**Quiz** samples and the quiz itself are created weekly. Links below only provide a preview of coming attractions.

**Lecture details** are edited at the beginning of the week and again at the end of the week.

**Examples** are edited weekly.

WEEK 1, Jan 12-16 Examples Lecture details
======
1.1; differential equation, mathematical model
1.2; integral as a general or particular solution
1.3; slope field
1.4; separable differential equation
Submit Exercise 1.2-2 on Wed Jan 14 for review. Returned with comments on Thu Jan 15 or Fri Jan 16. Details **Here**.
Quiz1 Sampleand Quiz1 Sample Solutions
Take-home Quiz1and Homework HW1due next Wednesday.
Thursday Problem Session Photo Directory Click Here
WEEK 2, Jan 19-23 Examples Lecture details
======
Monday Holiday, Martin Luther King. No classes.
1.5; linear differential equation
3.7; LR and RC circuits
2.1; mixture model, Malthus and Verhulst models, cascades and compartment models
2.2; autonomous u'=f(u), equilibrium solution, stability, harvesting
2.3; velocity, acceleration, Newton air resistance models
Quiz2 Sampleand Solutions with graphs
Take-home Quiz2and Homework HW2due next Wednesday.
Thursday Problem Session Photo Directory Click Here
WEEK 3, Jan 26-30 Examples Lecture details
======
2.3; Newton model examples, escape velocity, Jules Verne problem.
2.4, 2.5, 2.6; numerical solutions: Rectangular, Trapezoidal and Simpson rules
2.4; Euler method
2.5; Heun or Modified Euler method
2.6; Runge-Kutta method, RK4
Quiz3 Sampleand Solutions
Take-home Quiz3and Homework HW3due next Wednesday. Numerical Project PDF here
Numerical maple and matlab resources Directory Here
Problem Session on Quiz2 (from 2250) Photo Directory Here
Thursday Problem Session Photo Directory Click Here
WEEK 4, Feb 2-6 Lecture details
======
3.1; second order linear equations, Euler solution atoms
3.2; general solution, Picard theorem, independence, Wronskian, superposition
3.3; homogeneous constant-coefficient equations, Euler substitution, Euler solution atoms
3.4; mechanical vibrations
Quiz4 Sampleand Solutions
Take-home Quiz4and Homework HW4due next Wednesday.
No photo directory this week. All computer problem session.
WEEK 5, Feb 9-13 Lecture details
======
3.4; mechanical vibrations
3.5; forced equations, undetermined coefficients, variation of parameters
3.6; mechanical resonance
Quiz5 Samplewith solutions
Take-home Quiz5and Homework HW5 due next Wednesday.
Maple, MuPad, Matlab examples PDF
Thursday Problem Session Photo Directory Click Here
WEEK 6, Feb 16-20 Lecture details
======
Monday Holiday, President's Day. No classes.
3.6; mechanical resonance
3.7; LRC model, electrical resonance
7.1; Laplace, properties, table, piecewise continuous, existence, Lerch's theorem, inverse Laplace
Study Sample Exam 1 with solutionsfor Midterm 1 on Friday, Feb 27.
Study for matching content Old 2250 Examswhich used Edwards-Penney. Ch 1,2,3 in 2280 == Ch 1,2,5 in 2250.
Exam 1 will cover topics from week 1 to Friday of week 5.
Quiz6 Samplewith solutions and the network problem Solution
Take-home Quiz6and Homework HW6due Wednesday 5 March (after Exam 1).
One week warning: **Midterm Exam 1** on 27 February over weeks 1 to 5
Thursday Problem Session Blackboard Photo Directory

WEEK 7, Feb 23-27 Lecture details
======
7.2; derivative theorem L(y')=sL(y)-y(0) and extensions, spring-mass system, modeling, integral theorem
7.3; partial fractions, Heaviside's method, shift theorem, resonance
7.4; convolution, s-derivative theorem, s-integral theorem
Thursday Exam Review 12:55pm blackboard photo directory
Maple, MuPad, Matlab examples Click Here
Study Sample Exam 1and Sample Exam 1 Solutions for Midterm 1 on Feb 27.
Study for matching content Old 2250 Examswhich used Edwards-Penney.
Exam 1 will cover topics from week 1 to Friday of week 6.
Quiz7 does not exist. No Quiz this week, due to Exam 1.
Homework HW7due next Wednesday.
Friday, 27 Feb, **Midterm Exam 1** at 12:50pm until 1:50pm, over weeks 1 to 6
Midterm Exam 1 Solutions to all 7 problems
WEEK 8, Mar 2-6 Lecture details
======
7.5; unit step, pulse, ramp, second shift theorem, spring-mass, circuits, periodic function theorem
7.6; Dirac impulse, hammer hit model, unit impulse response, unit step response
4.1; first order system, brine cascade, spring-mass system, electrical network, Picard theorem
5.1; matrix systems u'=F(u), u'=Au+g(t), superposition, vector-matrix Picard theorem
Quiz8 Sample with interleaved solutions.
Take-home Quiz8and Homework HW8due next Wednesday.
WEEK 9, Mar 9-13 Lecture details
======
4.2; Cayley-Hamilton-Ziebur method (Example 4.2-1), Elimination method, Cayley-Hamilton theorem.
4.3; RK4 numerical algorithm for systems.
Extra Credit Quiz9 Samplewith interleaved solutions.
Extra Credit Take-home Quiz9is offered.
Homework HW9due next the Tuesday after Spring Break.
Thursday Problem Session 12:55pm blackboard photo directory
Due this week: Quiz8 (Linear DE, Laplace table), HW7 (7.4, 7.5 problems).
Please submit HW8 by Friday, if possible, otherwise by Wednesday, March 25.
WEEK 10, Mar 15-22 is Spring Break. No classes.
=======
No Lab. No Quiz10. No HW10.
Maple, MuPad, Matlab examples PDF
WEEK 11, Mar 23-27 Lecture details
=======
Maple Labs 2 and 3, Tuesday session in LCB115
5.2; Eigenanalysis method for u'=Au, brine tank cascades
5.3; mechanical systems Mx''=Kx, eigenpair solution, railway cars, resonance, earthquakes
5.4; generalized eigenpair, Jordan's two theorems, Cayley-Hamilton
5.4; Jordan form, chain algorithm, railway cars
Chapter 5 maple examples source directory
Computer Lab due: Maple 3, Laplace plus maple code, answers and notes
Computer Lab 2 due next week.
Quiz11 Samplewith interleaved solutions.
Take-home Quiz11and Homework HW11due next Wednesday.
Thursday Problem Session 12:55pm blackboard photo directory, problems 1, 7 on Sample Midterm Exam 2.
**One week warning: Midterm Exam 2** on Friday 3 April
Study Sample Exam 2 Problemsand Sample Exam 2 Solutionsfor Midterm 2 on April 3.
Study for matching content Old 2250 Examswhich used Edwards-Penney.
Exam 2 will cover topics from week 6 to Monday of week 11.
Exam 2 Solution key (posted 3 April)

WEEK 12, Mar 30 to Apr 3 Lecture details
=======
5.5; matrix exponential, Putzer algorithm, fundamental solution
5.6; vector-matrix variation of parameters, 3-tank brine cascade
6.1; equilibria, stability.
6.2; phase portraits for non-linear systems, Paste Theorem
Quiz12 Sampleand Sample Solutions
Take-home Quiz12due Friday 10 April, and Homework HW12due Wednesday 8 April.
Exercises Edwards-Penney Chapter 5 Fourth Edition
Thursday Problem Session 12:55pm blackboard photo directory, Exam 2 review
Study Sample Exam 2 Problemsand Sample Exam 2 Solutionsfor Midterm 2 on Friday April 3.
Friday, 3 April, **Midterm Exam 2** at 12:50pm until 1:50pm, over weeks 6 to 11
Exam 2 Solution key (posted 3 April)
WEEK 13, Apr 6-10 Lecture details
=======
6.3; populations and ecological models, predator-prey, competition, survival, extinction
6.3; competition, survival, extinction
6.4; nonlinear mechanical systems, hard and soft springs, nonlinear pendulum,
Skipped: 6.5; chaos, period doubling, pitchfork bifurcation, York-Li, Feigenbaum. Examples: Duffing, Lorenz, Roessler
Thursday, 9 Apr **4pm Exam review**, only one person showed, no photos.
Homework HW13due next Wednesday.
Maple Lab 4 is semester extra credit due Wednesday, May 6, at the exam or under the door JWB 113.
Direct link: Extra Credit Maple Lab 4
No take-home quiz this week.
Extra Credit Labs due Wednesday, May 6. See Extra Credit PDF Sources
WEEK 14, Apr 13-17 Lecture details
=======
9.1; periodic time signals, Fourier series, Gibbs overshoot, signal reconstruction from sampling, mpg music
9.2; Fourier-Dirichlet convergence theorem, Fourier coefficients, signal approximation, graphical intuition
9.3; Even and odd signals, Fourier sine and cosine series, differentiation and integration of Fourier series
No Take-home Quiz this week.
Homework HW14due next Wednesday.
Maple Lab 4 is semester extra credit due Wednesday May 6 at the final exam or under the door JWB 113.
Direct link: Extra Credit Maple Lab 4
One week warning: **Midterm Exam 3** on 24 April
Study Sample Exam 3 questions.
Reference Sample Exam 3 Answers and Solutions
WEEK 15, Apr 20-24 Lecture details
=======
9.4; Steady-state periodic solution, observable, damping effects, mechanical and electrical forcing effects
9.5; heat conduction, boundary value problem, superposition, separation of variables solution
9.5; ice-pack ends. Dirichlet problem.
9.6; Finite string equation in one dimension. Steady-state heat conduction on a plate.
Homework HW15due by 6pm Wednesday May 6 under the door JWB 113.
Study the Sample Final Exam Questionsand Answers and Solutions
Study the Final Exam Study Guide
Chapter 9 PDE slides: directory
Chapter 9 PDE problems, 4th edition: directory
Thursday Exam 3 Review Session 1pm to 4pm blackboard photo directoryall problems on Sample Midterm Exam 3.
Friday, 24 April, **Midterm Exam 3** at 12:50pm until 1:50pm, over weeks 11 to 13
Exam 3 Statements, Answers, Solutions (posted 24 April)
WEEK 16, Apr 27-28 Lecture details
=======
Sample Final Exam. Covers Chapters 1 to 9, skip Chapter 8.
Comprehensive Final Exam review started on Tuesday.
Study the Sample Final Exam Questionsand Answers
Study the Final Exam Study Guide
Final Exam Review sessions blackboard photo directory, includes problems removed from the sample final exam.
Shortened sample final exam Questionsand Answers
WEEK 17
=======
Final Exam Review Monday May 2 in LCB 323 4:00pm to 6:00pm
Final Exam Review sessions blackboard photo directory, includes problems removed from the sample final exam.
Shortened sample final exam Questionsand Answers
Finals week: Comprehensive final exam, Wednesday May 6, 12:45pm to 3:15pm in LCB 219
Extra credit homework and labs due by 6pm, under the door 113 JWB, Wednesday May 6.
Homework HW15 due by 6pm, under the door 113 JWB, Wednesday May 6
Final Exam S2015 Questions only (posted May 10)
Final Exam S2015 Questions and answers (posted May 10)

##### Sample Maple, MuPad, Matlab Code for 2280

The

**text** directory contains copy-and-paste maple sources.

Click Here for directory access

Click Here for a guide to the text files

Maple, MuPad, Matlab examples

PDF
Starting Maple, MuPad, Matlab from a remote terminal login. Text interface, no graphics.

TEXT Here
##### Maple Tutorials

- Maplesoft Quick Reference Cards Click
Here
- Douglas Meade's Quick Reference Card for Maple 12 to 17 Click
Here
- A rookie maple tutorial for the impatient from Indiana
University Click
Here
- Maple programming examples by topic from Kettering
University Click
Here
**Utah Maple tutorial 2015** in html format

Used in LCB115 maple intro lectures.

Click Here
- How to use maple 18 under unix, windows, OS/X (text)

Here
- Maple graphics and low speed internet

Maple at home
- Peter Stone's Maple Resource page
for undergraduate math topics
Click Here

##### Matlab Tutorials

- A one-page pdf Matlab cheat sheet from Strang's linear
algebra course at MIT Click
Here
- A matlab tutorial at MIT, contains basic information. No video camera, only code examples and text information. Link is HERE
- Mathworks matlab tutorials and documents are HERE. Register for the short tutorials, then try a few using your univ of Utah computer account. Matlab has a site license
valid for all campus computers.

##### Mathematica Tutorials

- Printed or free PDF tutorials on special topics are available at Wolfram Research: HERE
- New users can start with John McLoone's YouTube video (2010) HERE
- A complete set of short tutorial videos are available at Wolfram Research, addressing special topics HERE
- Wolfram videos and screencasts cover a wide range of applications and interests. See Wolfram Broadcast Videos

**Homework Problems**.

The

**Calendar** has the problem list(s), one PDF source per week. This is the best source for
finding due dates and the problem list.

A

**bookmark** can be printed, to fold into your textbook. The bookmark contains all the textbook problems and computer problems. Use this print to journal your homework assignments.

Bookmark Here
Enumeration is by week, where Week 10 is Spring Break, no homework in Week 10.

**Problem Notes** on graded problems can be found

Here
The notes sometimes have answers which are either not in the book or are different from the book answers. The notes originated from email messages, office visits and grader remarks.

**Thursday Problem Sessions**
Weekly Thursday sessions are held in LCB 219 at 12:50pm, to discuss HW due the next week. For example, Thursday of Week 4 would discuss HW4, which is due in Week 5. Blackboard photos of the Thursday session are posted, a link appearing in the Calendar.

**Extra Credit Problems** can be found

Here
These problems replace scores of zero or 50 on homework. They do not affect exam scores or quiz scores.

Extra credit is also possible by submitting a unique solution to a study guide problem.
Unique solutions will be posted, with a credit line to the solver in the form

*Carl G.*,
i.e., the credit uses only a last name initial.

##### Gustafson's 2280 Midterm and Final Exam Samples Spring 2015

**Studying for Exams**. Please read the study guide problems, none of which are due. For example, HW3 lists **2.4**: 2, 3, 4, 10, 12, 17 as study problems and boxed problem **6** as due in week 4. Reading the problems is important for developing problem-solving intuition.
Mostly, you look for problems that you know how to solve. Any mystery detected should be solved: be a good detective.

**Sample Exams** will be posted when available. Due to re-ordering of topics and syllabus changes, there are no old exam keys to study. Anything relevant will be added here, as extra study material.

- Sample midterm exam 1, Gustafson's 2280 course S2015.

Study Sample Exam 1 with solutionsfor Midterm 1 on Friday, Feb 27.

Study for matching content Old 2250 Examswhich used Edwards-Penney. Ch 1,2,3 in 2280 == Ch 1,2,5 in 2250.
- Sample midterm exam 2, Gustafson's 2280 course S2015.
- Sample midterm exam 3, Gustafson's 2280 course S2015.
- Sample final exam, Gustafson's 2280 course S2015.

##### Gustafson's 2280 Midterm and Final Exam Keys, Spring 2015

- Midterm Exam 1, Gustafson's 2280 course S2015. [Link will appear here when available]
- Midterm Exam 2, Gustafson's 2280 course S2015.
- Midterm Exam 3, Gustafson's 2280 course S2015.
- Final Exam, Gustafson's 2280 course S2015.

##### Math 2280-2 Differential Equations

**US Mail address:**
Grant B. Gustafson
155 South 1400 East Room 233
Salt Lake City, UT 84112-0090

**Office phone:** (801) 581-6879, in room JWB 113

**Email Address**:
Read the online

DoorCard
**Course Syllabus**:
The 2280-2 course syllabus for 2015 can be found

Here
(257K pdf)
**2280 Format Ideas for Written Reports**
How to improve your written work,

Writing reports.
( 79K pdf)
Internet archived files from previous semesters exist, which have homework solutions,
maple and matlab code, exam keys, syllabi and problem notes. A sampling of what is available can be found
at Professor Korevaar's site, which is mainly for instructors, but applicable to you, if you are searching for 2280 information.

List of previous 2280 instructors and home pages
Link to