Instructor: Roderich Tumulka
Phone: 732-445-2390 x 1322
Office: Hill 522
Office hours: Tuesday 4:20-5:00pm, Thursday 3:20-4:00pm
Email: instructor's last name, then @, then math.rutgers.edu

Homework

Assignment #1 (due 1/26):
A1*, A2*, A3*

Assignment #2 (due 2/2):
4.1: 2, 6*, 12, 24, 26*, 38, 41, 42
4.2: 2, 4, 6, 8, 16, 23*, 32, 36*, 38
4.3: 4, 8, 16*, 22*

Assignment #3 (due 2/9):
4.3: 40, 44*, 49-54
4.4: 4, 6, 32, 34*, 38*, 59
4.5: 2, 8*, 13
4.6: 2*, 15

Assignment #4 (due 2/16):
12.1: 1-4, 12*, 17-19, 21*, 22, 23(a)*
12.2: 1, 4, 5*, 17*, 18, 21*

Assignment #5 (due 2/23):
12.3: 2, 4, 6, 8, 28*, 35, 39*, 45, 52*

Assignment #6 (due 3/2):
12.4: 1, 2, 9*, 11*, 12

Assignment #7 (due 3/9):
15.3: 2, 3*, 9
15.4: 19*, 20

No assignments due on 3/23, 3/30, or 4/6.

Assignment #8 (due 4/13):
13.1: 2, 4, 8*, 18, 20*, 28, 29*, 30*
13.2: 2, 4*, 6, 8*, 10, 12
13.3: 3*, 4*

Assignment #9 (due 4/20):
13.4: 2, 4, 5*, 8*, 11
13.5: 2, 4*

Assignment #10 (due 4/23):
13.7: 2*

Assignment #11 (due 4/27):
13.8: 3*
14.1: 7*

Syllabus

Part I: Laplace transforms [Chap. 4]
Definition of the Laplace transform L, its properties; techniques for computing L and L^-1; application to ordinary differential equations. 6 lectures: Jan 19-Feb 5

Part II: Fourier series [Chap. 12, 15.3-15.4]
Expansion into orthogonal functions; Fourier series using real or complex numbers, their application in music and in ODEs with periodic driving force; even and odd functions, their Fourier series; Fourier integral. 6 lectures: Feb 9-26

Catch-up and review, 3 lectures: Mar 2-9
Midterm exam (about Laplace transform and Fourier series): Friday Mar 12, 12:00-1:20pm
Spring break: Mar 15-20

Part III: Numerical solutions of ordinary differential equations [Chap. 6.1-6.2]
Euler and Runge-Kutta Methods. 3 lectures: Mar 23-30

Part IV: Heat, wave, and Laplace's equation [Chap. 9.4-9.5, 13, 14.1]
Review of vector calculus, gradient and Laplace operator; heat, wave, and Laplace's equation; more general linear 2nd-order PDEs; boundary conditions; the method of separation of variables, Sturm-Liouville problems; heat equation in polar coordinates. 7 lectures: April 2-23

Catch-up and review, 2 lectures: April 27-30
Final exam (about all topics of the course): Thursday May 6, 12:00-3:00pm

Textbook

Grades

Participants who cannot attend a lecture or cannot hand in their homework in time are expected to contact me by email.