Math 3280 Differential Equations with Linear Algebra
Spring 2018
Prof. Peckham
Labs, Assignments and Tests
Labs
Lab Procedures and Guidelines.
- Lab 1 Introduction to Mathematica, Tuesday Jan. 16.
Due Thursday Jan. 18 to GTA Richa Rawat or to Prof. Peckham.
Link to Lab 1 assignment.
Link to Lab 1 Mathematica Notes/Hints.
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. 23. Due Th. Jan. 25. to Richa Rawat.
Link to Lab 2 assignment.
- Lab 3: Comparing Qualitative, Numerical, and Analytic Solutions to the Logistic Differential Equation.
Tuesday Jan 30 and Feb. 6.
Due Thursday Feb. 8 to Richa Rawat.
Link to Lab 3 assignment.
Link to Lab 3 Separation of Variables Template.
- Lab 4: Applications of First Order Differential Equations: Falling object.
Tuesday Feb. 6 and 13.
Due Thursday Feb. 15 (moved to Friday Feb. 16) to GTA Richa Rawat.
Link to Lab 4-6 assignment.
- Lab 5: Applications of First Order Differential Equations: Compartmental
Analysis.
Tuesday Feb. 20 and 27.
Due Thursday March 1 to Richa Rawat.
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 13 and 20.
Due Thursday March 22 to Richa Rawat.
Link to Lab 4-6 assignment.
- Lab 7: Resonant Forcing of a Spring-Mass System
Tuesday March 27 and April 3.
Due Thursday April 5. to Richa Rawat.
Link to Lab 7 assignment.
- Lab 8: Differential Equations and Linear Algebra with Mathematica
Tuesday April 10. Do in lab or submit writeup
Due Thursday April 12 to Richa Rawat. Due TBA.
Link to Lab 8 assignment.
- Lab 9: Systems of Differential Equations: Phase plane analysis.
Tuesday April 17 and 24.
Due Thursday April 26. to Richa Rawat.
Link to Lab 9 assignment.
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; 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 Jan. 12:
- 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.
- Set 2 Due Friday Jan. 19:
- 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 Jan. 26 :
- Set 3 Due Friday Jan. 26:
- 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 Feb. 2
- 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
Friday Feb. 9 NO CLASS
- TEST 1: Chapters 1 and 2. Monday Feb. 12 6-7:30. SCC 120.
Sample test 1 link:
here.
Partial solutions link:
here.
Partial solutions to a second practice test: here.
- Set 5 Due Friday, Feb. 16 (moved to Monday Feb. 19)
- 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, Feb. 23
- 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.
Monday Feb. 26 NO CLASS
Quiz 2 Thursday, March 1. Ch's 3-4 (3.1-3.6 and 4.1-4.3), and one DE substitution problem. Quiz 2 solutions.
- Set 7 Due Friday, March 2
- 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. Delay the rest to HW 8: 13, 14, 15, 19, 23.
- Spring Break: March 3-11
- Set 8 Due Thursday, March 15.
- Read Sections 5.1, 5.2
- Section 4.7: 13, 14, 15, 19, 23.
- 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.
Monday March 19, 6-7:30 SCC 120.
Sample test 2 link
here.
Partial solutions are
here.
Link to an (incomplete) summary of topics for TEST 2
here.
- Set 9 Due Friday, March 23..
- Read Sections 5.3, 5.4, 5.5
- 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 Friday March 30. Selected sections from Ch's 5: 5.1, 5.2, 5.3, 5.5.
- Set 10 Due Friday March 30.:
- 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: 1,2,8,24 (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 7.7 :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.
- Set 11 Due Friday April 6.:
- 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; EC 40.
- Section 10.2: 1,8.9.11
- Set 12 Due Friday April 13.:
- 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]; EC: 29 (turn in on a separate sheet)
- Section 10.5: 1,4,6,11,16,20, 25; EC: 32 (turn in on separate sheet).
- Quiz 4 Fri. April 13. Selected sections from Ch's 6,7,9?,10.
- TEST 3: Chapters 5,6,7,10, and labs on resonant forcing and phase planes.
Thursday, April 19, 6-7:30pm. SCC 120.
- Quiz 5: Thursday 10-10:50. Extra Credit. Points will be added to your quiz 1-4 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).
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.
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.
A link to Reading Notes for Chapters 9 and 10 is
here.
- Final Exam Mon. April 30, 10:00-11:55am. Life Sci 185.
Cumulative: All sections covered in Chapters 1 - 10 and labs.
Final Exam Review materials:
Abreviated course summary:
here.
Solutions to semester tests:
Test 1 partial solutions: here.
Test 2 partial solutions: here.
Test 3 partial answers: here.
Quizzes 1-5 solutions: here.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Friday, 19-Oct-2018 11:21:29 CDT.