421.
Advanced Calculus for Engineering
Fall
2014,
421:04.
TF 2 (10:20-11:40), SEC204
Instructor:
Simon Gindikin, Hill 524
Office
hours: Tue.12-1
Text: Dennis G. Zill,Warren, S.Wright ; Advanced Engineering Mathematics (fifth
edition); Jones and Bartlett, 2014;
(ISBN-978-1-4496-9172-1)
Announcements
1.
The grader:
Robert Kertz, robert.kertz@rutgers.edu .
2. MT1 will be on Friday, October 3 (Ch.4, The
Laplace transform, first 8 classes). See corrections at the
Syllabus.
3. It will be Quiz 3 on Fri. Oct.17 ;
it will cover orthogonal systems of functions (sect.12.1) and Fourier series
(sect.12.2).
4. It will be Quiz 4 on Fri..Oct.31; it
will cover Sine and Cosine Fourier series (sect.12.3) and complex Fourier
series (sect.12.4). See corrections at Syllabus.
5. See corrections at Syllabus after
Midterm 2.
6. It will be Quiz 5 on Friday, Nov.21,
on Sect.13.1,13.3, 13.4
(Heat and Wave equations).
7. Quiz 6 (the last one!) will be on
Tuesday, December 2 (D’Alambert’s formula, the Laplace equation at
rectangulars, polar coordinates; Sect. 13.4,133.5.14.1).
8. No class and office hours on Tue., Dec.9.
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
6,7
4.5
Delta-function
1,4,7,15
8 4.6
Systems
1,5,8
9 12.1
Orthogonal functions 1,2,4,7,10
11,12 12.2
Fourier Series
1,3,4,5,7,10,17,18,19
13 12.3 Cosine
and Sine Series
1,2,7
14 12.3 Cosine
and Sine Series 11,
16,19,20,23
(no
half-range expansions)
15,16
12.4
Complex Series
1,2,4
17,18 12.5
Sturm-Liouville Problem
1(without
approximations),4,5,9,10
19 12.5 Sturm-Liouville Problem
20 Midterm Exam 2 (Friday, November 7)
21
13.1,13.2 Partial
Differential Equat. 1,2,11
22 13.3 Heat
Equation
1,2,4
13.4 Wave
Equation
1,2,5
23,24
13.4,13.5
Laplace’s Equation
2,4,16
25 14.1 Polar
coordinates
1,2,7,11
26,27 Catch up and Review
Final
Exams: 421:04, Monday, December 15, 12-3
Final
Grade:
Midterm
Exams-20% each;
Quizes
&Homeworks- 30%;
Final
Exam – 30%.
Home assignments
Week
1(due Tue., Sept.9). Reading and problems from Lectures 1,2.
Week
2 (due Tue., Sept.16). Reading and problems from Lectures 3,4.
Week
3(due Tue.,Sept.23). Reading and problems from Lectures 5,6.
Week
4(due Tue., Sept.30). Problems from Lecture 8. To prepare for Midterm 1 which
will cover first 8 classes (Ch.4, The Laplace transform)
Week 5 (due Tue.,Oct.7). Reading and problems from Lecture
9.
Week 6 (due Tue.,Oct.14) Reading and problems from Lectures
11,12.
Week 7 (due Tue.,Oct.21) Reading and problems from Lecture
13,14.
Week 8 (due Tue.,Oct.28). Reading and problems from Lectures
15,16.
Week 9 (due Tue.,Nov.4). Reading and problems from Lectures
17,18. Prepare for Midterm 2 (Chapter 12).
Week 10(due Tue.,Nov.11). No written assigment
Week 11 (due Tue.,Nov.18). Reading and problems from
Lectures 21, 22.
Week 12 (due Wedn..,Nov.26). Reading and problems from
Lecture 23,24 and in Sect.13.4 read Problem 18c and apply d’Alembert’s
formula(14) to Problems 19,20.
Week13 (due Tue., Dec.2). Reading and problems from Lecture
25.
Week 14. No submitting assignment.