#### Math 2280-2 Spring 2015, Differential Equations

 Instructor G.B. Gustafson, Home Page (801) 581-6879, Email is preferred, address Here Office hours JWB 113, MTWF, after class, by appointment or door card times Here Lecture Section 2280-2 meets MTWHF, 12:55pm, in LCB 219. Thursday is a problem session. Midterm Exams Held from 12:50pm to 1:50pm on Friday 27 Feb, Friday 3 Apr, Friday 24 Apr. Final Exam Exam 12:45 PM to 3:15 PM on Wednesday 6 May. Text Differential Equations and Boundary Value Problems: Computing and Modeling, 5th Edition, by C. H. Edwards and D. E. Penney (Prentice-Hall, 2015) Syllabus 2280 syllabus (pdf) Online Grades Web site for Utah Canvas
 Last change: Tuesday, 12 May 2015 at 08:21AM

#### Calendar for Weeks 1-6 (Jan 12 to Feb 20)

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.

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.

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

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.

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
```

#### Calendar for Weeks 7-11 (Feb 23 to Mar 27)

```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
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.

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)
```

#### Calendar for Weeks 12-17 (Mar 30 to Apr 28)

```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)```

#### Maple, Matlab and Mathematica Tutorials

##### Sample Maple, MuPad, Matlab Code for 2280
The text directory contains copy-and-paste maple sources.
Starting Maple, MuPad, Matlab from a remote terminal login. Text interface, no graphics.TEXT Here
##### Maple Tutorials
3. A rookie maple tutorial for the impatient from Indiana University Click Here
5. Utah Maple tutorial 2015 in html format
Used in LCB115 maple intro lectures.
6. How to use maple 18 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.
##### 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