## Mathematics 3123B, Winter 2011: DIFFERENTIAL EQUATIONS

Course outline: pdf

Lectures: MWF 11:30am-12:30pm, in MC 107

OFFICE HOURS: Wed. April 6, 12:30-1:30 pm;
Tue. April 12, 2-3 pm;
Mon. April 18, 4-5 pm.

Instructor: Tatyana Foth

Textbooks:

Ordinary Differential Equations and Dynamical Systems by G. Teschl, published by the American Mathematical Society, available on-line here.

Elementary Differential Equations and Boundary Value Problems, by W. Boyce and R. DiPrima, published by Wiley.

Student Solutions Manual to accompany Boyce Elementary Differential Equations and Boundary Value Problems, published by Wiley. (OPTIONAL)

Exam dates: midterm exam - in class on Friday March 4th,
final exam - Tuesday April 19th, 1:00-4:00 pm, in MC 108.

### Final exam information:

it will cover everything we did, there will be long answer problems and true/false questions, it's a closed-book exam but a two page help sheet (standard size, with anything written on it, prepared at home in advance) will be allowed.

Topics include: classification, linear equations, systems of first order equations, method of integrating factors, separable equations, homogeneous equations, Bernoulli equations, exact equations, existence and uniqueness theorems, Lipschitz condition, Picard's method of successive approximations, Gronwall's inequality, continuation of solutions, dependence on the initial condition, 2nd order equations with the dependent or the independent variable missing, Wronskian, fundamental set of solutions, Abel's theorem, solving homogeneous linear equations with constant coefficients, method of undetermined coefficients, variation of parameters, mass-spring system (free vibrations), solving homogeneous linear systems with constant coefficients, power series solutions, flows, trajectories.

### Midterm exam information:

it will cover everything we did before the reading week, there will be 3 long answer problems and several true/false questions, it's a closed-book exam but a one page help sheet (standard size, one side, with anything written on it, prepared at home in advance) will be allowed.

Topics include: classification, 1st and 2nd order linear equations, method of integrating factors, separable equations, homogeneous equations, Bernoulli equations, exact equations, existence and uniqueness theorems, Lipschitz condition, Picard's method of successive approximations, Gronwall's inequality, continuation of solutions, dependence on the initial condition, equations with the dependent or the independent variable missing, Wronskian, fundamental set of solutions, Abel's theorem, solving 2nd order homogeneous linear equations with constant coefficients.

(Collected) homework:

Assignment 1 (due on Mon. Jan. 31)

Assignment 2 (due on Mon. Feb. 28)

Assignment 3 (due on Fri. April 1)

Recommended exercises:

(note: I am referring to the 8th ed. of Boyce-Di Prima)

Chapter 1 (BDP): 2,4,6,9, (1.3, p.24-25)
Chapter 2(BDP):
2.1(pages 39-41): 1-11 odd, part (c); 13-19 odd; 31
2.2(pages 47-50): 1,3,5,7; 9-19 odd, part (a); 31-37 odd, part (b)
2.4(pages 75-77): 1, 3, 5, 7, 9, 11, 29, 30
2.6(pages 99-100): 1-11 odd; 15, 19, 21
2.8 (page 117) Apply the method of successive approximations to the IVPs in 3,5 (find the first few functions in the sequence, guess the limit y(t), verify that y(t) is indeed a solution)
Special 2nd order equations (p. 133): 37, 41, 43, 47
Chapter 3(BDP):
3.1 (page 142): 1-15 odd; 21, 23
3.2 (pages 151-152): 1-11 odd; 17, 19, 23, 25
3.3 (pages 158-159): 1-9 odd, 15, 17, 21, 23, 25
3.4 (page 164): 7-21 odd
3.5 (page 172): 1-13 odd
3.6 (page 184): 1-9 odd, 13, 15, 17
3.7 (page 190): 1-19 odd
3.8 (page 203): find u(t) in problems 5, 7, 9, 11
Chapter 7(BDP):
7.3 (pages 383-384): 8, 9, 10, 12, 13
7.5 (pages 398-399): 1, 3, 5, 7, 13, 14, 15
7.6 (page 410): 1, 3, 5
7.7 (pages 420-421): 3, 11
7.8 (page 428): 1, 2, 7, 9
7.9 (page 439): 1
Chapter 4(BDP):
4.1 (pages 222-223): 1,3,5,7, 11, 13, 15, 21, 23
4.2 (page 230): 13, 16, 35
4.4 (page 240): 2, 13
Chapter 5(BDP):
5.2 (page 259): 1, 2, 5, 6, 7, 9, 10, 11, 12, 13
5.3 (page 265): 1, 2, 3

Some files for this course will be posted on webct.