Math 421
This is the catalog description of the course:

Math 421 is also a required course for Chemical and Biochemical Engineering (curriculum 155). The required course sequence 155:303-304 (transport) is usually taken in the junior year. The chemical engineering department advises their students to take Math 421 no later than the semester in which 303 is taken. Math 421 is also useful for Process Control.

The course will have three parts:

1. Laplace transforms (most of chapter 4 of the text).
2. Fourier series and applications to boundary value problems for partial differential equations, emphasizing the heat and wave equations (material selected from chapters 12, 13, and 14 of the text).
3. Linear algebra (from chapter 8 of the text). Although there is a small amount of linear algebra in Math 244 (the CALC 4 course usually taken by engineering majors), and in 650:231 (Computational Analysis and Design), experience has shown that this is insufficient for more advanced engineering courses. Students need to take advantage of symmetries (eigenvalues, etc.) and to know when and how to solve systems of linear equations. For example, this material is useful to know when applying the Finite Element Method.

Text
The text is Advanced Engineering Mathematics (third edition) by Dennis G. Zill and Michael R. Cullen. It is published by Jones and Barlett, 2006 (ISBN-10: # 0-7637-4591-X). This is a very large book. Only five of its twenty chapters will be covered in this course. However, other sections of the book will be useful in other math, physics, and engineering courses, and in other parts of students' careers.
Warning: As with all long and technical texts, there are misprints. Please read the book carefully. The publisher has (unfortunately) chosen to use red backgrounds or type for many complicated formulas, along with a very small size type. You may need a magnifying glass at times to read the exponents in the formulas.

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 procedures designed to handle these techniques. While I (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 done by software packages.

Grading
Exams: Two 80 minute exams will be given during class periods (see syllabus for dates). Each exam will count for 20% of the course grade. There will be a three-hour final exam (scheduled by the university), which will count for 40% of the course grade. Some formula sheets will be provided for the exams, and will posted on the course web page in advance.

Homework: Students are encouraged to do all the assigned homework. Selected problems from the homework list (marked by *) will be collected each week for grading (see the course syllabus for exercises and dates due). The homework will count for 10% of the grade. While I encourage students to work together studying the material, homework solutions must be written up independently. The writeups should be clear and give complete details showing how the answer is obtained (almost all of the homework problems assigned have answers in the back of the book). The point of doing homework is to learn the subject.

Office hours
My office is in Hill Center: Hill 428, telephone number: (732) 445-2390, ext. 3071. My formal office hours will be 2:00 - 3:00 Tuesday and Thursday. You can also make an appointment at a mutually convenient time. I usually check e-mail several times a day so it is probably the best way to communicate with me: goodman at math dot rutgers dot edu. You can ask also questions via e-mail and I'll try to answer them.

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 12/12/2008 Google reported about 4,130,000 results in response to the query Laplace transform while Amazon had 7,532 results under books and Laplace transform. Students who learn of useful references (especially interactive web pages) are encouraged to mention them to the class.

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