General information about Math 421, spring 2004

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 01:640:423
Laplace 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).
The course develops an assortment of topics which are necessary for advanced courses in the current Mechanical Engineering undergraduate curriculum. This semester the selection of topics has been modified from recent previous semesters following discussions with Professor A. Norris and Professor A. Cuitino, who are, respectively, the chair and vice-chair for the undergraduate program of Mechanical Engineering. In particular the general topic of nonlinear systems of o.d.e.'s and its phase plane analysis has been deleted. The course will have three parts:
  1. Laplace transforms (most of chapter 3 of the text).
  2. 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.
  3. 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).
Professors Norris and Cuitino remarked that knowledge of these topics is quite important for the required courses 650:443 (Vibrations and Controls) and 650:481 (Heat Transfer), as well as other optional courses in the 650 curriculum. Previous instructors and students of the course were consulted also.

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.

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 5th 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.

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 x3sin(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.

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: 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 and last modified 1/26/2004.