Math 251: Ordinary and Partial differential equations

Sections 4 and 9 in Fall 2007.

The syllabus is here available.

First Midterm: Thu Oct 4, 2007, 6:30pm, place 110 Wartik.

Second Midterm: Mon Nov 12, 2007, 6:30pm, place group 4: 158 Willard, group 9: 160 Willard.
If you have another exam on the same day, there is a makeup exam in the same week on Thursday (I think). If you wish to take this, please register in 104McAllister (at least 2days before the exam).

Final Exam Thu, Dec 20, 2007, 4:40P-6:30P, place group 4: 100 THOMAS, group 9: 101 CHAMbers
If you have another exam at the same day or another university approved excuse, please talk to me. There is a makeup-exam on Tuesday before.

Extra review session: Today Tue Dec 18, 2007. 7:00-8:10pm in 105 Osmond

Office hours: Thu 5:40-7:00pm, Fri 2:30-4:25pm until Dec.14 or by appointment in 402 McAllister. Remaining Office Hours Wed Dec 19 2:00-4:00pm.

Homework problems

(Solutions are no longer available, because we recycled the exercises for the next semester.)

Homework 1 due Sep 3rd, compressed postscript

Homework 2 due Sep 10th, conmpressed postscript.

Homework 3 due Sep 17th, compessed postscript; well these are exercises from the book:
 I: (5P) p.61 No.10,
 II: (5P) p.75 No.1,2,3
 III: (5P) p.89 No.2,4,9 where you don't have to sketch y'=f(y); hint: e^eps =1+eps+O(eps²)
 IV: (5P) p.99 No. 1,2,4,11

Homework 4 due Sep 24th, compressed postscript, these are the exercises from the book:
 I: (5P) p.142 No. 6,12,16; d) Find an ODE whose general solution is C₁e^-x +C₂e^-2x.
 II: (5P) p.151 No. 1,5,2,4
 III: (5P) p.173 No. 23,24,25,26 hint: use Abel's theorem.
 IV: (5P) p.164 No. 18,19,20,22

Homework 5 due Oct 1st, compressed postscript, these are the exercises from the book:
 0 (5P): p.164 No. 18,19,20,22 if you have not yet done so
 I (6P): p.172 No. 12,13,14
 II (7P): p.184 No. 2,11,3,8
 III (7P): p.190 No. 7,8,9,10

Homework 6 due Oct 8th, compressed postscript. These are the exercises from the book:
 0: (7P): p.190 No. 7,8,9,10 if you have not yet done them
 I: (5P): p.203f No. 5,6,17
 II: (5P): p.214f No. 1,3,5,6

Homework 7 due Oct 15th, compressed postscript. These are the exercises from the book:
 0: (5P): p.214f No. 1,3,5,6 if you have not yet done them
 I: (6P): p.312 No. 8,12,15,20
 II: (7P): p.322 No. 3,7,16,18
 III: (7P): p.330 No. 7,20,24,30

Homework 8 due Oct 22th, compressed postscript; these are the exercises from the book:
 -1: (7P) p.322 No. 3,7,16,18 if you have not yet done them
 0: (7P) p.330 No. 7,20,24,30 dito
 I: (7P) p.337 No. 1,7,15 hint: u_3π(t)=θ(t-3π)
 II: (7P) p.344 No. 4,7,6,12 hint: first simplify δ(t-2π)cos t
 III(6P) p.360 No. 1,5,7a,4

Homework 9 due Oct 29th, compressed postscript; these are the exercises from the book:
 -1: (7P) p.344 Nr. 4,7,6,12
 0: (6P) p.360 Nr. 1,5,7a,4
 I: (4P) p.372 Nr. 6,21
 II: (6P) p.398 Nr. 2,3,4,5 where you don't have to draw the direction field.
 III: (5P) p.389 Nr. 6a-c
 IV: (5P) p.410f Nr. 1,3,9 where you don't have to draw the direction field

Homework 10 due Nov 5th, compressed postscript. These are the following exercises from the book:
 -2: (6P) p.398 Nr. 2,3,4,5 where you don't have to draw the direction field.
 -1: (5P) p.389 Nr. 6a-c, if you haven't yet done them
 0: (5P) p.410f Nr. 1,3,9 where you don't have to draw the direction field, if you haven't yet done them
 I: (7P) p.420f Nr.1,3,6
 II: (7P) p.428f Nr.3,4,7
 III:(6P) p.492f Nr.1,4,5,6

Homework 11 due Nov 12th, compressed postscript. These are the following exercises from the book:
 -2: (7P) p.420f Nr.1,3,6
 -1: (7P) p.428f Nr.3,4,7
 0: (6P) p.492f Nr.1,4,5,6
 I: (5P) p.501f Nr.1,2,3,6ac where you can draw trajectories to solve 6c
 II: (7P) p.534f Nr.1,3,4 b,c,d,e where you can do d and e in one diagram each number

Homework 12 due Nov 26th, compressed postscript. These are the following exercises from the book:
 -1: (5P) p.501f Nr.1,2,3,6ac where you can draw trajectories to solve 6c
 0: (7P) p.534f Nr.1,3,4 b,c,d,e where you can do d and e in one diagram each number
 I: (5P) p.575 Nr.3,7,10
 II: (5P) p.575 Nr.16 where you only have to look for eigenvalues λ≥0

Homework 13 due Dec 3rd, compressed postscript. These are the following exercises from the book:
 I: (5P) p.585 Nr.2,3,8,19b hint:19a might simplify 19b
 II: (7P) p.592f Nr.2,4; 13,14,15 for ω∉ Z, hint: you can assume, that you can add infinitely many ODE solutions
 III: (3P) p.600 Nr.1-6
 IV: (5P) p.600f Nr.15,17 hint: be short in nr.17

Last homework due Dec 10th, compressed postscript. These are the following exercises from the book:
 I: (5P) p.610 Nr.1,2,8,23 hint 23: Try to write as a sum S₁(r)+S₂(θ)+S₃(t)=0 and argue why all S_1,2,3 must be constants.
 II: (5P) p.620f Nr.2,4,6,15 hint: you can use 10.4/39 without proving it
 III: (5P) p.632 Nr.9,16ab hint: same 10.4/39 here
 IV: (5P) p.645f Nr.5,8 hint for 8: first solve the ODE in x.

Some online Math tools possibly helpful for ODE. Here the precise formulation of the discussed in class problems for section 2.3. (Here in PDF). Further information about undergraduate mathematics studies can be found at Information about Math Courses.

example exams: 1st midterm

Exam I, Summer 2007, solutions
Spring 2007, solutions
Summer 2006, Solutions
Fall 2005, Solutions
Spring 2005, Solutions

2nd midterm

Summer 2007, Solutions.
Spring 2007.
Summer 2006, Solutions.
Fall 2005.
Spring 2005, Solutions.

Final

Spring 2007
Fall 2005, Solutions
Spring 2005
Spring 2004, Solutions
Fall 2003, Solutions

Approximately 60% of the final will cover sections 10.1-10.8. The other 40% will cover topics from the rest of the syllabus. However, the following topics will not appear on the final:

• Mixture Problems,
• Falling bodies with air resistance,
• Logistic Equation,
• Exact ODEs,
• Reduction of Order,
• Forced Vibs,
• Pred-Prey Eqns.

Here is a detailed Study Guide for the final.