**Math 421**

This is the catalog description of the course:

01:640:421. Advanced Calculus for Engineering (3) Primarily for mechanical engineering majors.
Prerequisite: CALC 4. Credit not given for both this course and
01:640:423Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation). |

- Laplace transforms (most of chapter 3 of the text).
- Further topics from linear algebra (selected from chapters 5 through 8 of the text). Although there is some coverage of linear algebra in Math 244 (the CALC 4 course usually taken by engineering majors) experience has shown that this is insufficient for Mechanical Engineering students. They need to take advantage of symmetries (eigenvalues, etc.) and to know when and how to solve systems of linear equations.
- Fourier series and simple applications to boundary value problems, including separation of variations for the heat and wave equations (material selected from chapters 16 and 17 of the text).

**An experimental syllabus ...**

We all believe that the changes in the syllabus will
improve the suitability of the course for mechanical engineering
students, the revised curriculum should be regarded as
*experimental* and, certainly, subject to reconsideration and
further revision as the semester proceeds and after the semester is
over.

**Text**

The text is **Advanced Engineering Mathematics** (fifth
edition) by Peter V. O'Neil. It is published by Brooks/Cole, 2003 and
has 1236+82[Answers]+9[Index] pages (ISBN# 0-534-40077-9). This is a
*very* large book. Only a few of its 27 chapters will be
covered. It is hoped that other sections of the book will be useful in
other courses, and in other parts of students' careers.

*Warning* Although this is the
5^{th} edition of the text, previous instructors and students
have remarked that there are still misprints and sometimes,
infelicities (!) of expression. Please read the book carefully.

**Technology**

Many of the computations needed to apply the techniques of this course
are quite elaborate. Therefore such software packages as
`Matlab` and `Maple` (and others) include many special
functions designed to handle these techniques. While we (strongly!)
encourage students to use these programs, course exams and most
homework should be done by hand. The exams will be designed to avoid
elaborate and tedious computation. Appropriate use of technology is
important, and, just as students should recognize that the
antiderivative of x^{3}sin(5x) is not likely to be exp(17x)
(!), enough facility with "hand computation" should be developed so
that students can check (approximately and appropriately) Laplace
transform, Fourier series, and linear algebra computations.

**Grading**

**Formal exams**
Several formal exams will be given during classes. These exams will be
announced in advance. There will be a three-hour final exam. Some
formula sheets may be used during portions of the exams. The times of
the exams and the format will be assigned in advance.

**Homework**
Students should do homework. Several problems will be collected each
week. While we encourage students to work together studying the
material, homework should be written up independently.

**Informal quizzes**
Informal quizzes may be given in any class. The results of these
quizzes will *not* be major components of the course grade, but
may be useful to both the instructor and the student regarding
progress in the course.

**A precise formula?**
I don't have an exact formula yet, but *tentatively* each in-clss
will count for 20%, the final exam for 40%, and the homework and QotD,
about 20%.

**Office hours**

My office is in Hill Center: Hill 542, telephone number: (732)
445-3074. I usually check e-mail several times a day so it is probably
the best way to communicate with me: greenfie@math.rutgers.edu.
I will usually have a sandwich in my office about 5 PM each class day,
and will welcome "office hour visits" from about 5:30 PM to 7 PM on
Tuesdays and Thursdays. I also encourage you to ask questions via
e-mail or after almost any class or to make an appointment at a
mutually convenient time.

**Other references**

Much of the material covered in this course has been an important part
of scientific and engineering education for a century. The amount of
literature available is extraordinary. For example, on 1/19/2004
`Google` reported about 48,300 web pages in response to the
query *Laplace transform* while `Amazon` had 889 results
under *books* and *Laplace transform*. Students who learn of
useful references (especially interactive web pages) are encouraged to
report them to their instructor.

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/26/2004.
**