Fall  2005


 

 

Math 211 (Section 2)

Ordinary Differential Equations and Linear Algebra

 

Instructor:

Ilie Ugarcovici

Time:

TR 9:25-10:40 am

Location:

210 Herzstein Hall

Office:

452 Herman Brown Hall

Office Hours: 

T, W, Th 2:30-3:30 (or by appointment)

Office Phone:

(713) 348-2385 (x2385)

E-mail:

idu@rice.edu

 

GRADES
 

Final Project (due Wednesday, Dec. 14 by 5:00 pm)

 

Course info

Homework and schedule

Computer and owlnet information

 

Tutorial sessions

 

Exams from previous semesters
  

Announcements:

 

(Posted Dec. 2)

  • Final exam  - is a comprehensive 3-hour exam; the distribution of the questions is 70% new material and 30% old material. New material means sections 8.1, 8.2, 8.3, 8.4, 8.5, 9.1, 9.2, 9.3, 9.4, 10.1, 10.2, 10.3, 10.4. I decided to exclude the numerical methods (euler, rk2, rk4) from the test.

      Also, my office hours during the exam period are:

         Monday (12/5) 2:00-4:00pm

         Tuesday (12/6) 2:30-3:30pm

         Wednesday (12/7) 2:00-4:00pm

         Thursday (12/8) 2:30-3:30pm

         Monday (12/12) 9:00-10:00am

         Wednesday (12/12) 2:00-4:00pm

      I asked the TAs to hold regular help sessions during this period, too.

 

(Posted Nov. 17)

·        Exam #2 solutions

 

(Posted Nov. 3)

  • Second Midterm exam - 75 minutes pledged take-home exam (no calculators, no notes, no books). The second take-home midterm exam is scheduled for the week of 11/08-11/14. It will be posted online on Tuesday (11/08) and it will be due to my office by Monday 11/14 (at 11:53am). The material covered is from sections: 6.1, 6.2, 6.3, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 8.1, 8.2, 8.3. Since the homework assignments cover up to section 8.2, I strongly encourage you to work some problems from section 8.3, too (in particular, #3,5,9).

 

(Posted Oct. 17)

Some comments/suggestions regarding the project:

 

- Part (e):

·        Hint #1: One needs to show that there are no extra fixed points (besides 0) if h>(a+1)^2/4.

·        Hint #2: In the case when extra fixed points exist, it is important to know their signs. Since these are roots of a quadratic equation, it is useful to notice the following property: if the quadratic equation is ax^2+bx+c=0, then the roots x1 and x2 satisfy the identities:
            x1+x2=-b/a    and   x1*x2=c/a
(One can easily prove these identities from the quadratic formula; hopefully, you've seen these identities before). Show that in our case, x1+x2=1-a  and x1*x2=h-a, and then proceed with a study of the signs, based on various situations.
In the ah-plane, the line h=a together with the parabola h=(a+1)^2/4 play an important role in separating different situations.

 

- Part (f): Please consider here r=1 so "t" is the same as "tau". In this part, you should present two separate plots: one (by using dfield) with different trajectories, and another plot showing approximations by those numerical methods. 

 

(Posted Oct. 6)

·        Exam #1 solutions

 

(Posted Sept. 27)

·        Here are some short matlab programs using the procedures eul, rk2, rk4 (the procedures are available here).
    euler.m ; rk2sample.m ; batch4.m

 

(Posted Sept. 24)

·        Homework #4 is now due Wednesday (September 28) by 12:00pm. The exam will be given to you on Thursday morning (September 29) and you need to return it by Monday (October 3) at 5:00pm to my office.

 

(Posted Sept.. 20)

·        First Midterm exam - 75 minutes pledged take-home exam (no calculators, no notes, no books). The material covered is from sections 1.1,1.2,1.3; 2.1, 2.2, 2.3, 2.4, 2.5, 2.7, 2.8, 2.9; 3.1, 3.3. The exam will be given to you on Tuesday morning (September 27) and you need to return it by Friday (September 30) at 5:00pm to my office.