421. Advanced Calculus for Engineering

 

Spring 2014,

421:03. MTh 2 (10:20-11:40), SEC212

421:08.MTH3(12-1:20), SEC212

Instructor: Simon Gindikin, Hill 524

gindikin@math.rutgers.edu

Office hours: Mond.2-3

Text: Dennis G. Zill,Warren, S.Wright ; Advanced Engineering Mathematics (fifth edition); Jones and Bartlett, 2014; (ISBN-978-1-4496-9172-1)

 

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  

8,9                        12.1        Orthogonal functions 1,2,4,7,10

 

10  Midterm Exam 1 (Monday, February 24)

 

11,12                           12.2        Fourier Series             1,4,5,7,10,17,18,19

 

13       12.3       Cosine and Sine Series               1,2,7

14       12.3       Cosine and Sine Series               11, 16,19,20,23

 

 

15           12.4       Complex Series                   1,2,4

16,17       12.5       Sturm-Liouville Problem     1(without                                                                                                                                                                                                            approximations),4,5,9,10

18           12.6.2       Legendre Series                    15,16,17

19         13.1        Partial Differential Equat.

 

20      Midterm Exam 2 (Monday, April 7) 

 

21         13.1,13.2   Partial Differential Equat.  13.1: 1,2,11        

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        14.1           Polar coordinates               1,2,7,11                      

26,27      14.3.1,15.3,15.4   Spherical coordinates

                                     Fourier Transform             

28                                                                                                            Catch up and Review

 

Final Exams: 421:08, Thursday, May 8, 8-11

                                           421:03, Monday, May 12, 8-11

                        

Final Grade:

                                           Midterm Exams-20% each;

                                           Quizes &Homeworks- 30%;

                                           Final Exam – 30%.

Home assignments

 

Week 1(due Mond., Jan.27). Reading and problems from Lectures 1.

Week 2 (due Mond., Febr.3). Reading and problems from Lectures 2, 3.

Week 3(due Mond.,Febr.10). Reading and problems from Lectures 4,5.

Week 4(due Mond., Febr.17). Reading and problems from Lectures 6,7.

Week 5 (due Mond.,Febr.24). To prepare for Midterm 1 which will cover first 7 classes

Week 6 (due Mond.,March 3) Reading and problems from Lectures 8,9 (see below corrections).                

Week 7 (due Mond., March 10) Reading and problems from Lecture 11,12,13.

Week 8 (due Thursd., March 27). Reading and problems from Lectures 14,15.

 

Week 9 (due Mond.,March 31). Reading and problems from Lectures 16,17.

 

Week 10(due Mond.,April 7). Reading and problems from Lecture 18(no submit). Prepare for Midterm 2 (Chapter 12).

 

Week 11 (due Mond.,April 14). Reading and problems from Lectures 21.

 

Week 12 (due Mond.,April 21). Reading and problems from Lecture 22,23. In Sect.13.4 read Problem 18c and apply d’Alembert’s formula(14) to Problems 19,20.

 

Week13 (due Mond., April 28). Reading and problems from Lecture 24,25.

Week 14. Reading from Lectures 26,27. No submitting assignment.

 

                                                                 Announcements

 

    1. Grader:

Vijayaraghavan Vembuli vijay.raghavan03@gmail.com

 

2. Quiz 1 will be on Thursday, February 6 on Lectures 1-3, HA1,2.

No texbooks, notes, calculators.

 

3. Due the cancelation of the class on Mond., Febr.3, Quiz 1

moves on Mond., Febr.10. The lecture on Thursd., Febr.6,

covers, Lectures 4,5 of the syllabus and HA3 as at the syllabus.

 

4. Lecture 7 on Thursd., March 13 was canceled. Correspondingly, HA4 includes only Lecture 6 (Sect.4.5).

 

5. 2/17/2014.  Quiz 2 will be on Thursday, February 20. Midterm 1 will be on Thursday, February 27.

 

6. 2/25/2014. Midterm 1 on Thursday, February 20 will cover all lectures on the Laplace transform.

       Changes at HA for Week 6 (due Mond.,March 3) Reading and problems from Lectures 8,10: Sect.12.1, Problems 1,2,4,7,10; Sect.12.2, Problems 1,2,4,7.

 

7. Quiz 3 on Mond., March 10. Covers Orthogonal systems and Fourier Series (sect.12.1,12.2).

      HA7 (Mond., March 10). Sect.12.2: problems 5,7,17,18,19; Sect.12.3,probl.1,2,7.

Next HA will follow the syllabus.

 

8. Midterm 2 on Monday, April 7, will include whole material on

Fourier series (Chapter 12):

-             Complet, Sine and Cosine Fourier Series;

-             Complex Fourier Series;

-             Sturm-Liouville Problems;

-             Legandre Polynomials and Legandre Fourier Series

 

Lecture Notes

 

Lecture 1

Lecture 2

Lecture 3

Lecture 4,5

Lecture 6

Lecture 8

Lecture 9

Lecture 10 (quiz 2)

Lecture 10

Lecture 12 (midterm 1)

Lecture 12

Lecture 13

Lecture 14

Lecture 15 (quiz 3)

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19(quiz 4)

Midterm2

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Lecture 25

Lecture 25 (quiz 5)

Lecture 26

Lecture 27

Lecture 28