**Quiz** samples and the quiz itself are created weekly. Links below 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 available for weeks 1,2,3 only.

WEEK 1, Jan 11-15 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
**First Exercise**. Submit Exercise 1.2-2 on Wed Jan 13 for review. Returned with comments on Thu Jan 14 or Fri Jan 15. Details **Here**.
Quiz1 Sample and Quiz1 Sample Solutions
Take-home Quiz1 and Homework HW1 due next Friday.
Thursday Problem Session Photo Directory Click Here

Some solved problems from Edwards-Penney can be found from the 2280 course of Professor Nathan Smale (2015) Here.
WEEK 2, Jan 18-22 Examples Lecture details
======
Monday Holiday, Martin Luther King. No classes.
1.5; linear differential equation
3.7; LR and RC circuits
Computer Lab 1 details
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 Sample and Solutions with graphs
Take-home Quiz2 and Homework HW2 due next Friday.
Quiz 2 had a typo: 0.95% instead of 95%
Thursday Problem Session Photo Directory Click Here
WEEK 3, Jan 25-29 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 Sample and Solutions
Take-home Quiz3 and Homework HW3 due next Friday. Numerical Project PDF here
Numerical maple and matlab resources Directory Here
Problem Session on Quiz2 (from 2015) Photo Directory Here
Thursday Problem Session Photo Directory Click Here
WEEK 4, Feb 1-5 Lecture details
======
Numerical methods, third lecture.
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
Tuesday is Lab 1 day, completed in LCB 115.
Quiz4 Sample and Solutions
Quiz4 resource on Picards's Theorem
Posting error. Correct Quiz4 posted on 10 February. Collection of Quiz4 delayed.
Take-home Quiz4 and Homework HW4 due next Friday.
Thursday Problem Session Photo Directory Click Here
WEEK 5, Feb 8-12 Lecture details
======
3.1-3.3 Continued. Independence. Wronskian Test.PDF: maple Example 1, section 4.3
3.4; mechanical vibrations
Computer Lab 2 details
3.5; forced equations, undetermined coefficients, variation of parameters
Maple Lab 1 Intro due this week or next Tuesday
Quiz5 Sample with solutions
Take-home Quiz5 and Homework HW5 due next Friday.
Maple, MuPad, Matlab examples PDF
Thursday Problem Session Photo Directory Click Here
WEEK 6, Feb 15-19 Lecture details
======
Monday Holiday, President's Day. No classes.
3.6; mechanical resonance
3.7; LRC model, electrical resonance
Maple Lab 2 Newton Cooling (pipes or cooler project) due this week.
Study Sample Exam 1 with solutions for Midterm 1 on Friday, Feb 26.
Study for matching content Old 2250 Exams which 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 Sample with solutions and the network problem Solution
Take-home Quiz6 and Homework HW6 due Friday 5 March (after Exam 1).
One week warning: **Midterm Exam 1** on 26 February over weeks 1 to 5
Maple from home, UofU Library Remote Maple 18 How To Use It
Thursday Problem Session Blackboard Photo Directory

WEEK 7, Feb 22-26 Lecture details
======
7.1; Laplace, properties, table, piecewise continuous, existence, Lerch's theorem, inverse Laplace
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
Thursday Exam Review 12:55pm blackboard photo directory
Maple, MuPad, Matlab examples Click Here
Study Sample Exam 1 with solutions for Midterm 1 on Friday, Feb 26.
Study for matching content Old 2250 Exams which 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 HW7 due Friday of week 9.
Friday, 26 Feb, **Midterm Exam 1** at 12:50pm until 1:50pm, over weeks 1 to 6
Midterm Exam 1 Solutions to all 7 problems (AVE=86, posted 28 Feb)
Letter Grade to Numerical Grading Table
WEEK 8, Feb 29 to Mar 4 Lecture details
======
4.1; first order system, brine cascade, spring-mass system, electrical network, Picard theorem [integrated with Ch 7]
7.4; convolution, s-derivative theorem, t-integral theorem
7.5; unit step, pulse, ramp, second shift theorem, spring-mass, circuits, periodic function theorem
Quiz8 Sample with interleaved solutions.
Take-home Quiz8 and Homework HW8 due in Week 11.
Thursday problem session 12:55pm blackboard photo directory
WEEK 9, Mar 7-11 Lecture details
======
7.6; Dirac impulse, hammer hit model, unit impulse response, unit step response
5.1; matrix systems u'=F(u), u'=Au+g(t), superposition, vector-matrix Picard theorem
4.2; Cayley-Hamilton-Ziebur method (Example 4.2-1), Elimination method, Cayley-Hamilton theorem.
Computer Lab 3 and Lab 4 details
maple Lab 3 laplace due Week 11 (week after Spring Break)
maple Lab 3 laplace, maple text for mouse-paste.
maple Lab 4 resonance due Week 13
Maple from home, UofU Library Remote Maple 18 How To Use It
Extra Credit Quiz9 Sample with interleaved solutions.
Extra Credit Take-home Quiz9 is offered.
Homework HW9 due after Spring Break, week 12.
Thursday Problem Session 12:55pm blackboard photo directory
Due in week 11: Quiz8 (Linear DE, Laplace table), HW7 (7.4, 7.5 problems take time).
WEEK 10, Mar 12-20 is Spring Break. No classes.
=======
No Lab. No Quiz10. No HW10.
Maple, MuPad, Matlab examples PDF
WEEK 11, Mar 21-25 Lecture details
=======
Maple Labs 2 and 3, Tuesday session in LCB115 for 30 min
4.3; RK4 numerical algorithm for systems.
Example 1: PDF: maple for section 4.3
5.2; Eigenanalysis method for u'=Au, brine tank cascades
5.3; mechanical systems Mx''=Kx, eigenpair solution, railway cars, resonance, earthquakes
Slides: Cayley-Hamilton-Ziebur Method for u''=Au
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 3 **Laplace** due this week.
Quiz11 Sample with interleaved solutions.
Take-home Quiz11 and Homework HW11 due next Friday.
Thursday Problem Session 12:55pm blackboard photo directory, problems 1, 7 on Sample Midterm Exam 2.
**One week warning: Midterm Exam 2** on Friday 1 April
Study for Midterm 2 on April 1: Sample Exam 2 Problems only,
Sample Exam 2 Problems and solutions and Sample Exam 2 (edited) from Spring 2015
Study for matching content Old 2250 Exams which used Edwards-Penney.
Exam 2 will cover topics from week 6 to Wednesday of week 11. Only topics on the sample exam will appear on Exam 2.

WEEK 12, Mar 28 to Apr 1 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 Sample and Sample Solutions
Take-home Quiz12 and Homework HW12 due Friday 15 April
Maple references for Exercises 6.3-4,5,6,7: PDF and WORKSHEET
Maple reference for Exercises 6.3-8,9,10: WORKSHEET
Exercises Edwards-Penney Chapter 5 Fourth Edition
Thursday Problem Session 12:55pm blackboard photo directory, Exam 2 review
Study for Midterm 2 on April 1: Sample Exam 2 Problems only,
Sample Exam 2 Problems and solutions and Sample Exam 2 (edited) from Spring 2015
Study for matching content Old 2250 Exams which used Edwards-Penney.
Exam 2 will cover topics from week 6 to Wednesday of week 11. Only topics on the sample exam will appear on Exam 2.
Friday 1 April: **Midterm Exam 2** at 12:50pm until 1:50pm, over weeks 6 to 11
Exam 2 Solution key (posted 6 Apr)
WEEK 13, Apr 4-8 Lecture details
=======
6.3; populations and ecological models, predator-prey, competition, survival, extinction
Computer Lab 5 details
6.3; competition, survival, extinction
Maple references for Exercises 6.3-4,5,6,7: PDF and WORKSHEET
Maple reference for Exercises 6.3-8,9,10: WORKSHEET
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 Problem Session 12:55pm blackboard photo directory
Homework HW13 due May 3.
Maple Lab 4 **Resonance** due this week.
No take-home quiz this week.
Extra Credit Labs due Tuesday May 3. See Extra Credit PDF Sources
WEEK 14, Apr 11-15 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 HW14 due May 3.
Maple Lab 4 is semester extra credit due May 3 under the door JWB 113.
Direct link: Extra Credit Maple Lab 4
Thursday Problem Session 12:55pm blackboard photo directory
One week warning: **Midterm Exam 3** on Friday 22 April
Study Sample Exam 3 questions and answers.
Reference Exam 3 Statements, Answers and Solutions from Spring 2015
WEEK 15, Apr 18-22 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 HW15 due by 6pm Tuesday May3 under the door JWB 113.
Study the Sample Final Exam Questions and Answers and Short Sample Questions only
Study the Final Exam Study Guide
Chapter 9 PDE slides: directory
Chapter 9 PDE problems, 4th edition: directory
Thursday Problem Session and Exam 3 Review 12:55pm blackboard photo directory
Friday, 22 April, **Midterm Exam 3** at 12:50pm until 1:50pm, over weeks 11 to 13.
Study the sample exam and reference exam posted in week 14.
Exam 3 Statements, Answers, Solutions (posted 26 Apr)
WEEK 16, Apr 25-27 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 Questions and Answers and Short Sample Questions only
Study the Final Exam Study Guide
Final Exam Review sessions blackboard photo directory
WEEK 17
=======
Final Exam Review Wed 27 Apr in LCB 323 4:00pm to 6:00pm
Final Exam Review sessions blackboard photo directory
Shortened sample final exam Questions
Finals week: Comprehensive final exam, Thursday April 28, 12:45pm to 3:15pm in LCB 219
Extra credit homework and labs due by 6pm, under the door 113 JWB,Tuesday May 3.
Homework HW15 due by 6pm, under the door 113 JWB, Tuesday May 3
Final Exam S2016 Questions only (posted after the exam)
Final Exam S2016 Questions and answers (posted after the exam)

##### Sample Maple Code for 2280

The directory also contains copy-and-paste

**text** maple sources, identified by file extension TXT or MPL.

Click Here for directory access

Maple, MuPad, Matlab command 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 Maple 2015 Click
Here
- A rookie maple tutorial (also Matlab and Mathematica) for the impatient from Indiana
University Click
Here
- Maple programming examples by topic from Kettering
University Click
Here
**Utah Maple tutorial 2016** in html format. Includes Setup and First Use.

Used in LCB115 maple intro lectures.

Click Here
- How to use maple 2015 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.

##### Remote Maple: Running Maple from Home

Maple can be run from home, a laptop, or even a phone or tablet, using a minimal internet connection. Instructions here for the UofU Library and the Math Department computers:

Maple from home, UofU Library Remote Maple 18

How To Use It
##### 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. The Calendar is the most reliable source for
finding due dates and the problem list.

The homework PDf files linked in the Calendar are labeled HW1, HW2, ... and they can be found in this Directory, which may be a quick way for you to check what is due.

The **Bookmark** is a complete list of what is due on Friday each week, 2 pages in length, suited for folding into your textbook. Find the PDF here: Bookmark

There is little difference between 4/E and 5/E editions of the textbook *Differential Equations and Boundary Value Problems: Computing and Modeling*. The major difference is isolated to Chapter 5.
In chapter 5, the 4/E problems agree exactly with the 5/E problems, except for numbering of sections, and an inserted section 5.3 (5/E). This causes the section numbers to be off by one, but the problem numbers are exactly the same. The HW problems will use the 4/E problem numbers, to stop confusion, with web site warnings about mis-matched problem references.
The chapter 5 contents appear below, where 4/E==4th Edition and 5/E==5th Edition.

**Chapter 5**. Linear Systems of Differential Equations
5.1 in 4/E and 5/E: Matrices and Linear Systems
5.2 in 4/E and 5/E: The Eigenvalue Method for Homogeneous Systems
5.3 in 5/E only: A Gallery of Solution Curves of Linear Systems [Inserted 2015]
5.3 in 4/E == 5.4 in 5/E: Second-Order Systems and Mechanical Applications
5.4 in 4/E == 5.5 in 5/E: Multiple Eigenvalue Solutions
5.5 in 4/E == 5.6 in 5/E: Matrix Exponentials and Linear Systems
5.6 in 4/E == 5.7 in 5/E: Nonhomogeneous Linear Systems

Therefore, you can use 4/E instead of 5/E. If you own edition 4/E, and you want to obtain a copy of the missing material 5.3 (5/E), then Copyright issues arise. Please know that the course web site has free PDF slides and PDF manuscripts on the topics covered in section 5.3 of 5/E. These resources have been in use for 5 or more years, and they will replace section 5.3 in the lectures. No homework is assigned from

*A Gallery of Solution Curves of Linear Systems*.

### Maple Computer Labs

There are seven (7) labs offered. The last three are extra credit, intended to replace math problems or computer labs.

- First Maple Lab never due, done in first LCB115 meeting
- maple Lab 1 intro due Week 5
- maple Lab 2 freezing pipes due Week 6 (choose pipes or cooler)
- maple Lab 2 swamp cooler due Week 6
- maple Lab 3 laplace due Week 11 (week after Spring Break)
- maple Lab 4 resonance due Week 13
- maple Lab 5 brine tank due May 3
- maple Lab 6 narrows due May 3
- maple Lab 7 earthquake due May 3

### 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.

### Bookmark of Problems Due

A

**bookmark** can be printed, to fold into your textbook.
The bookmark contains all the textbook problems and computer problems. Enumeration is by week, where Week 10 is Spring Break, no homework in Week 10.
Use this print to journal your homework assignments.

Bookmark Here
### Problem Notes for Graded Problems

**Problem Notes** exist, organized by chapter, for Chapters 1-7 and 9. Click here for the
problem notes

These 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.

**Extra Credit Problems** and **Extra Credit Maple Labs** 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 or by submitting an extra credit maple lab. Submit by May 3.
Maple labs 5, 6, 7 are extra credit.

**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 in the calendar when available.

Exam 1 S2016 solutions are posted one week after the exam date.

Sample Exam 1 S2016: Sample Exam 1 with solutions for Midterm 1 on Friday, Feb 26.

Similar 2280 exams were last given Spring 2015. The S2015 web site can be found Here.

**Exam Solution Keys** are posted in the calendar, as they become available.

Find old 2280-2 exam keys from Spring 2015 in the calendar at the web site link above.

##### 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 2016 can be found

Here
(310K 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.

Korevaar's list of previous 2280 instructors and home pages
To find more Utah 2280 courses, start with the

math department course schedule page. Then find instructor names and section numbers for 2280, for the past 3-4 years.
Go to the

math department Main Page to find the home pages of those instructors. Track down the old 2280 course from their home page. If this idea fails to give information, then try an internet browser search for "korevaar 2280" and "smale 2280" and see what surfaces.

Link to