Math 2280-2 | Spring 2018, Differential Equationsggustaf@math.utah.edu |

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 MTWF, 12:55pm, in LCB 219 and Thu 12:55 in LCB 225 for a problem session.
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 Monday 30 April |

Textbook | ggustaf@math.utah.edu
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 |

#### 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 equationFirst ExerciseDetailsHere. Submit Exercise 1.2-2 on Wed Jan 10 for review. Returned with comments on Thu Jan 11 or Fri Jan 12. 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 Examplesggustaf@math.utah.edu Lecture details ====== Monday Holiday, Martin Luther King. No classes. 1.5; linear differential equation 3.7; LR and RC circuits Computer Lab 1 details. First Lab session is Tuesday Week 4. Intro Maple Lab 0 is a typing lesson due Week 5. 2.1; mixture model, Malthus and Verhulst models, cascades and compartment models Quiz2 Sample and Solutions with graphs Take-home Quiz2 and Homework HW2 due Friday next week but collected the next Monday. Reference: Quiz2 problem session from 2015. Photo Directory Here Thursday Problem Session Photo Directory Click Here WEEK 3, Jan 22-26 Examples Lecture details ====== 2.2; autonomous u'=f(u), equilibrium solution, stability, harvesting 2.3; velocity, acceleration, Newton air resistance models maple Lab 1 quadratics and Jacobians due Week 6 Numerical Project HW3, a maple project, is due Week 7. There is no Lab on ch 2 numerics. Quiz3 Sample and Solutions Take-home Quiz3 due Friday next week but optionally collected the next Monday. This is a calculator project, no computer needed. Homework HW3 is the Numerical Project PDF here, due Friday Week 7 (Feb 23)ggustaf@math.utah.edu Numerical maple and matlab resources Directory Here Thursday Problem Session Photo Directory Click Here WEEK 4, Jan 29 to Feb 2 Lecture details ====== 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 3.1; second order linear equations, Euler solution atoms 3.3; homogeneous constant-coefficient equations, Euler substitution, Euler solution atoms Tuesday is the Intro Maple Lab 0 and Maple Lab 1 day. Start in LCB 219, then move to computer classroom LCB 115 at 1:00pm. Quiz 3 is due this Friday (issues? submit on Monday). HW3 is not due this week, but Friday of Week 7, because it uses computers. Quiz4 Sample and Solutions Quiz4 resource on Picards's Theorem Take-home Quiz4 and Homework HW4 due Monday Feb 12 [were Due Fri Feb 9] Thursday Problem Session Photo Directory Click Here WEEK 5, Feb 5-9 Lecture details ====== 2.6; Runge-Kutta method, RK4 Numerical methods, third lecture about the proofs. 3.2; general solution, Picard theorem, independence, Wronskian, superposition 3.1-3.3 Continued. Independence. Wronskian Test. 3.4; mechanical vibrations 3.7; LRC model Computer Lab 2 details Intro Maple Lab 0 due this week Quiz5 Sample with solutions Take-home Quiz5 and Homework HW5 due Friday next week, collected Tuesday 20 Feb. Maple, MuPad, Matlab examples PDF Thursday Problem Session Photo Directory Click Here One week warning:Midterm Exam 1on Friday 16 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 ====== 3.4; mechanical vibrations, continued: Beats 3.5; mechanical models, forced equations, undetermined coefficients, variation of parameters Quiz6 Sample with solutions and the network problem Solution Take-home Quiz6 and Homework HW6 due Friday next week, collected Monday 26 Feb. Friday, 16 Feb,Midterm Exam 1at 12:50pm until 1:50pm, over weeks 1 to 5 Study Sample Exam 1 (2018) with solutions Thursday Exam Review Blackboard Photo Directory Midterm Exam 1 2018 Problems and Solutions (Exam 1 solutions posted 21 Feb 2018) Convert exam scoring letter grades to demerits: Click Here Maple from home, UofU Library Remote Maple 18 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. 3.5; Examples: beats, undetermined coefficients, variation of parameters 3.6; mechanical resonance 3.7; electrical resonance 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 Maple Lab 2 Newton Cooling (pipes or swamp) due Monday March 5. Thursday Problem Session 12:55pm blackboard photo directory No one attended, no photos. Maple, MuPad, Matlab examples Click Here Extra-Credit Take-home Quiz7 and Sample quiz7; Quiz7 due by Apr 30. Take-home Quiz6 and Homework HW6 will be collected Wednesday 28 Feb. Homework HW7 due Friday March 9. Due Friday 23 Feb: Homework HW3, the Numerical Project PDF here 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] 7.3; partial fractions, Heaviside's method, shift theorem 7.4; convolution, s-derivative theorem, t-integral theorem 7.5; unit step, pulse, ramp, periodic function theorem Quiz8 Sample with interleaved solutions. Take-home Quiz8 and Homework HW8 due Friday Week 10. No Thursday problem session 12:55pm this week blackboard photo directory Due Wednesday 28 Feb: Take-home Quiz6 and Homework HW6 Lab day Feb 27 in LCB 115 (20 min): Maple Lab 2 Newton Cooling. Choose one: pipes or swamp maple Lab 2 freezing pipes due Mar 5 maple Lab 2 swamp cooler due Mar 5 if pipes not selected NO CLASS Thu-Fri March 1 and 2 WEEK 9, Mar 5-9 Lecture details ====== 7.3: 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 5.3; mechanical systems Mx''=Kx, railway cars, resonance Computer Lab 3 and Lab 4 details maple Lab 3 laplace due Friday Week 12 (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 Maple2017 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 14. Thursday Problem Session 12:55pm blackboard photo directory Due Monday March 12, Homework HW7 Due Monday of week 13, after Spring Break: Quiz8 (Linear DE, Laplace table),Maple Lab 3, 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 13 7.6; Dirac impulse, hammer hit model, unit impulse response, unit step response 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: 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 Computer Lab 3Laplacedue this week. Quiz10 Sample with interleaved solutions. Take-home Quiz10 and Homework HW10 due after Spring Break in Week 15. Thursday Problem Session 12:55pm blackboard photo directory, problems 1, 7 on Sample Midterm Exam 2.Two week warning: Midterm Exam 2on Friday 30 Mar Study for Midterm 2 on Mar 30: 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 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 ======= REF: Manuscript: Examples of Systems of Differential Equations 4.2; Cayley-Hamilton-Ziebur method (Example 4.2-1), Elimination method, Cayley-Hamilton theorem. 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 and Eigenanalysis Quiz12 Sample and Sample Solutions Take-home Quiz12 and Homework HW12 due Friday 20 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 (photos and references for Exam 2) Study for Midterm 2 on Mar 30: Sample Exam 2 Problems and solutions REF: Midterm 2 problems and typeset solutions 2017, PDF at this LINK (edited 29 March 2018) 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 REVIEW SESSION 29Mar2018, REPLICA of Exam 2 questions 1-5 LINK Friday 30 Mar:Midterm Exam 2at 12:50pm until 1:50pm, over weeks 6 to 11 2018 Midterm 2: Exam 2 Problems and answers (Posted April 4, 2018) No work due this week due to the exam. Due Monday week 13: Quiz8 (Linear DE, Laplace table), Maple Lab 3, HW8 (Ch 7 Ch4 problems). WEEK 13, Apr 2-6 Lecture details ======= Exam 2: REF: Slides: partial fractions: atoms, sampling, Heavide cover-up 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] 5.6; vector-matrix variation of parameters, 3-tank brine cascade REF: Slides: Matrix Exponential, Putzer Algorithm, Var Parameters 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 Thursday Problem Session 12:55pm blackboard photo directory One week warning:Midterm Exam 3on Friday 13 April Study S2018 Sample Exam 3 questions and answers. Study matching content Old Exam 3 Statements and handwritten solutions (Spring 2016, edited 2018) No take-home quiz this week or next. Homework HW13 due May 7. Extra Credit Labs due May 7. See Extra Credit PDF Sources Due Monday April 9: HW9 plus maple Lab 4. Quiz 9 is extra credit due by May 7. WEEK 14, Apr 9-13 Lecture details ======= 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 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 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 No Take-home Quiz this week. Homework HW14 due May 7. Thursday Exam Review 12:55pm blackboard photo directory (uploaded Thu 12 April) 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 3at 12:50pm until 1:50pm, over weeks 11 to 13. 2018 Midterm3: Exam 3 Problems and answers (Posted after the exam) Due Monday Week 15: Quiz 10 and HW10. All other Quizzes and HW due by May 7. There is no Quiz 11 or HW11 [Spring Break week]. WEEK 15, Apr 16-20 Lecture details ======= 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 Inner Product Spaces, orthogonal sets, special computations for Fourier coefficients. Shadow Projection formulas for orthogonal series. REFERENCES: Slides: Orthogonality and Manuscript: Inner Product Spaces 9.5; ice-pack ends. Dirichlet problem. Examples in Maple: DIRECTORY Homework HW14 due by May 7 under the door JWB 113 (last HW). Maple Lab 5 Brine Tanks due by May 7 under the door JWB 113 (last 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 Take-home Quiz12 and Homework HW12 due Friday 20 April Thursday Problem Session and Final Exam Review 12:55pm blackboard photo directory WEEK 16, Apr 23-24 Lecture details ======= 9.6; Finite string equation in one dimension. 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 apr26wavemaple.mw Sample Final Exam. Covers Chapters 1 to 9, skip Chapter 8. Comprehensive Final Exam review started last Thursday 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 sessions blackboard photo directory (25 Apr 4:30-6:30pm in LCB 215: photos uploaded 26 Apr) Final Exam Review 2280 offer from SIAM Chapter Utah Math HERE (Free help LCB215 11:30-1:00 April 24 from PhD math students) WEEK 17 ======= Final Exam Review Wednesday 25 Apr in LCB 215 4:30pm to 6:00pm Final Exam Review sessions blackboard photo directory Shortened sample final exam Questions and Answers Finals week: Comprehensive final exam, Monday April 30, 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 72018 Final ExamQuestions S2018 with student solutions (posted May 7, 2018)

#### 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

**Utah Maple tutorial 2018**in html format. Includes Setup and First Use.

Used in LCB115 maple intro lectures.

Click here for HTML- How to use maple 9.5 to 2017 under unix, windows, OS/X.

Click here for TEXT - Maple graphics and low speed internet, Maple at Home.

Click here for TEXT - Maplesoft Quick Reference Cards Click Here
- Douglas Meade's Quick Reference Card for Maple 12 to Maple 2017. Click here for PDF
- 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
- 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. 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

- 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