Isaac Newton, Leonhard Euler, Pierre-Simon Laplace, Joseph Fourier, Carl Friedrich Gauss and Gustav Dirichlet

 

Math 2280-2 Spring 2018, 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 2018
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 16 Feb, Friday 30 Mar, Friday 13 Apr.
Final Exam Exam 12:45 PM to 3:15 PM on Friday 27 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, 07 November 2017 at 09:12AM

Calendar for Weeks 1-6 (Jan 8 to Feb 16)

Quiz samples and the quiz itself might be edited during the semester. Examples are available for weeks 1,2,3 only.
WEEK 1, Jan 8-12  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 10 for review. Returned with comments on Thu Jan 11 or Fri Jan 12. Details Here.
Quiz1 Sample and Quiz1 Sample Solutions
Take-home Quiz1 and Homework HW1 due Friday next week.
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 15-19 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. Lab 1 session is Tuesday Week 4. Lab 1 is due Week 7 with Numerical Project HW3. Both are maple projects. 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. Reference: Quiz2 problem session from 2015. Photo Directory Here Thursday Problem Session Photo Directory Click Here WEEK 3, Jan 22-26 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 due Friday next week. This is a calculator project, no computer needed. Homework HW3 is the Numerical Project PDF here, due Friday Week 7 (Feb 23) Numerical maple and matlab resources Directory Here Thursday Problem Session Photo Directory Click Here WEEK 4, Jan 29 to Feb 2 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. Start in LCB 219, then move to computer classroom LCB 115 at 1:10pm. Quiz4 Sample and Solutions Quiz4 resource on Picards's Theorem Take-home Quiz4 and Homework HW4 due Friday next week. Thursday Problem Session Photo Directory Click Here WEEK 5, Feb 5-9 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. Maple, MuPad, Matlab examples PDF Thursday Problem Session Photo Directory Click Here One week warning: Midterm Exam 1 on 17 February over weeks 1 to 5 Study Sample Exam 1 with solutions Study for matching content Old Exam 1 with solutions (2017) WEEK 6, Feb 12-16 Lecture details ====== 3.6; mechanical resonance 3.7; LRC model, electrical resonance Quiz6 Sample with solutions and the network problem Solution Take-home Quiz6 and Homework HW6 due Monday 19 Feb (after Exam 1). Friday, 16 Feb, Midterm Exam 1 at 12:50pm until 1:50pm, over weeks 1 to 5 Study Sample Exam 1 with solutions Thursday Exam Review Blackboard Photo Directory Midterm Exam 1 2018 How To Use It

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

WEEK 7, Feb 19-23 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
Maple Lab 2 Newton Cooling (pipes or swamp) due this week.
Thursday Problem Session 12:55pm blackboard photo directory
 Maple, MuPad, Matlab examples Click Here
Quiz7 is an extra credit quiz, due to Exam 1:  Take-home Quiz7 and Sample quiz7
Homework HW7 due Friday of week 8.

WEEK 8, Feb 26 to Mar 2 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 5-9 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 12-16 Lecture details
=======
Maple Labs 3 and 4, Tuesday session in LCB115 for 30 min:
   maple Lab 3 laplace due Friday Week 12 (week after Spring Break)
   maple Lab 3 laplace, maple text for mouse-paste.
   maple Lab 4 resonance due Friday Week 12
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.

Quiz10 Sample with interleaved solutions.
Take-home  Quiz10 and Homework HW10 due Friday after Spring Break.

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

Two week warning: Midterm Exam 2 on Friday 30 Mar
Study for Midterm 2 on Mar 30: Sample Exam 2 Problems and solutions
Study for matching content Old Exam 2 Problems and solutions (2017)
Exam 2 will cover topics from week 6 to Friday of week 10. Only topics on the sample exam will appear on Exam 2.

WEEK 11, Mar 17-25 is Spring Break. No classes.
=======
No Lab. No Quiz11. No HW11.
Maple, MuPad, Matlab code examples PDF

Calendar for Weeks 12-17 (Mar 26 to Apr 24)

WEEK 12, Mar 26-30 Lecture details
=======
5.5; matrix exponential, Putzer algorithm, fundamental solution

Quiz12 Sample and Sample Solutions
Take-home Quiz12 and Homework HW12 due Monday 9 April
    Maple references for Exercises 6.3-4,5,6,7: PDF and WORKSHEET
    Maple reference for Exercises 6.3-8,9,10: PDF and WORKSHEET
Exercises Edwards-Penney Chapter 5 Fourth Edition

Thursday Exam Review 12:55pm blackboard photo directory, Exam 2 review
Study for Midterm 2 on Mar 30: Sample Exam 2 Problems and solutions
Study for matching content Old Exam 2 Problems and solutions (2017)

Friday 30 Mar: Midterm Exam 2 at 12:50pm until 1:50pm, over weeks 6 to 11
      2018 Midterm 2: Exam 2 Problems and answers (Posted after the exam)

WEEK 13, Apr 2-6 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
Computer Lab 5 details
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
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 13 April
Study S2018 Sample Exam 3 questions and answers.
Study matching content Old Exam 3 Statements and handwritten solutions (Spring 2016)

No take-home quiz this week or next.
Homework HW13  due May 7.
Extra Credit Labs due May 7. See Extra Credit PDF Sources

WEEK 14, Apr 9-13 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 7.

Thursday Exam Review 12:55pm blackboard photo directory
Study S2018 Sample Exam 3 questions and answers.
Study matching content Old Exam 3 Statements and handwritten solutions (Spring 2016)

Friday, 13 April, Midterm Exam 3 at 12:50pm until 1:50pm, over weeks 11 to 13.
2018 Midterm3: Exam 3 Problems and answers (Posted after the exam)

WEEK 15, Apr 16-20  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 May 7 under the door JWB 113.
Study the Sample Final Exam Questions and Answers and Short Sample with answers
Study the Final Exam Study Guide
Old Final Exam problems and student solutions 2017, PDF at this LINK
Old Final Exam problems and typeset solutions 2016, PDF at this LINK

Thursday Problem Session and Exam Review 12:55pm blackboard photo directory


WEEK 16, Apr 23-24 Lecture details
=======
Sample Final Exam. Covers Chapters 1 to 9, skip Chapter 8.
Comprehensive Final Exam review starts on Tuesday.
Study the Sample Final Exam Questions and Answers and Short Sample with answers
Study the Final Exam Study Guide
Old Final Exam problems and student solutions 2017, PDF at this LINK
Old Final Exam problems and typeset solutions 2016, PDF at this LINK

Final Exam Review sessions blackboard photo directory (25 Apr 4:30-6:30pm)

WEEK 17
=======
Final Exam Review Wednesday 25 Apr in LCB 219 4:30pm to 6:00pm

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

Finals week: Comprehensive final exam, Friday April 27,  12:45pm to 3:15pm in LCB 219
Extra credit homework and labs due by 6pm, under the door 113 JWB, May 7.
Homework HW15 due by 6pm, under the door 113 JWB, May 7

2018 Final Exam Questions with student solutions (posted after the exam)

Maple, Matlab and Mathematica Tutorials

Sample Maple Code for 2280
The Maple Directory contains worksheets plus copy-and-paste text maple source code, identified by file extensions MW, TXT or MPL.
Click here for maple directory LINK

Maple, MuPad, Matlab command examples. Click here for PDF
Starting Maple, MuPad, Matlab from a remote terminal login with non-graphical text interface. Click here for TEXT
Maple Tutorials
  1. Utah Maple tutorial 2018 in html format. Includes Setup and First Use.
    Used in LCB115 maple intro lectures.
    Click here for HTML
  2. How to use maple 9.5 to 2017 under unix, windows, OS/X.
    Click here for TEXT
  3. Maple graphics and low speed internet, Maple at Home.
    Click here for TEXT
  4. Maplesoft Quick Reference Cards Click Here
  5. Douglas Meade's Quick Reference Card for Maple 12 to Maple 2017. Click here for PDF
  6. A rookie maple tutorial (also Matlab and Mathematica) for the impatient from Indiana University Click Here
  7. Maple programming examples by topic from Kettering University Click Here
  8. Peter Stone's Maple Resource page for undergraduate math topics Click Here
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. Utah has a Matlab 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: How to use it, click here for TEXT
Mathematica Tutorials
  1. Printed or free PDF tutorials on special topics are available at Wolfram Research: HERE
  2. New users can start with John McLoone's YouTube video (2010) 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

Homework Problems, Maple Labs, Thursday Problem Sessions

Problem Notes, Extra Credit Problems

Exam Samples and Exam Solution Keys

Contact Information and Written Reports

Previous 2280 Courses

Link to Department of Mathematics, University of Utah