Math 3280 Differential Equations with Linear Algebra
Spring 2014
Prof. Peckham
Labs, Homeworks and Tests
Labs
Lab Procedures and Guidelines.
- Lab 1 Introduction to Mathematica, Tuesday Jan. 21.
Due Wednesday Jan. 29 to GTA Long Chen.
Link to Lab 1 assignment.
Link to Lab 1 Mathematica Notes/Hints.
OP?
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 Wed. Feb. 5. to Long Chen.
Link to Lab 2 assignment.
- Lab 3: Comparing Qualitative, Numerical, and Analytic Solutions to the Logistic Differential Equation.
Tuesday Feb. 4 and 11.
Due Wednesday Feb. 12 to Long Chen.
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. 18,
Due Wednesday Feb. 26 - MOVED TO Friday Feb. 28 to Long Chen.
Link to Lab 4-6 assignment.
- Lab 5: Applications of First Order Differential Equations:Compartmental
Analysis.
Tuesday Feb. 25,
Due Wednesday Mar. 5 MOVED TO Wednesday March 12 to Long Chen.
Link to Lab 4-6 assignment.
Link to First Order Linear DE template.
- Lab 6: Applications of First Order Differential Equations: Parameter Matching.
Tuesday Mar. 4, 11.
Due Wednesday Mar. 12 MOVED TO Wednesday March 26 to Long Chen.
Link to Lab 4-6 assignment.
- Lab 7: Resonant Forcing of a Spring-Mass System
Tuesday Mar. 25, Apr. 1.
Due Wednesday, Apr. 2 to Long Chen.
Link to Lab 7 assignment.
- Lab 8: Differential Equations and Linear Algebra with Mathematica
Tuesday Apr. 8, 15. Do in lab or submit writeup by
Wednesday, Apr. 16 to Long Chen.
Link to Lab 8 assignment.
- Lab 9: Systems of Differential Equations: Phase plane analysis.
Tuesday, Apr. 22, 29.
Due Wednesday, Apr. 30. to Long Chen.
Link to Lab 9 assignment.
HW and TESTS
HW 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 HW turned in should conform to
Departmental Minimum HW Standards.
Scratch work will not be accepted.
- Set 1 Due Friday Jan. 24:
- 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
- Section 1.2: 2,8,12,19,24. EC: 44 (suggestion: use Mathematica.). Additional: 1,31
- Set 2 Due Friday Jan. 31:
- Read Sections 1.3, 1.4, 1.5.
- Section 1.3: 1-6 (photocopy provided in class), 13,14,17,18,21
- Section 1.4: 2,8,17,20,27. Additional 1,9.
- Section 1.5: 2,4,10
- Set 3 Due Friday Feb. 7:
- Read Sections 1.6 (except for Flight Trajectories and Exact Differential Equations sections), Chapter 1 summary, 2.1, 2.2
- Section 1.4: 36, 49, 51; EC: 69
- Section 1.5: 12,24,32,34,36; EC: 38
- Section 1.6: 2,22,23,46; EC: 32.
- Section 2.1: 9.13
- Section 2.2: 1,4,14. For all 3 problems, ignore the book instructions.
Instead, construct a phase line diagram and use it to (i) describe the long term fate of solutions for ALL initial conditions, and (ii) sketch several representative solution curves.
- Set 4 Due Tuesday Feb. 11:
- Read Sec. 2.3 (skim Resistance Proportional to Square of Velocity and Variable Gravitational Acceleration sections), 2.4 (through Example 2)
- Section 2.3: 10
- Section 2.4: 1,10
- TEST 1: Chapters 1 and 2. 6-7:30pm Thursday Feb 13 in LSci 175.
Sample test 1 link
here.
Non graphical solutions
here.
- Set 5 Due Friday, Feb. 21 (moved to Tuesday, Feb. 25)
- Read Sections 3.1, 3.2, 3.3
- 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)
- Set 6 Due Friday, Feb. 28
- Read Sections 3.4 ,3.5, 3.6
- Section 3.4: 2, 5, 9. 13, 17, 24, 26, 31, 40
- 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
- Set 7 Due Friday, March 7
- Read Sections 4.1, 4.2, 4.3, 4.4
- Section 4.1: 1, 4, 7, 8, 9, 16, 21, 22, 25, 32, 33; EC: 41.
- 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
- Set 8 Due Friday, March 14.
- Read Sections 4.7, 5.1, 5.2 (skip sections 4.5, 4.6)
- Section 4.7: 1, 3, 5, 6, 9, 10, 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.
Spring Break Sat. March 15 - Sun. March 23
- TEST 2: Chapters 3 (secs 1-6), 4 (secs 1-4,7), 5 (secs 1,2)
and Lab 4-6 material.
Thursday Mar. 27, 6-7:30pm in LSci 175. (No class Friday Mar. 28)
Sample test 2 link (available later)
here.
Partial solutions are
here.
Link to an (incomplete) summary of topics for TEST 2
here.
- Set 9 Due Friday, April 4.
- Read Sections 5.3, 5.4, 5.5, 5.6
- Section 5.2: 25, 26
- 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.
- Section 5.6: No problems assigned other than Lab 7.
- Set 10 Due Friday April 11:
- Read Sections 6.1, 7.1 (skip Examples 5,6,7), 7.2, 7.3, 7.6 (through example 1 only)
- Section 5.5: 47
- 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 April 18:
- 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.
- Set 12 Due Friday April 25.:
- Section 10.5: 1,4,6,11,16,20; EC 25; EC: 32.
- TEST 3: Chapters 5,6,7,9,10, and labs on resonant forcing and phase planes.
Thursday May 1, 6-7:30 in LSci 175. (No class Fri. May 2)
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.
- Final Exam Mon. May 12, 10:00-11:55 am. Room SCC 120..
Cumulative: All sections covered in Chapters 1 - 10 and labs.
Final Exam Review materials:
Abreviated course summary:
here.
Test 1 partial answers: here.
Test 2 partial answers: here.
Test 3 partial answers: here.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Wednesday, 07-May-2014 22:20:21 CDT.