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Winter 2015: Math/Mech 358, Section 201: Engineering Analysis

`http://www.math.ubc.ca/~coombs/358/math358.html`

Instructor: Dr. Daniel Coombs.

Office hours: Mathematics Annex, Room 1109. TBA and by appointment. I will also usually be available right after class for quick questions.

**Math department tutoring centre** is located in LSK 301/302.

Email: coombs (at) math (dot) ubc (dot) ca

Office phone: 604-822-2859

This course is cross-listed as Mech 358.

**Text:**
There is no required textbook for the course, but the following are recommended.

Elementary Differential Equations and Boundary Value Problems (10th ed.) by
W.E. Boyce & R.C. DiPrima.
The online textbook Diffy Qs by J. Lebl. You can download the book (for free) or order a copy (for cheap) to be sent to you from this page:
http://www.jirka.org/diffyqs.
Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems) (4th ed.) by Richard Haberman
Any of the zillion books with titles like "Differential Equations with Matlab". One such book is Applied Numerical Methods with Matlab (2nd ed.) by Steven Chapra
### Important Dates:

First class: 11am, January 6th, 2014.
Midterm: Thursday, March 5th
Final exam: **Monday, April 14th, 3.30pm **

### Subject matter:

The study of analytical and numerical solutions of ordinary and partial differential equations,
with emphasis on those arising in Mechanical Engineering applications.
Prerequisites are multivariable calculus including partial differentiation and integration; linear
algebra and matrix theory; a first course in ordinary differential equations; and elementary
numerical analysis.

### Grading

The breakdown of marks between course elements will be as follows:
Final exam: 30%. Midterms: 20% each. Labs: 20% total. Homework: 10% total.
Missing a midterm normally results in a mark of 0. Exceptions may be
granted in two cases: prior consent of the instructor or a medical
emergency. In the latter case, the instructor must be notified within 48
hours of the missed test, and presented with a doctor's note immediately
upon the student's return to UBC. No make-up midterms will be given.
Assignments will be handed out approximately every two weeks.
These will contain problems that you should work and understand before
completing the computer labs. Collaboration is allowed on
homework assignments, with the usual warning that you
should be sure you understand
the material even if you collaborate and you must hand in only your own work.
The computer labs should be done independently.
Note: You will have difficulty passing the exams and the
course if you don't understand the labs.
You have to submit only your own computer labs and homework.
Although you are welcome to study together and discuss the
homework with other students, the work you submit (electronically or on paper)
must be your own. UBC policies on cheating and plagiarism are extremely strict.
If in doubt, enquire before submitting.

### Homework assignments

Homework 1 (now revised to correct typo and issue with Q4). I have changed my mind about how you can hand this in. Please submit in class on Thursday, Jan 23 or to my office (under door if needed) by 9am on Monday, Jan 27. This will no longer be collected electronically. Please make sure that your name and student number are clearly marked on your homework and that it is **stapled**.
Solutions to HW1.
Homework 2
Please submit in class on Thursday, Feb 6th or to my office (under door if needed) by 4pm on Friday, Feb 7th. Please make sure that your name and student number are clearly marked on your homework and that it is **stapled**.
Solutions to HW2 (updated Feb 19 to correct typo in solution 3).
Homework 3 (updated Feb 17 to correct typo in problem 3c).
Please submit in class on Thursday, Feb 27th or to my office (under door if needed) by 4pm on Friday, Feb 28th. Please make sure that your name and student number are clearly marked on your homework and that it is **stapled**.
Solutions to HW3.
Homework 4
Please submit in class on Thursday, March 13th or to my office (under door if needed) by 4pm on Friday, March 14th. Please make sure that your name and student number are clearly marked on your homework and that it is **stapled**.
Solutions to HW4.
Homework 5
Please submit in class on Tuesday, April 1. Please make sure that your name and student number are clearly marked on your homework and that it is **stapled**. Problems 1 and 2 are relevant for Midterm 2.
Solutions to HW5

### Computer lab assignments

Note **no labs** will be held during first week of term.
**Week 2:** Optional Matlab review and opportunity to start Lab zero, during regular lab session. Review during 1st hour of lab time. See below for Matlab help links and review files.
**Week 3:** Lab zero must be completed and handed in (electronically) by 8pm on Friday, Jan 24th. Download Lab zero [PDF]. To submit your work, log in to connect.ubc.ca and then access Mech/Math 358.
Solutions to lab zero.
**Week 4:** Lab one must be completed and handed in (electronically) by 8pm on Friday, Jan 31st. Download Lab one (updated version) [PDF]. Submission online via connect.ubc.ca
Solutions to lab one. Also: matlab files for the solutions:
[prob1a_int_ode.m]
[prob1b_numsol.m]
[prob2a_nonlinBVP_bisection.m]
[prob2a_nonlinBVP_secant.m]
[nonlinBVP.m]
[func2.m].
**Week 5 and 6:** Lab two must be completed and handed in (electronically) by 8pm on Monday, Feb 24th. Download Lab two [PDF]. Submission online via connect.ubc.ca
Solutions to lab two. Also: matlab files for the solutions:
[Lab2question1.m]
[Lab2_Q2ab.m]
[Lab2_Q2bc.m]
[Lab2Q3.m]
**Week 7 and 8:** Lab three must be completed and handed in (electronically) by 8pm on Monday, March 10th. Download Lab three [PDF]. Submission online via connect.ubc.ca
Solutions to lab three. Also: matlab files for the solutions:
MECH358_Lab3_P1.m
MECH358_Lab3_P2.m
**Week 9 and 10:** Lab four must be completed and handed in (electronically) by 8pm on Monday, March 24th. Download Lab four [PDF]. Submission online via connect.ubc.ca. Also: MATLABTutorial_Surf.m may be helpful to see how to make contour plots for problem 3.
Solutions to lab four. Also: matlab files for the solutions:
Crank_1.m
Crank_2a.m
Crank_2b.m
Fourier_3.m
GS_3.m
difference.m
**Week 11 and 12:** Lab five must be completed in groups and handed in (electronically) by 8pm on Monday, April 7th. Download Lab five [PDF]. Submission online via connect.ubc.ca.
**NOTE**: Each group must also write a statement listing the exact contributions of each member of the group to the submitted work. The statement, signed by all members of the group, must be submitted to me in class on Tuesday, April 8th (last day of classes).

### Course notes and readings

An approximate SCHEDULE of topics. Updated to reflect midterm test date changes.
Class notes Jan 7
Class notes Jan 9
Class notes Jan 14
More than you want to know about rounding and floating point numbers.
Class notes Jan 16
Class notes Jan 21
Class notes Jan 23
Class notes Jan 28
Class notes Jan 30
Class notes Feb 4 (hopefully with fewer +/- mistakes than in class). Updated Apr 11 to remove error in Parseval's formula.
Class notes Feb 6
Class notes Feb 11
Some useful handouts on numerical methods have been posted to the connect web site. For copyright reasons I cannot post them here.
Class notes Feb 13. Also: swf animations for the two heat equation examples, solved via forward difference central space, from class: Stable h- and k- choices. UNstable h- and k- choices.
Class notes Feb 27
Class notes Mar 4
Class notes Mar 6 includes solutions to midterm one.
Class notes Mar 11
Review problems with solutions on Fourier Series and BVPs. See also the list of suggested textbook problems in the midterm one list of topics.
Class notes Mar 13
**Review problems on heat equation**: See the current course site for Math 257/316. Suggested homework: Homework 6, 7 and 8. Many other high quality problems and solutions are available from this site.
Some suggested problems from another free online book (Trench): s12.1 (heat): 10, 11, 13, 43-46, 48-53; s12.2 (wave): 2, 8, 17, 20, 28, 35, 56; s12.3 (Laplace): 7, 10.
**(More) Notes and Review, including problems with solutions** on separation of variables (heat, wave, Laplace, etc) from Anthony Peirce's version of Math 257/316. Suggested homework sets: 6, 7 (Heat), 8 (wave) and 9 (Laplace). Course site. Note that we have not yet covered alternative coordinate systems so a few of the problems are not yet relevant.
Class notes Mar 18
Class notes Mar 20
Class notes Mar 27
Class notes Apr 1.
Midterm 2 solutions
Class notes Apr 3
Class notes Apr 8.
Solutions to multiple choice questions.

### Midterms

List of topics for midterm one
Formula sheet for midterm 1. Updated Feb 19 - now with fewer errors.
Midterm one and solutions: see March 6 class notes above.
**List of topics for midterm two.**
Formula sheet for midterm 2.

### Final

Final list of topics for the exam.
The math department offers the course Math 257/316 which is reasonably close to this course. You can find a range of past exams for that course, many of which have solutions available. You can safely ignore any question from that course that involves the words "singular point", "Bessel function" or "Frobenius".
Math dept past final exams
Math Exam and Education Resources wiki
MATH 257 collection
maintained by UBC's Engineering Physics Student Association.
There are a few solved past final exams on
Professor Peirce's MATH 257/316 pages.
The UBC Math Club has packets of past final exams with
solutions for sale in the Math Annex.
Math Club website.
Don't forget the Math
Learning Centre in rooms 300–302 of the L. S. Klinck building.
~~The final exam will contain the same formula sheet as Midterm 2.~~ The final exam will contain this formula sheet.
Here are the final exam and midterm two from last year.
Last year's final; Last year's midterm. The style is different than this year because they have an open-book section and a closed-book section. We will just have a closed-book exam. However, the problems are all relevant to this course.
### Matlab

Click here for the zip-file containing the materials for Matlab review, including some sample m-files. Written by Ida Karimfazli.
Click here for just the powerpoint slides.
Click here for the ODE tutorial.
UBC Math Matlab resources page.

Daniel Coombs
/ Department of Mathematics /
University of British Columbia