640:421:03 Advanced Calculus for Engineering

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You may find a copy of our section's syllabus and homework assignment at http://math.rutgers.edu/~zchan/421/07/syllabus.html. It is adapted from the extensive course webpages of Professor Steve Greenfield, and is subject to adjustment. Any updated information should be posted on this web page. However, the most accurate information will be from the lectures. You may find more information about this course from our department course page.

At the bottom portion of this document you can find information about our homework/exams/grading.

Here are links to dated material, as our course progresses.

To test for your readiness for this course, here is an "entrance exam" for you to check for your mastery of the necessary background skills presumed for this course. Familiarity with all of the material tested here is necessary for success in this course. You should do this self test at home before our second meeting on Jan. 23, at which time solutions will be handed out.

You will find a formula sheet here for the quizzes.

You will find a formula sheet here for the first midterm. The midterm problems are mostly similar to the assigned problems. The course webpages of Professor Steve Greenfield contains review guides/sample exams/past actural exams for this course. We may have had slightly different emphasis, but the material on these webpages give you a sense of how we may ask questions from various different angles.

Here is a proposed formula sheet for the final exam. If you have any comments, please email them to me by Thursday, May 3. You may use a past final exam by Professor Greenfield as guidance for review of our final exam.

The course develops an assortment of topics which are necessary for advanced courses in the current Mechanical Engineering (650) undergraduate curriculum. The assortment of topics chosen this semester will be different from the catalog description but similar to what was done since spring 2004. Discussions with faculty members in Mechanical and Chemical Engineering have supported this change.

Very recently Math 421 has also been made a required course for Chemical Engineering (155). Professor Davidson, who is teaching the transport sequence (303-304), usually taken in the junior year, has urged 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. Further topics from linear algebra (most of chapter 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. For example, this material is useful to know when applying the Finite Element Method.
3. Fourier series and applications to boundary value problems, including separation of variations for the heat and wave equations (principally material selected from chapters 12 and 13 of the text).

Text
The text, new since the fall semester of 2004, is Advanced Engineering Mathematics (second edition) by Dennis G. Zill and Michael R. Cullen. We are using the 3rd edition since fall 2006, which is published by Jones and Barlett, 2006 and has 929+86 [Appendices, Answers and Index] pages (ISBN-10: 0-7637-4591-X, ISBN-13: 978-0-7637-4591-2; Paperback: ISBN-10: 0-7637-3914-6, ISBN-13: 978-0-76373914-0).
This is a very large book. Only a few of its 20 chapters will be covered. Other sections of the book will be useful in other courses, and in other parts of students' careers.
Warning As with all long and technical texts, there are misprints. 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 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.

Exams

Two formal midterm exams will be given during classes. These exams will be announced in advance. There will be a three-hour final exam, which will be on May 9, 8:00--11:00am, in SERC 204. Some formula sheets may be used during portions of the exams.

Homework and Quizzes
Homework problems will be assigned at each lecture more or less according to the syllabus and assignment schedule at http://math.rutgers.edu/~zchan/421/07/syllabus.html. While we encourage students to work together studying the material, homework should be written up independently. Select homework problems will be collected and graded. Sometimes quizzes will be given in lieu of collecing the homework problems. It is important for you to complete all assigned problems in a timely fashion. The quizzes and exams will be closely related to the homework problems, including those not designated for submission.

Your grade will be determined on the following 500-points basis:

• 80 points (16%) for collected homework and quizzes.
• 120 points (24% each) for each of the two in-class midterm exams.
• 180 points (36%) for the final exam (scheduled on May 9, 8:00--11:00am, SERC 204).