(Term 2, 2010/2011: Jan, 2011 -- April, 2010)

MATH 257:201

WebCT Vista webpage: https://www.vista.ubc.ca

Math 257 Home | Schedule/Plan/Progress/Summary |
Notes | Homework | Resources | Midterms | Final Exam |

Introduction to partial differential equations; Fourier series; the heat, wave and potential equations; boundary-value problems; numerical methods.

Instructor:
Young-Heon Kim.

Office: MATH 235.
Email: yhkim "at" math "dot" ubc 'dot' ca

Class:
Mon
Wed
Fri
11:00--12:00 Mathematics Annex 1100

Office hours (subject to
change): Mondays 2pm--3:50pm
at Math 235, or by
appointment. For appointment at other time, please email at yhkim
"at"
math "dot" ubc 'dot' ca

First class: Wednesday, January 5.
Last
class: Wednesday, April 6.

Announcements:

- Jan. 4. There is a change to the two midterm dates (Feb 11 and March 18) and HW submission dates (Wednesdays, starting from Jan 12) and. See below.
- Jan 4. HW 1 is now posted. Due, Wed, Jan 11.

- Jan 6 (Friday). HW 1 Problem 6 will NOT be graded. (That is, only Problems 1, 2, 3, 4, 5 will be graded.)
- Jan 12. Office hours are set-up: Mondays 2pm-- 3:50pm at Math 235 (my office)
- Jan 12. HW 2 is now posted. HW 1 solution set is now posted.

- Jan 12. Review power series. Be familiar with the operations with
them. see e.g.
http://tutorial.math.lamar.edu/Classes/DE/PowerSeries.aspx

especially, http://tutorial.math.lamar.edu/Classes/DE/PowerSeries.aspx#Index_Shift - Jan 24. Typo in the notes Lecture
10. page 51 in equation (8.2). It should be read as " ........=
Constant = - \lambda^2" <--- Here, \lambda means the Greek letter
'lambda' and ^2 means sqaure.

- Jan 28. Please parcitapate in the
online
survey. The link is here http://www.surveymonkey.com/s/85Z7YBS
You
need
the password I have
sent to you in a separate email. This survey will be closed on
Wednesday. Your participation is important for us.

- Feb 11. Final exam date is now decided. Tue APR 19, 3:30pm,
(duration 150min.) Location to be determined.

- March 1. There was a typo/mistake in HW 6, Problem 4(b). The
corrected HW is now posted. For Problem 4 (b), you can hand in it in
the class on Friday, March 4. For other problems (up to Problem 4 (a)),
the due date is Wed, March 2.

Recommended Textbook:

W.W. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems (9th. ed.), Wiley, 2009.

Earlier editions are also fine.

Final Grading Scheme: The higher one in either of

- HW including spreadsheet projects (15%), Two Midterms
(17.5%
each),
Final exam (50%)

- HW including spreadsheet project (15%), Best of Two Midterms (15%), Final exam (70%)

- Homework will be collected at the beginning of lecture each Wednesday starting on Jan 12.
- Homework
will
be
collected
ONLY
IN
CLASS:
for example, I will NOT accept homework submission at my office.
This policy is to motivate students keep attending the lectures.

- Late
homework
will not be accepted.

A missed homework will result in 0 mark.

Two lowest homework grades will be dropped in computing the final grade. - Your homework should be written in a clear manner so that the grader can understand easily what you are doing. Also it should be handwritten neatly. Unreadable or very hard to read homework may get zero or very low mark.
- You are encouraged to discuss the homework with other students,
but you must produce and write the solutions on your own.

- It is probable that only a subset of those problems turned in would be graded, and you will not be informed (in advance) which ones these are. For example, if your homework does not contain any of the problems to be graded (which will be decided after the deadline), you will get zero mark. So, it would be better for you to do all the problems to be handed in.

- The midterms will be held during class hours on February 11 (Friday) and March 18 (Friday).
- No make-up midterms!

- Missing a midterm normally results
in a mark of 0. Exceptions may be granted ONLY with

prior consent of the instructor, and with ofﬁcial documentation supporting the student’s reason for

missing the exam. In case of a medical emergency, the instructor must be notiﬁed within 48 hours

of the missed test, and presented with a doctor’s note immediately upon the students return to UBC.

A physician’s note should speciﬁcally state that the student was medically unﬁt to write the missed

exam on that speciﬁc day.

- The date of
the ﬁnal exam is yet to be declared. Do not make any travel plans until
the exam schedule

has been announced.

- IT IS ESPECIALLY
IMPORTANT that students know that IF THEY DO NOT FULFILL THE COURSE
REQUIREMENTS DURING THE TERM (including not writing the midterm
test(s) even if you agree to transfer the weight to the final) AND THEN MISS THE FINAL EXAMINATION, THEY
MAY BE DEEMED INELIGIBLE FOR A DEFERRED FINAL.

- Students will be required to bring Photo ID to all tests and exams.
- Calculators, books, or aids of any kind will NOT be allowed in midterms or in the ﬁnal.
- Complaint
of
the
mark
on
the
midterm exams should be made right at the time you get the
exam back. Later claims will NOT
be considered.

For computational problems, to earn lots of credit, you have to get the right answer with proper set-up of the calculation.

In many cases (especially for the easier problems), about half the points will be given for setting up the calculation properly and about half for computing the numerical answer correctly. For more difficult problems, more percentage will be given for properly setting-up the calculation. You may loose most (sometimes, all) of points for setting up the calculation incorrectly, even if the subsequent computations are correct. Also, you may loose half the points for not finding the correct final answer, even if the initial set-up is correct.

IMPORTANT! Academic Integrity/Honesty

Please see

http://www.science.ubc.ca/sites/science.ubc.ca/files/faculty/teaching/sep05acadhonesty.pdf

and also

Student Conduct and Discipline:

http://www.students.ubc.ca/calendar/index.cfm?tree=3,54,0,0

Rough Schedule of Topics (with approximate lecture time, and corresponding Boyce & DiPrima sections)

- Introduction to Partial Differential Equations (PDE) (1 hour)
- The heat (10.5), wave (10.7), and Laplace (10.8) equations
- Some Review (2 hours)

- Review of ODE methods (especially 2.1-2.2, 3.1-3.4)
- Review of sequences, series, power series, \& Taylor
series (5.1)

- Series Solutions of Differential Equations (6 hours)

- Series solutions at ordinary points (5.1-5.3)
- Regular singular points (5.4-5.7)

- Introduction to Computation Using Spreadsheets (4 hours)

- Fourier Series and Separation of Variables (13 hours)

- The heat equation and Fourier series (10.1-10.6)
- The wave equation (10.7)
- The Laplace equation (10.8)

- Boundary Value Problems and Sturm-Liouville Theory (7 hours)

- Eigenfunctions and eigenvalues (11.1)
- Sturm-Liouville boundary value problems (11.2)
- Nonhomogeneous boundary value problems (11.3)