Rutgers Math 421 – Advanced Calculus for Engineering

General Information

This page has been revised to reflect a change of textbook. The version used with the previous textbook is also available. Other information about both the history and the future of the course can be found on the main course page.


Current Semester


Textbook and Syllabus

Textbook: Peter V. O'Neil; Advanced Engineering Mathematics (fifth edition); Brooks/Cole, 2003 (1236+82[Answers]+9[Index] pp.); (ISBN# 0-534-40077-9)

A list of errata appears below the syllabus.

Syllabus: Since this is the first use of the current textbook, this is a tentative syllabus. It is intended mainly to guide instructors in planning. The selection of topics is based on those used with the previous text. There is also a list of suggested homework problems for each section mentioned in the syllabus.

The order of the material may also be changed. Individual Section (or semester) pages should contain current details.


 
 
Session Section in Text
or other Activity
Topics
1
3.1
Laplace transforms: Basic Properties.
2
3.2
Initial Value Problems.
3
3.3
Shifting Theorems; Heaviside Functions.
4
3.4
Convolution.
5
3.5
Impulses and Delta Functions.
6
3.6
Solution of Systems.
7
3.7
Equations with Polynomial Coefficients.
8
13.1
13.2
Fourier Series: Introduction.
9
13.4
Cosine and Sine Series.
10
13.5
integration and Differentiation of Fourier Series.
11
Review.
12
First Midterm Exam.
13
16.1
16.2
The wave equation;
Fourier series solution.
14
16.2
16.4
Fourier series and d'Alembert
solutions of the wave equation.
15
16.7
Vibrations of a Rectangular Membrane.
16
17.1
17.2
The heat equation;
Fourier series solution.
17
17.2
17.5
Heat conduction in interval
and rectangle.
18
Review.
19
10.1
10.2
Nonlinear systems;
Phase planes.
20
10.3
Phase portraits of linear systems.
21
10.3 (continued)
More phase portraits of linear systems.
22
Second Midterm Exam
23
10.4
Critical points; stability.
24
10.5
Almost linear systems.
25
Instructor's
Choice
26
27
28

Here are some errors (or infelicities) in O'Neil 5th edition discovered by students and instructors in the course of using the text at Rutgers.


Here are similar notes about the accompanying Solutions Manual.

Archives

This text seems more efficient, so space is left at the end for additional topics, indicated by the phrase "Instructor's Choice". Possible additional topics are


 

Comments on this page should be sent to: R. T. Bumby
Last updated: September 05, 2002