeneous differential equations to solve, one using Laplace transforms, and the other by converting to a system and using the eigenvalue-eigenvector method. A table of Laplace transforms will be provided.
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.
• TEST 3: Chapters 5,6,7,10, and labs on resonant forcing and phase planes. Friday Dec. 5, in MonH 70.
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. A link to Reading Notes for Chapters 9 and 10 is here.

• Set 12 Due Thurs. Dec. 11.:
• Section 10.5: 1,4,6,11,16,20; EC 25; EC: 32.

• Final Exam Fri. Dec 19, 8:00-9:55am. BohH 90. SWITCHED to MONTAGUE 80!!!!!!. Cumulative: All sections covered in Chapters 1 - 10 and labs.
Final Exam Review materials:
Abreviated course summary: here.
Test 1 partial solutions: here.
Test 2 partial solutions: here.