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
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
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