## Maple Release 5 - Differential Equations- Math 3130

EXTRA CREDIT - Extra Credit will be granted to those who find errors in a Maple command within any Maple Worksheet One extra credit per error (whoever is first).

### Dr. Sarah's Maple Demos

Demo 1 Wed, January 13th
Demo 2 on y'=y^2-4, Fri, January 15
Demo 3 on exact DEs, Fri, Jan 28
Demo 4 on the Cooling Experiment of Cafe au Lait versus Black Coffee, Wed, Feb 23
Demo 5 on Numerical Methods
Demo 6 on Maple's Built in Numerical Methods
Demo 7 on 4.6 and 4.7, Fri, March 31.
Maple Commands
Demo 8 on 5.1, Wed, April 5
Demo 9 on 5.2, Fri, April 7
Demo 10 on 5.3, Wed April 12
Demo 11 Parachute, Wed April 19
PSD Solutions
Demo 12 on 5.4, Fri April 21
Demo 13 on Laplace, Wed, May 3

### Highlights from Class

• Mon, Jan 10 - Intro to DEs, velocity and acceleration, separable des, dependent and independent variables, solving for constant using initial condition, p. 32 number 16, method of substitution, integration by parts (Int v du = uv - Int u dv), 2.1-2.2 HW Read 2.1 and 2.2, p. 32 18, 19, and 20.
• Wed, Jan 13 Proof that the method of separability works, method of partial fractions, go over syllabus and web pages, assign groups and a problem from 33-37 for each group, pass out roach assignment, begin Maple Demo 1 HW for Fri Book p. 32 17, 21, Maple manual read p. 41-44.
• Fri, Jan 15 - Groups meet each other to arrange meeting times to work on presentation of their problem, Maple Demos 1 and 2 HW Roaches due Fri 22 at 5pm, For Mon, Jan 25, do the following DE's by hand: 1) y'=xe^x, 2) y'={2x^2+3x+3}/(x+1)^3, 3) y'= {4x-7}/{x^2-3x+2}. Review Demos 1 and 2, Prepare a presentation on p. 34 33-37.
• Mon, Jan 18th MLKJ Holiday
• Wed 20th, and Fri 22nd, No Class due to Conference - Roaches Due Fri 5pm 326 Walker
• Mon, Jan 24 Group Presentations on 33-37, review half of demo 1, gave hint on #2 from Fridays HW. HW for Wed Review Demos 1 and 2 again, revisit Fridays DE's by hand with #2's hint.
• Wed, Jan 26 Go over demos 1 and 2, students present de hw, HW for Fri Review demos 1 and 2 again, break up into groups of 2 or 3 for Maple Project 1 (see main web page under Writing/Maple Projects and Tests). , and groups of 2 for Maple Project 2.
• Fri, Jan 28 Intro to exact des via p. 41 # 24. Demo 3, HW for Mon p. 41 #20 and 21, and review Demo 3.
• Mon, Jan 31Students present HW, Review Demo 3 on exact DEs, Intro to 1st order linear equations via example p. 48 #9 , HW for Wedp. 48 1-4, 10, 11.
• Wed, Feb 3Students present HW, Proof that 1st order linear works, intro to homogeneous equations via p. 62#10, learn how to submit Maple files from 203. HW for Frip. 62 9,16, p. 65 32,33,36,38.
• Fri, Feb 5Students present HW, Learn how to submit Maple files from 203(Only 10 are allowed to connect at any given time). On Maple in groups of at least 2, do p. 65 #32,33,36,38 and compare to by hand work (write text comments about the comparisons and make sure that all of your names are at the top of the Maple document. SAVE OFTEN to the public saves folder or your disk). Submit completed Maple sheets onto my computer to ONE of your group member's folder.
• Mon Feb 7Section 3.2 Compartmental Analysis and Population Models. Break up into groups- HW for WedEach group works on one of p. 81 1,2,5,6,7,8, 9, 14, 17, 19, 23, 24. Work on Project 2 due next Tuesday at 5pm.
• Wed Feb 9 Create Maple Worksheet for your group problem from Wed. Discuss problem, explain set-up in detail, and compare the Maple solution to your solution by hand. Submit your work to my computer as page81#.mws (ie page812.mws would represent problem number 2 on page 81). into one of your group member's folders. HW for Fri Look at the problem solutions for p. 81 Extra Credit - which takes less time to boil? Hot or cold water? For EC, (due Friday) write up your experiment and the results. Number 1, Number 5, Number 6, Number 7, Number 8, Number 9, Number 14, Number 17, Number 19, Number 23, Number 24.
• Fri, Feb 11Intro to Heating and Cooling via which boils faster - hot or cold water? Peer review of Wed's Maple worksheet. HW for Monp. 90 #14
• Mon, Feb 14Meet by 3rd floor elevators. CBL unit coffee cooling experiment
• Wed, Feb 16Presentations on Maple Project 2 from Problem Set B:
Number 2 and Review Comments for Keith and Sarah, Number 2 and Review Comments for Jon T and Anthony, Number 3 and Review Comments for John C and Katie M, Number 6 and Review Comments for Chris and Gabriel, Number 9 and Review Comments for Katie C and Amanda, Number 10 and Review Comments for James and Jeremy Peer review of todays presentations and initial impression of worksheets due today at 5 HW for Fri Review Presentations that we did in class, and start studying for test 1 (see below).
• Fri, Feb 18 Presentations Continued Number 11Number 11 and Review Comments for Andrew and David, Number 12 and Review Comments for Kate H and Love, Number 13 and Review Comments for Stephen and Eric, Number 14 and Review Comments for Melinda and Byron, Number 15 and Review Comments for Rebekah and Calman, Number 16 and Review Comments for Michelle and Gabe Peer review of todays presentations and initial impression of worksheets due today at 5
Discuss Presentations. HW for Mon Go over all presentations and study for test 1.
• Mon, Feb 21 Discuss Presentations via questions and comments from students, Newtonian Mechanics HW for Wed Do assigned problem from Newtonian Mechanics section p. 96 1,2,5,6,7,8,9,10,12,13,18,21.
• Wed, Feb 23 Demo 4 on Coffee Cooling, create worksheet on problem from Mon.
Page 96 number 1 Anthony and Jon T
Page 96 number 2John C and Sarah
Page 96 number 5Katie M and Calman
Number 6 had an error in the initial de, so I've left it off
Page 96 number 7Katie C and Amanda
Number 8 had no comments in it, so I've left it off
Page 96 Number 9Kate H and Love
Page 96 number 10 Keith and Michelle
Page 97 number 12Stephen and Eric
Page 97 number 13James and Jeremy
Page 97 number 18Rebekkah and Melinda
Page 98 number 21 Gabe
• Fri, Feb 25 Review Demo 4, Review Newtonian Mechanics
• Mon, Feb 28 Test 1 - by hand. 1 8.5 by 11 sheet with writing on both sides allowed. Study Maple Project 1 and 2, material we covered in class, maple demos 1-4 and hw. Topics to study: separable, exact, 1st order linear and homogeneous, compartmental analysis, population growth, heating and cooling, and newtonian mechanics.
• Wed, March 1Hand out next problem from Set C, due next Tues at 5 (presentations start Wed), Demo 5 on Numerical Methods. HW for Fri Review Demo 5, read p. 99-117 in textbook.
• Fri, March 3Demo 6 on Numerical Methods.HW for Mon Review Demos 5 and 6 and bring a printout of them to Monday's class, skim p. 99-117 in the textbook, work on Maple Project C.
• Mon, March 6Review Demos 5 and 6 and elaborate on the differences in the various numerical methods.HW for Wed Review Demos 5 and 6 again, prepare for presentations.
• Wed, March 8PresentationsDr. Sarah's Comments are on WebCT
C1 by Stephen and Andrew
C4 by Anthony and Jon T
C5 by Calman and John C
C6 by Eric and Byron
C7 by Michelle and Gabe
C8 by Chris and Gabriel
C9 by Katie C and Amanda
C10 by Katie M and Sarah
C12 by James and Jeremy
C13 by Keith and David
C14 by Melinda and Rebekah
C15 by Kate H and Love
• Fri, March 10PresentationsHW for spring break Review Presentations and study for test 2 on numerical methods. Be sure that you know
Demos 5, 6 the presentations and class discussions
how to save to the public saves folder
how to submit files to your folder on my computer
by hand methods from test 1
analysis of d.e. using function techniques (as in B 10).
the difference between Euler, Improved Euler and Runge Kutta in demo 5
general Maple techniques that we have used regularly since the begining (you may wish to review all the Maple demos) - (unapply, dsolve, rhs, display, plot, fsolve, textcomments in Maple).
• Mon, March 20Review Demo 6
• Wed, March 22Finish reviewing example 7 in demo 6, quiz on test 1 material, go over WebCT bulletin boards and presentation comments on the bulletin boards under the Forum Maple Project C.
• Fri, March 24 Test 2 on Numerical Methods HW for Mon post a MATH comment about the extra credit on the test onto the bulletin board under the Forum Maple Test 2 on Numerical Methods.
• Mon, March 27Give out hints for test revisions, and return tests, go over 2nd order linear d.e.s, discuss the differences between homogeneous first order d.e. (y'=f(y/x)) and homogeneous 2nd order d.e. (y''+p(x)y'+q(x)y=0). For this next chapter, homogeneous will always means for 2nd order d.e. (y''+p(x)y'+q(x)y=0). Proved that if y1 and y2 are solutions to a 2nd order homogenous d.e., then c1 y1 + c2 y2 are also solutions to the d.e., for any real c1 and c2. HWWork on test revisions due Mon april 2nd at 5pm.
• Wed, March 29 Class notes and HW are under COURSE CONTENT(click on Wednesday, March 29 and then use the "pg fwd" button to proceed to the other pages - there are four pages total) at WebCT . If you are confused about how to get there, or how to maneuver the pages, see Directions for WebCT
Office hoursWed 9:30-10, 3-5:30, Thur 11-1,2:45-4, Mon,April 3 9:30-10,12-1,3-5:30, or by e-mail or the bulletin board.
HW for FriSee the last course content page under webct - post answers (see my directions!) to one oftextbook p. 146 7-12, and also take the webct quiz.
• Extra Credit Opportunity for Thurday 4-4:45 Colloquium on 3rd floor WalkerDr. Eric Marland is a job candidate doing research in des related to cells (ie biology) - his talk should be accessible to you-
• Fri, March 31 Maple Demo 7 on 4.5 and 4.6HW for Mon textbook p. 158 15-18, p. 165 21-22. Post your work on the even numbers to webct under the Forum - Second Order Linear, Test 2 revs are due Monday. I will be answering bulleting board questions over the weekend!
• Mon, April 3Proof that the 2nd order linear procedure works
• Wed, April 5 Demo 8 on Section 5.1, Maple Command SheetHW for Fri at 5pm One problem assigned to your group turned in as a Maple Worksheet to my computer. Your solution should contain the problem statement, and an explanation of your work.
• Fri, April 7 Review the First Part of Demo 8, Spend 5 minutes on Example 2 of demo 8, and then Demo 9 on Section 5.2. HW for Mon Review Maple Worksheets from p. 203, review demos 8 and 9. Forget about p. 210!
203 num 1 by Love, Kate H, and David
203 num 2 by Amanda, Katie C, and Eric
203 num 3 by Rebecca, Melinda and Andrew
203 num 5 by Gabe, Gabriel, and Chris
203 num 6 by Calman, John C and Katie M
203 num 7 by Keith, Michelle and Sarah
203 num 8 by James, Jeremy, Anthony and Jon T.
• Mon, April 10 Non-homogeneous 2nd order linear differential equation solutions HW for Wed Find every solution to Ex 1-4 (ie homog parts and add them to the particular solution), and First posted on Forum "Section 4.8", first served choose 1 problem in section 4.8 to do by hand and then post your work on the WebCT bulleting board Forum "Section 4.8". Your posted problem must be different from all the other posts, so you must read the other post subjects to do this. In the subject line of the post, place the page and problem number
• Wed, April 12 Demo 10 on Section 5.3 HW for Mon PS D 3-7, Review demos 8, 9 and 10 which will consist of the bulk of test 3, if you haven't already scored a perfect score on both webct quizzes, take the quiz over again until you have.
• Fri, April 14 Use class time to do research for your final project proposal, which is due NEXT Fri. I will be answering WebCT bulleting board questions on Problem Set D Forum or other quesions Thur-Sun (hopefully at least once a day).
• Mon, April 17 Review by hand parts of demos 8, 9 and 10 HW for WebReview demos 7-10, work on Final Project Proposal, Look at Review Sheet for Test 3 on WebCT under "course content", look at revised Maple Command Sheet (see list of demos at the top of this page).
• Wed, April 19 Demo 11 on Parachute Problem HW for FriLook at PSD Maple Solutions and Review Parachute Problem, Bring textbook to class on Friday
• Fri, April 21 WebCT quiz 3, Demo 12 on Electric Circuits. HWReview for Test 3.
• Mon, April 24 Easter Break
• Wed, April 26 Review of Demos
• Fri April 28 Test 3 on Maple
• Mon, May 1 Laplace By Hand
• Wed, May 3 WebCT quiz 4, hand out Laplace notes, and Laplace Demo 13
• Wed, May 10 3-5pm Party and Final Project Presentations in 203
Maple worksheet on your final project due onto my computer by Wed at 2:30 pm, bring your own drinks to 203
Your Maple worksheet should include all of your work, with detailed explanations (ie it should be self explanatory). Your presentation will summarize highlights of your project -
2 person group should have less than an 8 minute presentation,
1 person should have less than a 4 minute presentation
Be sure to include references
Amanda and Katie C on the Eiffel Tower
Rebekah and Melinda on Newton's law of cooling on ordinary household objects
James on Skateboarding
David on the bouncing of a ball
Calman and John C on the collapse of the Tacoma Narrows Bridge, as modeled by a second order de
Anthony on modeling the forces on a wrist pin of an Internal Combustion Engine
Kate H and Love on world population and resource consumption
Michelle on radioactive decay of barium 137
Stephen on Equations of Motion of a Projectile in a Variable Density Atmosphere.
Keith on Aids and HIV statistics
Andrew on resonance in a guitar string
Jon T on projectile motion
Eric on DE Exploration of Solar Development
Gabe on US population
Chris and Gabriel on snow hare population
KatieM and SarahT's project on ozone depletion