Math 253, fall 2003

Parts of this page include: Examinations | Schedule | Supplementary notes

All scores: Included are: the three exam marks, the three homework marks, and the course mark (based on the scheme below). The marks reflect the results of all objections.

Note (added 2004.1.26): the score-file that was here last week may not have contained all scores from the make-up exam. The present file should contain all of these. If something is missing, let us know.)

Minimum marks for letter-grades:

AA	85
BA	80
BB	75
CB	65
CC	55
DC	50
DD	45

Textbook:

Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, 7th edition (New York: John Wiley & Sons, 2001).

Supplementary notes:

on the ODE architect program (under "Assignments" below);
on Laplace transforms:
- pdf
- ps
- dvi
- tex
on series-solutions at singular points:
- pdf
- ps
- dvi
- tex

Instructors:

	Office	Hours	Email
Sıtkı Irk	M-228		matsitki@metu.edu.tr
Bülent Karasözen	M-127	Tu 13.30–15.30	bulent@metu.edu.tr
David Pierce	M-Z37	see schedule	dpierce@math.metu.edu.tr

Assistants:

	Office	Hours	Email
Canan Bozkaya	M-232	Tu 13.30–15.30	canan@math.metu.edu.tr
Cemil Büyükadalı	M-206	Wd 13.30–15.30	e110866@yahoo.com
Beste Güçler	M-203		beste@math.metu.edu.tr

Grading:

First in-term examination	25%
Second in-term examination	25%
Assignments	15%
Final examination	35%

Assignments:

Due on October 31.
- pdf
- ps
- dvi
- tex
Note: Equations (i) and (iii) in Problem 1(a) are now different from those on the sheet handed out in class. The equations should be y'=(y-1)(y-2) and y'=y²/2 respectively.
Results (xls file). Papers can be picked up in M-206.
Due on December 5.
- pdf
- ps
- dvi
- tex
Due on December 26 (a week later than announced on the sheet).
- pdf
- ps
- dvi
- tex
The system in question is

x' = ax + by
y' = cx + dy
Results.

Here are three documents that may be helpful in the use of the ODE Architect program:

Examinations:

November 8, Saturday, 13.00, covering weeks 1–6:
- locations (xls file);
- solutions:
  - pdf
  - ps
  - dvi
  - tex
- scores (xls file)
Papers will be shown:
- December 9 (Tuesday), 13:30–15:30, by the assistants
- December 12 (Friday), 13:00–14:00, by Beste Güçler, to students who took the exam in Th-1, Th-2, Th-3, Th-7, B-14, B-104 and Dr-143
- December 16 (Tuesday), 10:00–11:00, by Canan Bozkaya, in M-203, to students who took the exam in Th-6, Th-8, P3, P1, P6, Dr-2 and U1
- December 16 (Tuesday), 18:00–19:00, by Cemil Büyükadalı, in M-206, to students who took the exam in P2, P4, P5, Th-4, U2 and U3
December 13, Saturday, 13.00, covering weeks 1–10. We shall not cover ch. 7 on this exam. We may ask about topics covered also on the first exam or the homework.
- Locations;
- solutions:
  - pdf
  - ps
  - dvi
  - tex
- scores.
Papers will be shown January 9, Friday, 13:00–15:00 (location to be announced).
Final examination: 2004, January 9, 16:00:
- locations;
- scores.
Papers will be shown January 20, Tuesday, 15:00.
Make-up: Thursday, January 15, 18:00, in M-13. (Note: Earlier, instead of 15, I had written 14, but this was a mistake; we instructors had agreed on the 15th.)

Schedule:

Week 1 (Sept. 22): 1.1 Direction fields
1.3 Classification of differential equations
2.1 Linear equations with Variable Coefficients
Week 2 (Sept. 29): 2.2 Separable equations,
2.3 Modeling with first order equations
Week 3 (Oct. 6): 2.4 Differences between linear and nonlinear equations
2.6 Exact equations and integrating factors
2.7 Numerical approximations: Euler's method
Week 4 (Oct. 13): 2.8 The existence and uniqueness theorem
3.1 Homogeneous equations with constant coefficients
3.2 Fundamental solutions of linear homogeneous equations
Week 5 (Oct. 20): 3.3 Linear independence and the Wronskian, Complex numbers
3.4 Complex roots and the characteristic equation
3.5 Repeated roots; reduction of order
Week 6 (Oct. 27): 3.6 Nonhomogeneous equations; method of undetermined coefficients
3.7 Variation of parameters. Modelling of second order mechanical systems
Week 7 (Nov. 3): 4.1 General theory of nth order linear equations
4.2 Homogeneous equations with constant coefficients
4.3 The method of undetermined coefficients
Week 8 (Nov. 10): 6.1 Definition of the Laplace transform
6.2 Solution of initial value problems
Week 9 (Nov. 17): 6.3 Step functions
6.4 Differential equations with discontinuous forcing functions
6.5 Impulse functions
6.6 The convolution integral
Week 10 (Nov. 24): (Holidays)
Week 11 (Dec. 1): Linear algebra
Week 12 (Dec. 8): 7.5 Homogeneous linear systems with constant coefficients
7.6 Complex eigenvalues
7.8 Repeated eigenvalues
Week 13 (Dec. 15): 5.2 Series Solution near an ordinary point, Part I
5.3 Series Solution near an ordinary point, Part II
5.4 Regular singular points
Week 14 (Dec. 22): 5.5 Euler Equations
5.6 Series Solution near a regular singular point, Part I
(5.7 Series Solution near a regular singular point, Part II—this was on the original schedule, but will not be on the final exam)
Week 15 (Dec. 29): Review

The math department's web-page on the undergraduate program [had] the following description of the course:

MATH 253 Introduction to Ordinary Differential Equations (3-0)3 First order equations and applications. Higher order linear differential equations: Constant coefficient equations, method of undetermined coefficients, variation of parameters. Power series solutions. The Laplace Transform. Solution of initial value problems, convolution integral. Solution of systems of linear differential equations by Laplace Transform.
Prerequisites: MATH 152, MATH 156 or MATH 158

Schedules from previous semesters (consulted in the planning of this course):

spring 2002/3
spring 2001/2, taken from the original page

An obsolete account of the course from the Service Courses page of the math department.