# Rutgers Math 421 -- Advanced Calculus for Engineering

## General Information

There are two sections this semester.

SectionTimePlaceInstructor
01 MW5 SEC-206 Bumby
02 MW8 ARC-207 Kruskal

Since SEC-206 is a moderately large room, students in Section 2 who wish to take the final exam earlier are invited to join Section 1 in SEC-206 from 12-3 PM on Friday, May 4 for the final exam.

Prof. Kruskal will not be available during the week of April 30 to May 4. However, Prof. Bumby will be holding office hours in Hill 438 from 1 to 7 PM on Tuesday, May 1, and for the same hours on Wednesday, May 2, and all aspects of this course may be discussed then.

In both sections, the grade basis will be

• 10% Quizzes
• 10% Homework
• 20% Midterm #1
• 20% Midterm #2
• 40% Final Exam

Grade distribution for midterm exams can be found near the end of the page.

## Textbook and Syllabus

Erwin Kreyszig; Advanced Engineering Mathematics (eighth edition); Wiley (text), 1999; (ISBN# 0-471-15496-2)

Here is a schedule of lectures, quizzes and exams for the Spring 2001 semester, including revisions caused by weather problems. It is expected that both sections will follow this syllabus. Too avoid clutter, a separate page contains a list of homework problems with their due dates.

Session Day Date Section in Text
or other Activity
Topics
1 Wed Jan 17
5.1
Laplace transforms; inverse transforms; linearity; shifting.
2 Mon Jan 22
5.2
Transforms of derivatives and integrals.  Differential equations.
3 Wed Jan 24
5.3
Diagnostic Quiz
Unit step function; second shifting theorem; Dirac delta function.
4 Mon Jan 29
5.4
Differentiation and integrations of transforms.
5 Wed Jan 31
5.5
Convolution; integral equations.
6 Mon Feb  5
5.6
Partial fractions; differential equations.
7 Wed Feb  7
5.7
Quiz #1 (5.1-5.6)
Catchup; Review
Systems of differential equations
8 Mon Feb 12
10.1
Periodic series; trigonometric series.
9 Wed Feb 14
First Midterm Exam
10 Mon Feb 19
10.2
Discussion of exam
Fourier series.
11 Wed Feb 21
10.3
Functions of any period.
12 Mon Feb 26
10.4
Even and odd functions; half-range expansions.
13 Wed Feb 28
11.1
11.2
Quiz #2 (10.1-10.4)
Partial differential equations: basic concepts.
Modeling:  vibrating strings and the wave equation.

14 Mon Mar  5
SNOW - No class
15 Wed Mar  7
11.3
Separation of variables; use of Fourier series.
Mon Mar 12
Spring Recess - No class
Wed Mar 14
Spring Recess - No class
16 Mon Mar 19
11.5
The heat equation; solution by Fourier series.
17 Wed Mar 21
11.7
11.8
Quiz #3 (11.1-11.3)
Membranes, Two dimensional wave equation;
Rectangular membrane, use of double Fourier series
18 Mon Mar 26
11.12
Solution by Laplace transforms.
19 Wed Mar 28
11.4
Quiz #4 (11.5-11.8)
Catchup; Review
D'Alembert's solution of the wave equation.

20 Mon Apr  2
3.0
3.1
Introduction to systems of differential equations.
21 Wed Apr  4
Second Midterm Exam
22 Mon Apr  9
3.2
Discussion of exam
Basic concepts and theory.
23 Wed Apr 11
3.3
Constant coefficient homogeneous equations; phase plane.
24 Mon Apr 16
3.4
Criteria for critical points; stability.
25 Wed Apr 18
3.5
Qualitative methods for nonlinear systems.
26 Mon Apr 23
3.6
Non-homogeneous linear systems.
27 Wed Apr 25
Quiz #5 (3.0-3.5)
Catchup

28 Mon Apr 30
Review

Letter grades have been assigned for the midterm exams to help estimate the course grade. For the second midterm, there seemed to be a slight difference in the way that partial credit was assigned, so grades in Section 2 were adjusted upward by 5 points before a common scale was determined. Students who took their exam in that section should adjust these ranges for exam 2 downward by 5 points to interpret their grades.

Exam 1
A 94-98 2
B+ 79-83 5
B 74-76 4
C+ 66-69 3
C 61-64 4
D 45-54 8
F 26-41 4

Exam 2
A 84 1
B+ 74-77 4
B 66-69 7
C+ 61-64 3
C 48-54 4
D 37-46 7
F 25-34 3

The contribution to the grade from quizzes an homework is still incomplete and has not been tabulated. The course grade will be based a combined numerical score of all components, not on an average of letter grades. However, it is expected that final grades will have a similar distribution.