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## Calculus 250a: Advanced Calculus I, Fall 2006

 Instructor: Dan Christensen Office: Middlesex 103B Phone: 661-2111 x86530 E-mail: jdc@uwo.ca Office Hours: Mondays 2:30-3:30, Tuesdays 11:30-12:30, MC103B TA Help Sessions: Wednesdays 3-4, Thursdays 1-2, both in MC106 Section 1 Section 2 Class times: MWF 1:30-2:30 MWF 10:30-11:30 Class location: SSC-2024 NS-7 Text: Multivariable Calculus, Fifth Edition, by James Stewart. Brooks/Cole. Should be on 2-hour reserve at Taylor by late August. Student Solutions Manual for Multivariable Calculus, Fifth Edition, by James Stewart. Brooks/Cole. (Optional.) Prerequisites: A minimum mark of 60% in Calculus 051a/b or Applied Mathematics 026, or a minimum mark of 85% in Calculus 081a/b. Pre- or Corequisites: Linear Algebra 040a/b or the former Mathematics 202a. Antirequisites: Calculus 280a/b, Applied Mathematics 290a.

### Course outline:

Differential calculus of functions of several variables: level curves and surfaces; limits; continuity; partial derivatives; total differentials; Jacobian matrix; chain rule; implicit functions; inverse functions; curvilinear coordinates; derivatives; the Laplacian; Taylor Series; extrema; Lagrange multipliers; vector and scalar fields; divergence and curl.

We will also cover the required background about vectors in 3-dimensional space, e.g. dot products, cross products, lines, planes, etc.

The course material corresponds to Chapters 13, 14 and 15 and Sections 17.1 and 17.5 from the text, plus a few additional topics.

### Evaluation of Student Performance:

 Assignments: 15% Midterm Examination: 35% Final Examination: 50%

There will be 6 assignments with due dates: Friday, September 22; Friday, October 6; Friday, October 20; Friday, November 3; Friday, November 17; Friday, December 1. (Every two weeks.) They are due at the beginning of class. Click here for a list of exercises and the procedures for handing in homework. The lowest (or missing) assignment grade will be dropped when computing the course grade. Here is what the assignments are out of: HW1 30, HW2 37, HW3 38, HW4 29, HW5 TBA, HW6 TBA.

The midterm exam will be on Thursday, October 26, 7-10 pm. It will take place in Talbot College rooms 342, 343, 348A, 348B. Room assignments are now available. You must look up which room you are to write in. The midterm covers up to section 15.2.

The final exam is scheduled for Monday, December 11, 2-5 pm at Alumni Hall stage. It will cover the entire course, but will emphasize material not already covered on the midterm.

For both exams, questions will be similar to homework and recommended exercises. The best way to prepare is to do all of those exercises, plus as many additional questions as you can. Please read the section below if you have a conflict with either exam.

There will be help sessions before both exams. Both exams will contain a mix of multiple choice questions and long answer questions. Calculators are not permitted at either exam.

### Make-up exams and conflicts

For the midterm:

In the event that you must miss the midterm due to a valid conflict, the make-up exam will be given before the regular exam. Usually this will be earlier on the same day, or on the day before. If you are in this situation, you must let us know at least two weeks before the exam date.

If you miss the midterm due to illness, you must present a doctor's note to the appropriate Dean's office, and you may be given a make-up exam as soon as possible after the regular exam, or have the weight of the midterm transferred to the final exam. If you are in this situation, you should contact your instructor as soon as you realize that you will miss the exam.

For the final exam:

If you have a conflict with another final exam, you must contact Rob Downes in the Registrar's Office by mid November to arrange a special time/place to write the final. If you have a conflict with a midterm for a year-long course, you must contact the instructor of the other course. If you have three final exams in 3 consecutive periods, you must contact the Dean of your faculty. In all cases, please let your instructor know. If we need to give you a make-up exam, it will be given before the regular exam.

If you miss an exam due to illness, you must present a doctor's note to the appropriate Dean's office, and you will be given a make-up exam as soon as possible after the regular exam. If you are in this situation, you should contact your instructor as soon as you realize that you will miss the exam.

Failure to follow these rules will result in a grade of zero.

### What is expected of the student:

The aim of the course is for you to learn the techniques of multivariable calculus and to gain an understanding of the concepts on which the techniques are based. To accomplish this, it will be necessary to attend all classes, do all of the suggested exercises, and keep up to date with the material. We highly recommend reading the text and doing the exercises throughout the term, not only immediately before tests and assignment due dates.

The assignments are to be thought of as take-home exams and should be done entirely on your own. All those involved in copying will receive a negative grade on the assignment in question. In addition, all academic offenses will be reported to the Dean's office, and may result in further penalties. Regarding Scholastic Offences and Penalties, see pp. 39-41 of the Academic Calendar or refer to Academic Penalties.

### A note to all students from the office of the Dean of the Faculty of Science:

You are responsible for ensuring that you have successfully completed all course prerequisites and that you have not taken an antirequisite course. Lack of prerequisites may not be used as the basis of appeal. If you are not eligible for a course, you may be removed from it at any time, and will receive no adjustment to your fees. These decisions cannot be appealed.

If you do not have the course prerequisites, and have not been granted a special permission to take the course by the department, it is in your best interest to drop the course well before the end of the add period. Your prompt attention to this matter will not only help protect your record, but will ensure that spaces become available for students who require this course for graduation.

Please check the exercises page and the course web page regularly for announcements and other information.