Instructor: Roderich Tumulka
Phone: 732-445-2390 x 1322
Office: Hill 522
Office hours: WTh 11am-12pm
Email: instructor's last name, then @, then math.rutgers.edu

Final Exam

• Practice exam for the final exam, model solution to the practice exam.
• The final exam takes place on Tuesday May 8, 12-3pm, in the usual room SERC-211.
• The following sections of the book will be covered on the final exam: 4.1-6, 12.1-4, 13.1-6, 14.1, 15.3-4
• The following sections will NOT be on the final: 6, 12.5-6, 13.7-8, 14.2, 15.5

Homework

Assignment #1 (due 1/25):
A1*, A2*

Assignment #2 (due 2/1):
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 2/8):
4.3: 40, 44*, 49-54
4.4: 4, 6, 32, 34*, 38*, 59

Assignment #4 (due 2/22):
4.5: 2, 8*, 13
4.6: 2*, 15

12.1: 1-4, 12*, 17-19, 21*, 22, 23(a)*
12.2: 1, 4, 5*, 17*, 18, 21*

Assignment #5 (due 2/29):
12.3: 2, 4, 6, 8, 28*, 35, 39*, 45, 52*

Assignment #6 (due 3/5):
12.4: 1, 2, 9*, 11*, 12

Assignment #7 (due 3/28):
15.3: 2, 3*, 9
15.4: 19*, 20

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

Assignment #9 (due 4/11):
13.3: 3*, 4*
13.4: 2, 4, 5*, 8*, 11
13.5: 2, 4*

Assignment #10 (due 4/18):
13.6: 5*, 13
14.1: 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 18-Feb 6

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 8-27

Catch-up and review, 2 lectures: Feb 29-Mar 5
Midterm exam (about Laplace transform and Fourier series): Wednesday Mar 7, 1:40-3pm
Spring break: Mar 10-18

Part III: Numerical solutions of ordinary differential equations [Chap. 6.1-6.2]
Euler and Runge-Kutta Methods. 3 lectures: Mar 19-26

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: Mar 28-April 18

Catch-up and review, 3 lectures: April 23-30
Final exam (about all topics of the course): Tuesday May 8, 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.