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

 

Math 2280-1 Spring 2019, 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 2280-1 meets MWF, 8:00am to 9:20am in LCB 215.
Computer Lab at 7:30am in LCB 115 on select Tuesdays.
Problem sessions Tuesdays 8:35-9:25am in JTB 120. Problem Session Dates Here.
Midterm and Final Exams Friday Midterms from 7:30-9:25am on Feb 22 and Apr 5. Final Exam 7:30-10:00am on Tuesday April 30.
Homework Due dates for HW: Jan 25, Feb 15, Mar 8, Mar 22, Mar 29, Apr 12, May 7, in seven (7) packages.
Maple Labs Due dates Feb 1, Feb 15, Mar 1 and May 7, in four (4) packages.
Semester Project Due dates: March 1, April 19 and May 7, in three (3) packages. Project
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 May 2019 at 19:50PM

Calendar for Weeks 1-6 (Jan 7 to Feb 15)

Examples are available for weeks 1,2,3 only.
WEEK 1, Jan 7-11  Examples Lecture details
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First Day Info Here 
Topics in the course Here
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 Details Here.
Submit Exercise 1.2-2 by Fri Jan 11 for review. Returned Week 2 with comments, Wed Jan 16.
Homework HW1 due Friday of Week 3: 25 Jan.
Some solved problems from Edwards-Penney can be found from the 2280 course of Professor Nathan Smale (2015) Here.

WEEK 2, Jan 14-18 Examples Lecture details
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1.5; linear differential equation
3.7; LR and RC circuits
Homework HW2 due Friday of Week 3: 25 Jan.
Computer Lab 1 details. First Lab session is Tuesday Week 4 in LCB 115 at 7:30am. 
  Intro Maple Lab 0 is a typing lesson due the first Friday of February.

WEEK 3, Jan 21-25 Examples  Lecture details
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Monday Holiday, Martin Luther King Day. No classes.
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
  maple Lab 1 quadratics and Jacobians due Feb 15
  Numerical Work HW3, a maple homework, is due Week 6. There is no Lab on ch 2 numerics. 
Homework HW3 is the Numerical Homework PDF here, due Friday Week 6: 15 Feb
Numerical maple and matlab resources Directory Here

WEEK 4, Jan 28 to Feb 1 Lecture details
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2.3; Newton model examples, escape velocity, Jules Verne problem.
2.4, 2.5, 2.6; numerical solution background: Rectangular, Trapezoidal and Simpson rules
2.4; Euler method
2.5; Heun or Modified Euler method
2.6; Runge-Kutta method, RK4
  Numerical methods, proofs.
3.1; second order linear equations, Euler solution atoms
Tuesday is the Intro Maple Lab 0 and Maple Lab 1 day. Meet at 7:30am in LCB 115.
HW3 is due Friday of Week 6, because it uses computers.
Homework HW4 due Friday Week 6: 15 Feb
Intro Maple Lab 0 due this Friday.
Computer Lab 2 details

WEEK 5, Feb 4-8 Lecture details
======
3.3; homogeneous constant-coefficient equations, Euler substitution, Euler solution atoms
3.2; general solution, Picard theorem, independence, Wronskian, superposition
3.1-3.3 Continued. Independence. Wronskian Test. 
3.5; Intro to the method of undetermined coefficients: y'+4y=sin(Pi*x)
  How to find the unique T-periodic solution, T=(2*Pi)/omega=2.
3.1,3.2,3.3; Euler's theorems for construction of an Euler solution atom basis.
3.4; Spring-mass model mx''+cx'+kx=0
3.7; LRC model LI''+RI'+(1/C)I=E'(t)
Homework HW5 due Friday Week 9: 8 Mar. This is only section 3.5.
Maple, MuPad, Matlab examples PDF
No lab or HW due this week. Both HW5 and HW6 have been modified due to the snow day Feb 6.
Tuesday Exam 1 Review Blackboard Photo Directory 

WEEK 6, Feb 11-15 Lecture details
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3.4; mechanical vibrations. Beats and resonance.
3.5; mechanical models, forced equations, undetermined coefficients, variation of parameters
Homework HW6 due Friday Week 9: 8 Mar. Includes snow day delays 3.6, 3.7.
REMINDER: Numerical Homework HW3, source file PDF here, is due Friday 15 Feb.
Tuesday Maple Lab 1: LCB 115 at 7:30-8:25; Math Center at 8:30 until 9:30.
One week warning: Midterm Exam 1 on Friday 22 February over weeks 1 to 5
Study Sample Exam 1 with solutions
(Some topics not on the exam, due to the Feb 6 snow day)
Maple from home, UofU Library Remote Maple 2017 How To Use It

Calendar for Weeks 7-11 (Feb 18 to Mar 22)

WEEK 7, Feb 18-22 Lecture details
======
Monday Holiday, President's Day. No classes.
3.5; Examples: beats, undetermined coefficients, variation of parameters
3.6; mechanical resonance
3.7; electrical resonance
7.1 History of Laplace's quadrature method. Lerch's contribution. Laplace's method solves differential equations.
Maple Lab 2 Newton Cooling (pipes or swamp) due Friday March 1.
 Maple, MuPad, Matlab examples Click Here
 Homework HW7 due Friday Week 11: 22 Mar.
Friday, 22 Feb, Midterm Exam 1 at 7:45am until 9:25am, over weeks 1 to 5
Study Sample Exam 1 (2019) with solutions
Midterm Exam 1 2019 Problems and Student Solutions (posted 25 Feb 2019)
Convert exam scoring letter grades to demerits: Click Here

WEEK 8, Feb 25 to Mar 1 Lecture details
======
7.1; Laplace integral, properties, table, piecewise continuous, existence, Lerch's theorem, inverse Laplace
7.2; derivative theorem L(y')=sL(y)-y(0) and extensions, integral theorem 
7.3; shift theorem
7.4; convolution, s-derivative theorem, t-integral theorem
7.5; unit step, pulse, ramp,  periodic function theorem
Homework HW8 due Friday Week 11: 22 Mar.
Lab day Tuesday Feb 26 in LCB 115 7:30am: Maple Lab 2 Newton Cooling. Choose one: pipes or swamp
  maple Lab 2 freezing pipes due Mar 1
  maple Lab 2 swamp cooler due Mar 1 if pipes not selected

Semester project package 1 due March 1 is postponed until Monday March 4. Only the maple lab is due on March 1.

WEEK 9, Mar 4-8 Lecture details
======
4.1; first order system, brine cascade, spring-mass system, electrical network
4.1; Picard theorem [integrated with Ch 7]
7.2; spring-mass system, modeling
7.3; resolvent identity for systems, partial fractions, Heaviside's method, Resonance
7.5; spring-mass, circuits, second shift theorem
5.1; matrix systems u'=F(u), u'=Au+g(t), superposition, vector-matrix Picard theorem
5.1; Cayley-Hamilton-Ziebur shortcut for 2x2 systems: 2 brine tanks
  Slides: Cayley-Hamilton-Ziebur Method for u'=Au
5.3; mechanical systems Mx''=Kx, railway cars, resonance
7.4 Convolution theorem L(f*g)=L(f)L(g), f*g=int(f(t-x)g(x),x=0..t) = conv. f and g
7.5; Periodic function theorem L(f)=int(f(x)exp(-sx),x=0..T)/(1+exp(-sT), f(t+T)=f(t)
Computer Lab 3 and Lab 4 sources and due dates            
   maple Lab 3 laplace due May 7
   maple Lab 3 laplace, maple text for mouse-paste.
   maple Lab 4 resonance due May 7
   Maple from home, UofU Library Remote Maple2017 How To Use It
Homework HW9 due Friday Week 12: 29 Mar (after Spring Break week 10).

WEEK 10, Mar 9-17 is Spring Break. No classes.
=======
No Lab. No HW.
Maple, MuPad, Matlab code examples PDF

WEEK 11, Mar 18-22 Lecture details
=======
7.5; Impulses, second shifting theorem
Maple Labs 3 and 4, Tuesday session in LCB115 at 7:30am, 8:30 in the Math Center
   maple Lab 3 laplace (revised 19 Mar) due by May 7
   maple Lab 3 laplace, maple text for mouse-paste.
   maple Lab 4 resonance 
   maple Lab 4 resonance due by May 7
   Xcredit maple Lab 5 brine tank due by May 7
   Xcredit maple Lab 6 narrows due by May 7
   Xcredit maple Lab 7 earthquake due by May 7
4.2; Cayley-Hamilton-Ziebur method (Example 4.2-1), Elimination method, Cayley-Hamilton theorem.
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
5.1; Cayley-Hamilton-Ziebur shortcut for 2x2 systems: 2 brine tanks
Slides: First Order Cayley-Hamilton-Ziebur Method for u'=Au
5.2; Eigenanalysis method for u'=Au, brine tank cascades
Chapter 5 maple examples source directory
Homework HW7 due Friday Week 12: 29 March
Homework HW8 due Friday Week 12: 29 March
Homework HW9 due Friday Week 14: 12 April (no HW10, Spring Break)
Homework HW11 due Friday Week 14: 12 April

Calendar for Weeks 12-17 (Mar 25 to May 7)

WEEK 12, Mar 25-29 Lecture details
=======
  REF: Manuscript: Examples of Systems of Differential Equations
4.2; Cayley-Hamilton-Ziebur method (Example 4.2-1)
5.1; Cayley-Hamilton-Ziebur shortcut for 2x2 systems: 2 brine tanks
Slides: Cayley-Hamilton-Ziebur Method for u'=Au
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
Chapter 5 maple examples source directory
5.4; generalized eigenpair, Jordan's two theorems, Cayley-Hamilton
5.4; Brief intro to Jordan form, Jordan chain algorithm
  REF: Manuscript: Jordan Form
  REF: Jordam Form maple examples (see also jordan-form-examples.mw)
Homework HW12 due Friday Week 15: 19 Apr
    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
5.5; matrix exponential, Putzer algorithm, fundamental solution
REF: Manuscript: Matrix Exponential and Putzer Algorithm
REF: Manuscript: Jordan Form and Eigenanalysis
REF: Manuscripts: Systems of Differential Equations [Directory]

Exercises Edwards-Penney Chapter 5 Fourth Edition

Tuesday Exam 2 Review blackboard photo directory, Exam 2 review (photos and references for Exam 2, updated 2apr2019)

One week warning: Midterm Exam 2 on Friday 5 April
Study for Midterm 2 on April 5: Sample Exam 2 Problems and solutions
REF: Midterm 2 problems and typeset solutions 2017, PDF at this LINK
REF: Midterm 2 problems and typeset solutions 2016, PDF at this LINK
REF: Midterm 2 problems and typeset solutions 2015, PDF at this LINK
Exam 2 will cover topics from week 6 to Friday of week 11. Only topics on the sample exam will appear on Exam 2. In particular, only chapters 1 to 5 and 7,
with chapter 6 moved to the final exam.
Due Friday: HW7, HW8. Submit HW9 in Week 14, after Exam 2.

WEEK 13, Apr 1-5 Lecture details
=======
Exam 2: REF: Slides: partial fractions: atoms, sampling, Heavide cover-up
5.6; vector-matrix variation of parameters, 3-tank brine cascade
  REF: Slides: Matrix Exponential, Putzer Algorithm, Var Parameters
Class Apr 3: Putzer and Var Parameters Example and lecture topics Ch5
REF: Manuscript: Putzer Proof
  REF: Slides: systems Eigenanalysis and the 4 methods
  REF: Manuscript: system examples, brine tanks to helicopter logging
  REF: Slides: brine tank and heating examples
6.1; equilibria, stability.
6.2; phase portraits for non-linear systems, Paste Theorem

  REF: Slides: Dynamical Systems Introduction
  REF: Manuscript: dynamical Systems
  REF: Slides: Dynamical Systems Classification
  REF: Slides: Dynamical Systems Phase Portraits
  REF: Slides: Dynamical Systems Stability
                                                           
Friday 5 April: Midterm Exam 2 at 7:30am until 9:25am, over weeks 6 to 11
   2019 Midterm 2: Exam 2 Problems Only (Posted 5 Apr 2019)
   2019 Midterm 2: Exam 2 Problems and answers (Posted 15 Apr)

Homework HW13  due by Midnight 7 May, under door JWB 113
      
Extra Credit Labs due May 7. See Extra Credit PDF Sources

WEEK 14, Apr 8-12 Lecture 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
  REF: Slides: Dynamical Systems Introduction
  REF: Manuscript: dynamical Systems
  REF: Slides: Dynamical Systems Classification and Pasting Theorem
  REF: Slides: Dynamical Systems Phase Portraits and Maple Interactive Plots
  REF: Slides: Dynamical Systems Stability, Jacobian Matrix, Linearized u'=Ju
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
Gibbs overshoot apr15-gibbs-S2017.mw DIRECTORY
Friday 12 Apr 2019 blackboard photos, periodic functions, Fourier coefficients, Gibbs overshoot DIRECTORY
Homework HW14 due by Midnight 7 May, under door JWB 113
Due Friday: HW9, HW11

WEEK 15, Apr 15-19  Lecture details
=======
9.1, 9.2 continued.
  Orthogonality relations for the trig system
  Clasical method to determine Fourier coefficients.
  Inner Product Spaces, orthogonal sets, special computations for Fourier coefficients. 
  Shadow Projection formulas for orthogonal series.
  REFERENCES: Slides: Orthogonality and Manuscript: Inner Product Spaces
  Monday 15 Apr 2019 blackboard photos, Fourier coefficients DIRECTORY
9.3; Even and odd signals, Fourier sine and cosine series, differentiation and integration of Fourier series
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.
  Examples in Maple: DIRECTORY
  Fourier Coefficients, Square wave, inner product space guide PDF SLIDES
  Blackboard photos Wed 17 Apr, Lemma for X''+lambda X=0, X(0)=X(L)=0: PHOTO DIR

Homework HW15 due by Midnight 7 May, under door JWB 113
Xcredit Maple Lab 5 Brine Tanks due by May 7 under the door JWB 113 (Xcredit maple lab).
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

Tuesday Final Exam Review blackboard photo directory (uploaded after the review)
Study the Sample Final Exam Questions and Answers and Short Sample with answers
Study the Final Exam Study Guide
   maple Lab 3 laplace (revised 19 Mar) Due by May 7
   maple Lab 3 laplace, maple text for mouse-paste.
   maple Lab 4 resonance 
   maple Lab 4 resonance due by May 7
   Xcredit maple Lab 5 brine tank due by May 7
   Xcredit maple Lab 6 narrows due by May 7
   Xcredit maple Lab 7 earthquake due by May 7

WEEK 16, Apr 22, 23 Lecture details
=======
LAST DAY: Tuesday 23 April. READING DAY is Wednesday 24 April.
9.6; Finite string equation in one dimension. Methods: Steady-state heat conduction on a plate.
   Reference: Standing Waves on a string Standford Physics Dept 2004
   Reference: Maple worksheet for the wave equation and standing waves apr22wavemaple.mw
Sample Final Exam. Covers Chapters 1 to 9, skip Chapter 8.
Comprehensive Final Exam review started last Tuesday continues on Tuesday-Wednesday. 
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 session blackboard photo directory (23 Apr 8:00-9:25am in JTB 120: photos uploaded after the review)
Outline of the final exam problems: PDF Outline (uploaded Sunday 28 April)

WEEK 17
=======
Finals week: Comprehensive final exam, Tuesday April 30,  7:30am to 10:15am in LCB 215
  See the sample exam outline above uploaded 28 April.
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

2019 Final Exam Questions S2019 with student solutions (posted 7 May)

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 2019 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 2018 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 2018. Click here for PDF
  6. Maple programming examples by topic from Kettering University Click Here
  7. 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, Maple Labs, Problem Notes and Extra Credit

Semester Project

Exam Samples and Exam Solution Keys

Contact Information and Written Reports

Previous 2280 Courses

Link to Department of Mathematics, University of Utah