Math 2280-2 Spring 2017, Differential Equations Instructor G.B. Gustafson, Syllabus Here (pdf) Office hours JWB 113 after class and by appointment. (801) 581-6879. Email preferred, Door Card and Email Address Here Lecture Section 2280-2 meets MTWHF, 12:55pm, in LCB 219. Computer Lab in LCB 115 on select Tuesdays. Problem sessions are daily, voluntary attendance: Problem Session Schedule Here. Midterm Exams Held from 12:50pm to 1:50pm on Friday 17 Feb, Friday 31 Mar, Friday 14 Apr. Final Exam Exam 12:45 PM to 3:15 PM on Friday 28 April Textbook Differential Equations and Boundary Value Problems: Computing and Modeling, 4th Edition, by C. H. Edwards and D. E. Penney (Pearson, 2008) or 5th Edition (Pearson, 2015). View the two book covers and ISBN numbers Here. If the campus bookstore has no 2280 textbook stock, then get the first chapter of the textbook as a PDF from here: Sections 1,2,3and Sections 3,4,5 Online Grades Web site for Utah Canvas
 Last change: Tuesday, 30 May 2017 at 16:57PM

#### Calendar for Weeks 1-6 (Jan 9 to Feb 17)

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 9-13  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 11 for review. Returned with comments on Thu Jan 12 or Fri Jan 13. Details Here.
Quiz1 Sample and Quiz1 Sample Solutions
Take-home Quiz1 and Homework HW1 due Friday next week.
Some solved problems from Edwards-Penney can be found from the 2280 course of Professor Nathan Smale (2015) Here.

WEEK 2, Jan 16-20 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 Friday next week.

WEEK 3, Jan 23-27 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 Friday next week. Numerical Project PDF here, due the first class meeting in March
Numerical maple and matlab resources Directory Here
Problem Session on Quiz2 (from 2015) Photo Directory Here

WEEK 4, Jan 30 to Feb 3 Lecture details
======
Numerical methods, third lecture.
3.1; second order linear equations, Euler solution atoms
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
Take-home Quiz4 and Homework HW4 due Friday next week.

WEEK 5, Feb 6-10 Lecture details
======
3.2; general solution, Picard theorem, independence, Wronskian, superposition
3.1-3.3 Continued. Independence. Wronskian Test.
3.4; mechanical vibrations
Computer Lab 2 details
3.5; forced equations, undetermined coefficients, variation of parameters
Maple Lab 1 Intro due this week
Quiz5 Sample with solutions
Take-home Quiz5 and Homework HW5 due Friday next week.
One week warning: Midterm Exam 1 on 17 February over weeks 1 to 5
Study Sample Exam 1 with solutions (posted 9 Feb 2017)
Study for matching content Old 2250 Exams which used Edwards-Penney. Ch 1,2,3 in 2280 == Ch 1,2,5 in 2250.

WEEK 6, Feb 13-17 Lecture details
======
3.6; mechanical resonance
3.7; LRC model, electrical resonance
Maple Lab 2 Newton Cooling (pipes or cooler project) due this week.
The swamp cooler PDF was corrected 18 Apr.
Quiz6 Sample with solutions and the network problem Solution
Take-home Quiz6 and Homework HW6 due Friday 24 Feb (after Exam 1).
Friday, 17 Feb, Midterm Exam 1 at 12:50pm until 1:50pm, over weeks 1 to 5
Midterm Exam 1 2017 How To Use It
Thursday Exam Review Blackboard Photo Directory
```

#### Calendar for Weeks 7-11 (Feb 20 to Mar 24)

```WEEK 7, Feb 20-24 Lecture details
======
Monday Holiday, President's Day. No classes.
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 Problem Session 12:55pm blackboard photo directory
Quiz7 is extra credit this week, due to Exam 1:
Sample quiz7
Take-home Quiz7 and Homework HW7 due Friday of week 8.

WEEK 8, Feb 27 to Mar 3 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 Friday Week 9.
Thursday problem session 12:55pm blackboard photo directory

WEEK 9, Mar 6-10 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 Friday Week 11 (week after Spring Break)
maple Lab 3 laplace, maple text for mouse-paste.
maple Lab 4 resonance due Friday 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 Friday after Spring Break, week 12.
Thursday Problem Session 12:55pm blackboard photo directory
Due Friday week 11: Quiz8  (Linear DE, Laplace table),  Quiz11 (Laplace), HW8 (Ch 7 Ch4 problems).

WEEK 10, Mar 11-19 is Spring Break. No classes.
=======
No Lab. No Quiz10. No HW10.

WEEK 11, Mar 20-24 Lecture details
=======
Maple Labs 3 and 4, Tuesday session in LCB115 for 30 min:
maple Lab 3 laplace due this Friday Week 11 (week after Spring Break)
maple Lab 3 laplace, maple text for mouse-paste.
maple Lab 4 resonance due Friday Week 13
4.3; RK4 numerical algorithm for systems.
Example 1: PDF: maple for section 4.3
SYSTEM Reference: Manuscript: Numerical methods for systems
Slides: Numerical methods, scalar and vector formulas
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 Friday next week.

Thursday Problem Session 12:55pm blackboard photo directory, problems 1, 7 on Sample Midterm Exam 2.

One week warning: Midterm Exam 2 on Friday 31 Mar
Study for Midterm 2 on Mar 31: Sample Exam 2 Problems only, Sample Exam 2 Problems and solutions
Old Exam 2 Problems and solutions from 2016

Study for matching content Old 2250 Exams which used Edwards-Penney.
Exam 2 will cover topics from week 6 to Friday of week 11. Only topics on the sample exam will appear on Exam 2.
```

#### Calendar for Weeks 12-17 (Mar 27 to Apr 25)

```WEEK 12, Mar 27-31 Lecture details
=======
5.5; matrix exponential, Putzer algorithm, fundamental solution

Quiz12 Sample and Sample Solutions
Take-home Quiz12 and Homework HW12 due Monday 10 April
The answer to problem 2(c) has been corrected. Browser refresh will show the replacement.
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 Exam Review 12:55pm blackboard photo directory, Exam 2 review
Study for Midterm 2: Sample Exam 2 Problems only, Sample Exam 2 Problems and solutions
Old Exam 2 Problems and solutions from 2016

Friday 31 Mar: Midterm Exam 2 at 12:50pm until 1:50pm, over weeks 6 to 11
2017 Midterm 2: Exam 2 Problems only, Answers later.

WEEK 13, Apr 3-7 Lecture details
=======
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
To be skipped due to lack of time:
Computer Lab 5 details
skipped: 6.3; populations and ecological models, predator-prey, 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
skipped: 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

One week warning: Midterm Exam 3 on Friday 14 April
Study S2017 Sample Exam 3 questions and answers.
Reference Old Exam 3 Statements and handwritten solutions (Spring 2016)

No take-home quiz this week or next.
Skipped: Homework HW13 never due
Extra Credit Maple Lab 4 Resonance due May 4.
Extra Credit Maple Lab 5 due May 4: PDF: maple Lab 5 brine tank
Extra Credit Labs due Thursday May 4. See Extra Credit PDF Sources

WEEK 14, Apr 10-14 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 4.

Thursday Exam Review 12:55pm blackboard photo directory
Study S2017 Sample Exam 3 questions and S2017 Sample Exam 3 solutions
Reference Old Exam 3 Statements and handwritten solutions (Spring 2016)

Friday, 14 April, Midterm Exam 3 at 12:50pm until 1:50pm, over weeks 11 to 13.
Study the sample exam and reference exam posted above.

WEEK 15, Apr 17-21  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 Thursday May 4 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 Review 12:55pm blackboard photo directory

WEEK 16, Apr 24-25 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 2016 Final Exam (last year) Questions only and Questions with solutions
Study the Final Exam Study Guide

Final Exam Review sessions blackboard photo directory (26 Apr 4:30-6:30pm)

WEEK 17
=======
Final Exam Review Tuesday 26 Apr in LCB 219 4:30pm to 6:00pm

Final Exam Review sessions blackboard photo directory
Shortened sample final exam Questions

Finals week: Comprehensive final exam, Friday April 28,  12:45pm to 3:15pm in LCB 219
Extra credit homework and labs due by 6pm, under the door 113 JWB, Thursday May 4.
Homework HW15 due by 6pm, under the door 113 JWB, Thursday May 4

2017 Final Exam Questions with student solutions
```

#### Maple, Matlab and Mathematica Tutorials

##### Sample Maple Code for 2280
The directory also contains copy-and-paste text maple sources, identified by file extension TXT or MPL.

Maple, MuPad, Matlab command examples PDF
Starting Maple, MuPad, Matlab from a remote terminal login. Text interface, no graphics.TEXT Here
##### Maple Tutorials
3. A rookie maple tutorial (also Matlab and Mathematica) for the impatient from Indiana University Click Here
5. Utah Maple tutorial 2017 in html format. Includes Setup and First Use.
Used in LCB115 maple intro lectures.
6. How to use maple 2015 under unix, windows, OS/X (text)
Here
7. Maple graphics and low speed internet
Maple at home
##### Matlab Tutorials
1. A one-page pdf Matlab cheat sheet from Strang's linear algebra course at MIT Click Here
2. A matlab tutorial at MIT, contains basic information. No video camera, only code examples and text information. Link is HERE
3. 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
1. Printed or free PDF tutorials on special topics are available at Wolfram Research: HERE
3. A complete set of short tutorial videos are available at Wolfram Research, addressing special topics HERE
4. Wolfram videos and screencasts cover a wide range of applications and interests. See Wolfram Broadcast Videos

#### Previous 2280 Courses

Link to Department of Mathematics, University of Utah