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

Section 1 meets MTh3 in SEC 216.

Section 2 meets TTh6 in SEC 216.

Section 3 meets MW7 in Hill 124.
Textbook and Syllabus
Textbook: Peter V. O'Neil; Advanced Engineering
Mathematics (fifth edition); Brooks/Cole, 2003 (1236+82[Answers]+9[Index] pp.); (ISBN# 0534400779)
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.
 p 114 In Example 3.2, third line after displayed equations
The statement "G(s) is defined for all real s" is
misleading or worse, since the calculation is
correct only for s positive.
 p 450 4th line from bottom
"not stable" should read "unstable".
 p 639 top  Figure 13.10
The leftmost of the five connected pieces of the
graph (of which one is an isolated point and the
four others are arcs of curves) has noticeably
incorrect ordinate at its maximum and at its
minimum. Also, the abscissa of the isolated
point (which is also the abscissa of ends of two
of the arcs) is slightly but not unnoticeably
wrong.
 p 868 line after third displayed equation from bottom
"T(0)=b=0" should read "T(0)=a=0".
 p 911 third displayed equation from bottom
"Y_m(x)" should read "Y_m(y)".
 p A59 in the answers to the oddnumbered problems from 1 to 19
"y(x,t)" should read "u(x,t)".
 p A62 second line from bottom
In the answer to problem 3 of section 16.7, "cos"
should be replaced by "sin"
Here are similar notes about the accompanying Solutions Manual.
 p 289 in page heading
"13.4" should read "13.3".
 p 385 lower half of page, in solution to problem 1 of section 16.2
The formulas for b_n and its simplified version for
b_{2n} are wrong by an overall sign, for instance
they both give b_2 < 0 , whereas b_2 is (I think)
manifestly positive; consequently the final formula
for y(x,t) is also wrong by an overall sign.
 p 386 in last line of answer to problem 3 (of section 16.2)
"cos" should be replaced by "sin"
 p 414 in last line (displayed) of answer to problem 3 of section 16.4
The second occurrence of the fraction 1/2 (right
after the second equals sign) should be deleted.
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
 (A) 4.1  4.3: Series solutions of Differential Equations.
 (B) 10.6  10.9: Special systems of Differential Equations.
 (C) 14.1  14.3: The Fourier Integral.
 (D) 16.5  16.6: Vibrations of a circular membrane (requires (A)).
 (E) 17.3: Heat conduction in infinite media (may require (C)).
 (F) 18.1  18.2: Dirichlet's Problem
Comments on this page should be sent to: R. T. Bumby
Last updated: September 05, 2002