421. Advanced Calculus for Engineering

Fall 2009,

MTh2 (10:20-11:40), SEC212

MTh3(12-1:20),SEC216

Instructor: Simon Gindikin, Hill 524

gindikin@math.rutgers.edu

Office hours:Mond 2-3

Text: Dennis G. Zill and Michael R. Cullen ; Advanced Engineering Mathematics (third edition); Jones and Bartlett, 2006; (ISBN# 0-763-74591-X)

Preliminary Syllabus:

Lecture Reading Topics Problems

1 4.1 Laplace transform 1,3,6,13,23,28,37,38

2 4.2 Inversion and 7,10,23,31,35,36

Derivatives

3 4.3 Translations 3,7,12,23,37,58,63

4,5 4.4 Additional 3,7,8,12,15,19,31

properties 37, 38, 41,43,45

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

7 4.6 Systems 1,6,9

8 12.1 Orthogonality 1,3,7

9 12.2 Fourier Series 1,5,10,17

10 Midterm Exam 1 (Monday, October 5)

11,12 12.3 Cosine and Sine Series 1,2,6, 15,19,20,23, 35,37,38

13 12.4 Complex Series 1,2,4,9

14,15 12.5 Sturm-Liouville Problem 1(without approximations),3,5,10

16 12.6 Legendre Series 15,16,17

17 13.1,13.2 Partial Differential Equat. 13.1: 1,2,11

18 13.3 Heat Equation 1,2,4

19 13.4 Wave Equation 1,2,5,13,14

20 Midterm Exam 2 (Monday, November 9)

21,22 13.5 Laplace’s Equation 3,4,16

23 13.8 Series in 2 variables 1,2,3

24,25 14.1 Polar coordinates 1,2,7

26 14.3 Spherical coordinates 1, 3

27 15.3,15.4 Fourier Transform None

28 Catch up and Review

Final Exam: Class MTh2 - Fri, Dec.18, 8-11

Class MTh3 – Mond, Dec 21. 12-3

Final Grade:

Midterm Exams-20% each;

Quizes &Homeworks- 30%

Final Exam – 30%.

Home assignments

Week 1(due Tue, Sept. 8). Reading and problems from Lecture 1.

Week 2 (due Mond, Sept. 14). Reading and problems from Lecture 2,3.

Week 3(due Mond, Sept. 21). Reading and problems from Lecture 4,5.

Week 4(due Tue, Sept.28). Reading and problems from Lectures 6, 7.

Week 5. 1)To prepare for Midterm 1 (Mond, October 5) which will cover first 7 classes (Ch.4)

2) Reading and problems from lectures 8,9. Due Mond, Oct.12.

Week 7 (due Monde,Oct.19). Reading and problems from Lecture 11,12,13.

Week 8(due Mond, Oct.26). Reading and problems from Lectures 14,15.

Week 9 (due Mond., Nov.2). Reading and problems from Lecture 16, 17.

Week 10. Prepare for Midterm 2 (Lectures 8-16) on Mond, Nov.9.

Week 11 (due Mond., Nov.16). Reading and problems from Lectures 18,19 above. In Sect.13.4 read Problem 12 and apply d’Alembert’s formula to Problems 13,14.

Week 12 (due Mond., Nov.23). Reading and problems from Lecture 21,22,23.

Weeks13,14 (due Thursd., Dec.3). Reading and problems from Lecture 24,25.

Additions and corrections.

1. Office hours of the grader Moulik Balasubramanian

(moulik@math.rutgers.edu): Tue., 10-11 am, Hill 103.

2. Midterm 1 on October 8.

3.HA for Mond., Oct.12: Sect.12.1, 12.2.

4. HA for Mond., Oct.19: Sect.12.3.

5. HA for Mond., Oct.26: Sect.12.4, 12.5 (without #10).

6. HA for Mond., Nov.2: Sect. 12.5, #9,10; Sect.12.6.

7. HA for Mond.,Nov.16: Sect.13.1, 13.2(reading), 13.3,13.4(#1,2,5).

8. HA for Mond.,Nov.23. In Sect.13.4 read Problem 12 and apply d’Alembert’s formula to Problems 13,14. Section 13.5(reading and problems #3,4,16.