MTH 306

Grades

Grades
Final Exams can be picked up from an envelope taped to my office door. Please check grading and gradesheet. Let me know of any errors right away.
Happy Holidays!

Last words

Final Exam Solutions
You may bring one (1-sided) 8.5"x11" sheet of notes to the Final Exam.
I will hold a final "office hour" on Monday, December 16, from 1-2pm in Math. Bldg., Room 250.
Keep an eye on the website in case I decide to give any last-minute hints for the Final Exam.
Also check the GRADESHEET ASAP for correctness of your scores, especially where corrections were requested: let me know right away if any changes are needed.
The Final Exam is Wednesday, December 18th, 11:45am-2:45pm, in Fronczak 422. Good luck on all your Finals!

Homework Assignments

HW#12, due at the beginning of class Thursday, Dec 5, 2002.Solutions
HW#11, due at the beginning of class Tuesday, Nov 26, 2002. Solutions
HW#10, due at the beginning of class Tuesday, Nov 19, 2002. Solutions
HW#9, due at the beginning of class Tuesday, Nov 12, 2002. Solutions
HW#8, due at the beginning of class Tuesday, Nov 5, 2002. Solutions
HW#7, due at the beginning of class Tuesday, Oct 29, 2002. Solutions
HW#6, due at the beginning of class Tuesday, Oct 22, 2002. Solutions
HW#5, due at the beginning of class Tuesday, Oct 8, 2002. Solutions
HW#4, due at the beginning of class Thursday, Oct 3, 2002. Solutions
HW#3, due at the beginning of class Thursday, Sep 19, 2002. Solutions
Note typo in HW#2: I meant 1.6.36, not 1.6.46. Because of this typo, this problem will not be graded.
HW#2, due at the beginning of class Thursday, Sep 12, 2002. Solutions
HW#1, due at the beginning of class Thursday, Sep 5, 2002. Solutions
Preview of all the Homework

2nd Project Notes

If you're looking for an example of how to do Euler's method for a system, see the Van der Pol example worksheet further down this page.
I will be available Wednesday, Nov 27, from 12:30-1:30pm. Call 645-6284 ext 147 if Math Bldg doors locked.
Also Monday, Dec 2, 12:30-1:30pm as usual.

Homework Grade sheet

Grade sheet.
Note: I may have HWs 4 and 5 reversed.

Laplace transform method with Maple

laplace_exercise.mws

Plotting level curves of a function with Maple

2nd projects

If you have not signed up for a 2nd Project please do so immediately. If you have signed up, you should already have received a partnership assignment (if you indicated a preferred group and haven't heard from me, it means your group is OK.)

Lorenz system

Lorenz system.

Tests

Final Exam is Wednesday, December 18th, 11:45am-2:45pm, in Fronczak 422.
Test #2 is Thursday October 31st. Solutions
Coverage is all of Chapters 2 and 3 (excluding 3.8).
You may bring one 8"x5" index card of notes with you to the Test.
No calculators allowed.
Test #1 Solutions

Repeated eigenvalue issue

The book is correct. The missing piece of information was that for a matrix with a repeated eigenvalue, (A - lambda I)^2 = 0 (the zero matrix). See Ex. 16, p314.

Section 5.1. Linearization

vanderpol.mws
vanderpol_linearized.mws

Mixing sin and cos

sinpluscos.mws

3D linear examples

3D_examples.mws

Labs

Lab 1: Coffee cooling
Lab 2: Slope fields with Maple
Lab 3: Euler's method with Maple
Lab 4: Bifurcation in fishery model
Lab 5: Parametric curves in the plane
Lab 6: Oct 1 & 3 in Park & O'Brian
Lab 7: Oct 8 & 10 in Hochstetter 139.
Lab 8: Oct 15 & 17 in Park & O'Brian. (Develop TD diagram.) Solution.

Maple Guides

The HTML files can be opened with any browser. You need Maple to open the mws files.
Maple as calculator: HTML, mws.
Maple for Ch. 1 slope fields: HTML, mws.
Maple as analytical tool: HTML, mws.
Maple for Ch. 2: HTML, mws.
Maple as programming language: HTML, mws.
Maple for pictures: HTML, mws.
Maple for 3D pictures: HTML, mws.

My Office Hours

Me: Mondays 12:30-1:30pm, and by appointment.
TA: Jemal Mohammed-Awel, jemalm@acsu.buffalo.edu, Math Bldg 138, 645-6284 ext. 169.

Projects are due Tuesday, Oct 15

I have now e-mailed partner assignments to everyone who signed up and did not select their own partners.
Get to work ASAP. Let me know if you are unsure about anything.
Air Friction:
1 coffee filter 0.6g 1 penny 2.5g
Note that the "k"s in the two friction models are different constants. Maybe we should call them k₁ and k₂.
Also note that the integral of 1/(a²-x²) is (1/a)tanh^-1(x/a).

Competing species model

A solution curve that goes near the unstable co-existence equilibrium (1,1), and then veers off towards the equilibrium at (0,3):

Van der Pol oscillator: xy-plane, and x vs. t and y vs. t

Click this: for Maple worksheet that shows the solution curve in 3D (x,y,t)-space.

Vector field and direction field plots for 2D autonomous systems

Maple worksheet

Help Center, Math Bldg 110

The Math Dept. runs a Help Center in Room 110.
The staff is guaranteed competent up through Calc III, but many of the staff will do an excellent job with 306 too. The schedule is below. If you report back to me about who among the staff you've found to be good for 306, I will mark the schedule accordingly so everyone can know.

Labs

Week 4: Labs of Sep. 17&19 will be in Park 440 and O'Brian 212 respectively.
Week 3: Labs of Sep. 10&12 will be in Hochstetter 139.
Week 2: Labs of Sep. 3& 5 will be in Hochstetter 139.
Week 1: Labs of Aug. 27&29 will be in Park 440 and O'Brian 212 respectively.

Technical Job Fair, Sep. 25

Euler's method demo

Interactive demo

Apollo 13

Control center

Office Hours

I'll be available in my office, Math Bldg. 206, on Monday from 9 to 9:50am, to help you with any difficulties you might have with the homework due Tuesday.
Oops. Forgot Monday is Labor Day. I'll have another office hour Tuesday 11-11:50am, and postpone collection of HW#1 till Thursday.

Labs, Week 2.

Labs of Sep. 3&5 will be in Hochstetter 139.

Slope field for dy/dt = (y-t)/2

Applications

launch, weather
pollution

Class Handouts

First-Day Handout, Fall 2002 (PDF format)
First-Day Handout, Fall 2002 (HTML format)
Syllabus
Please note that the Labs start in the first week (Aug 27 & 29, 2002).


	Grades Final Exams can be picked up from an envelope taped to my office door. Please check grading and gradesheet. Let me know of any errors right away. Happy Holidays!


	If you're looking for an example of how to do Euler's method for a system, see the Van der Pol example worksheet further down this page. I will be available Wednesday, Nov 27, from 12:30-1:30pm. Call 645-6284 ext 147 if Math Bldg doors locked. Also Monday, Dec 2, 12:30-1:30pm as usual.


	If you have not signed up for a 2nd Project please do so immediately. If you have signed up, you should already have received a partnership assignment (if you indicated a preferred group and haven't heard from me, it means your group is OK.)


	Final Exam is Wednesday, December 18th, 11:45am-2:45pm, in Fronczak 422. Test #2 is Thursday October 31st. Solutions Coverage is all of Chapters 2 and 3 (excluding 3.8). You may bring one 8"x5" index card of notes with you to the Test. No calculators allowed. Test #1 Solutions


	The book is correct. The missing piece of information was that for a matrix with a repeated eigenvalue, (A - lambda I)^2 = 0 (the zero matrix). See Ex. 16, p314.


	Lab 1: Coffee cooling Lab 2: Slope fields with Maple Lab 3: Euler's method with Maple Lab 4: Bifurcation in fishery model Lab 5: Parametric curves in the plane Lab 6: Oct 1 & 3 in Park & O'Brian Lab 7: Oct 8 & 10 in Hochstetter 139. Lab 8: Oct 15 & 17 in Park & O'Brian. (Develop TD diagram.) Solution.


	The HTML files can be opened with any browser. You need Maple to open the mws files. Maple as calculator: HTML, mws. Maple for Ch. 1 slope fields: HTML, mws. Maple as analytical tool: HTML, mws. Maple for Ch. 2: HTML, mws. Maple as programming language: HTML, mws. Maple for pictures: HTML, mws. Maple for 3D pictures: HTML, mws.


	Me: Mondays 12:30-1:30pm, and by appointment. TA: Jemal Mohammed-Awel, jemalm@acsu.buffalo.edu, Math Bldg 138, 645-6284 ext. 169.


	I have now e-mailed partner assignments to everyone who signed up and did not select their own partners. Get to work ASAP. Let me know if you are unsure about anything. Air Friction: 1 coffee filter 0.6g 1 penny 2.5g Note that the "k"s in the two friction models are different constants. Maybe we should call them k₁ and k₂. Also note that the integral of 1/(a²-x²) is (1/a)tanh^-1(x/a).


	A solution curve that goes near the unstable co-existence equilibrium (1,1), and then veers off towards the equilibrium at (0,3):


	Click this: for Maple worksheet that shows the solution curve in 3D (x,y,t)-space.


	The Math Dept. runs a Help Center in Room 110. The staff is guaranteed competent up through Calc III, but many of the staff will do an excellent job with 306 too. The schedule is below. If you report back to me about who among the staff you've found to be good for 306, I will mark the schedule accordingly so everyone can know.


	Week 4: Labs of Sep. 17&19 will be in Park 440 and O'Brian 212 respectively. Week 3: Labs of Sep. 10&12 will be in Hochstetter 139. Week 2: Labs of Sep. 3& 5 will be in Hochstetter 139. Week 1: Labs of Aug. 27&29 will be in Park 440 and O'Brian 212 respectively.


	I'll be available in my office, Math Bldg. 206, on Monday from 9 to 9:50am, to help you with any difficulties you might have with the homework due Tuesday. Oops. Forgot Monday is Labor Day. I'll have another office hour Tuesday 11-11:50am, and postpone collection of HW#1 till Thursday.


	First-Day Handout, Fall 2002 (PDF format) First-Day Handout, Fall 2002 (HTML format) Syllabus Please note that the Labs start in the first week (Aug 27 & 29, 2002).