421. Advanced Calculus for Engineering

Spring 2011,

421-06. TF 2 (10:20-11:40), SEC206

Instructor: Simon Gindikin, Hill 524

gindikin@math.rutgers.edu

Office hours: Tue 12-1

Text: Dennis G. Zill,Warren S.Wright and Michael R. Cullen ; Advanced Engineering Mathematics (fourth edition); Jones and Bartlett, 2011; (ISBN-13:978-0-7637-7966-5;10:07637-7966-0)

Grader: Xukai Yan, Hill 103

xkyan@math.rutgers.edu

Office hours: Fri 5-6

Preliminary Syllabus:

Lecture Reading Topics Problems

1 4.1 Laplace transform 1,4,5,13,23,28,37,38

2 4.2 Inversion and 7,10,23,31,35,37

Derivatives

3 4.3 Translations 4,7,11,23,37,58,64

4 4.4.1 Derivatives 2,7,8,11

5 4.4.2 Transforms of integrals 19,31,37, 38, 41,43,46

6 4.5 Delta-function 1,4,7,15

7 4.6 Systems 1,5,8

8 12.1 Orthogonal functions 1,2,4,7,10

9,10 12.2 Fourier Series 1,4,5,7,10,17,19

11 Midterm Exam 1 (Tuesday, February 22)

12,13 12.3 Cosine and Sine Series 1,2,7,11, 16,19,20,23

14 12.4 Complex Series 1,2,4

15,16 12.5 Sturm-Liouville Problem 1(without approximations),4,5,9,10

17,18 12.6.2 Legendre Series 15,16,17

19,20 13.1,13.2 Partial Differential Equat. 13.1: 1,2,11

21 Midterm Exam 2 (Tuesday, April 5)

22 13.3 Heat Equation 1,2,4

23 13.4 Wave Equation 1,2,5,13,14

24 13.5 Laplace’s Equation 2,4,16

25,26 14.1 Polar coordinates 1,2,7,11

27 14.3,15.3,15.4 Spherical coordinates

Fourier Transform 14.3:1

28 Catch up and Review

Final Exams: 421:01(MTh2), Thursday, May 5, 12-3

Final Grade:

Midterm Exams-20% each;

Quizes &Homeworks- 30%;

Final Exam – 30%.

Home assignments

Week 1(due Tue., Jan.25). Reading and problems from Lectures 1,2.

Week 2 (due Tue., Febr.1). Reading and problems from Lectures 3,4.

Week 3(due Tue.,Febr.8). Reading and problems from Lectures 5.6

Week 4(due Tue., Febr.15). Reading and problems from Lectures 7,8.

Week 5 (due Tue.,Febr.22). To prepare for Midterm 1 which will cover first 8 classes

Week 6 (due Tue.,March 1) Reading and problems from Lectures 9,10.

Week 7 (due Tue., March 8) Reading and problems from Lecture 12,13,14.

Week 8 (due Fri., March 25). Reading and problems from Lectures 15,16.

Week 9 (due Tue.,March 29). Reading and problems from Lectures 17,18.

Week 10. Prepare for Midterm 2 (Chapter 12) on Tuesday, April 5.

Week 11 (due Tue.,April 12). Reading and problems from Lectures 19,20,22.

Week 12 (due Tue.,April 19). Reading and problems from Lecture 23,24. In Sect.13.4 read Problem 12 and apply d’Alembert’s formula to Problems 13,14.

Week13 (due Tue., April 26). Reading and problems from Lecture 25,26.

Week 14. Reading from Lectures 27,28. No submitting assignment.