MATH 100: Differential Calculus

Winter 2011, section 109

T/Th, 9:30-11:00 AM, Mathematics Building, room 100

All registration changes are handled centrally by the mathematics department, and not by me. See

http://www.math.ubc.ca/Ugrad/ugradRegistration.shtml

This class, intended for students who have already mastered precalculus and had some prior exposure to calculus, treats differential calculus: the concept of the derivative and its numerous applications. We will work together so that by the end of the course, you will be able to do all of the following. (This is not a complete list!)

• Understand various approaches to the definition of a limit (graphical, numerical, algebraic), and be able to evaluate limits or determine that they do not exist.
• Define continuity and to relate it to graphs of functions.
• Define and motivate the definition of the derivative. Know how to use this definition to compute derivatives of simple functions.
• Know when to use the basic rules for derivatives (chain rule, product rule, etc.) to find derivatives of possibly very complicated functions.
• Understand the relationship between the derivative of a function and basic physical concepts (velocity, acceleration).
• Understand the information that the first and second derivatives yield about the shape of a graph.
• Explain what an antiderivative is and discuss its physical meaning.
• Define the Taylor and Maclaurin polynomials and use them to approximate functions.
• Understand what is so special about "exponential growth" and how it arises from certain differential equations (e.g., Newton's law of cooling).
• Explain how the derivative helps one to find extreme values of a function and solve related optimization problems.
• Use derivatives to approximate zeros of functions iteratively (Newton's method).

For a more comprehensive description of the learning objectives for this class (and examples), please see

http://www.math.ubc.ca/~kliu/math100and180/objectives.pdf.

I would encourage you to participate in class, by answering my questions and by asking questions of your own when you are confused. If you are confused, chances are you're not alone. One of the lessons you learn as you continue on in math is that a number of people will nod when they aren't really understanding; don't be one of them!

I would also ask that you be considerate of the other students and myself by (a) turning off cellphones before class and (b) not using laptops.

Calculus: Early transcendentals, 7th edition
by James Stewart

It is important you have the seventh edition, since homework problems are taken from there.

We will aim to cover Chapters 2—4. An up-to-date list of reading assignments and corresponding homework can be found at

http://www.math.ubc.ca/~pollack/100/schedule.html

You are responsible for checking that page on a regular basis to keep up to date with reading assignments and homework.

Lectures are T/Th, from 9:30 AM - 11:00 AM in room 100 of the Mathematics Bldg. (Yes, MATH 100 in Room 100 -- beautiful synchronicity, isn't it?)

The instructor for this course is:

My office hours are there for your benefit; please take advantage of them! This time is already set aside for you; you are not interrupting.

Homework is assigned weekly. Written homework assignments should be carefully handwritten (or typed) and should be stapled. Your answers should make your thought process transparent to the grader; unintelligible work will receive no credit.

Homework is due at the start of class on the days indicated. Late assignments will not be accepted.

There will be two in-class midterm exams as well as a final exam. You will not need a calculator for the exams, and they are not permitted. Formula sheets are also not allowed.

Midterm exam 1: Thursday, October 6, 2011
exam 2: Thursday, November 10, 2011

Final exam (cumulative): December TBA

If you miss a midterm exam, you must provide me with valid documentation before the start of the next class period, or you will receive a 0 on the exam. An example of valid documentation is a note from a physician specifically stating you were medically unfit to take the exam that day. You must also promptly schedule a meeting with me to discuss possible options (such as a make-up exam).

The breakdown for final grades is as follows:

• Homework: 8 percent

• Midterms: 42 percent/2 exams

• Final exam: 50 percent

The final exam is universal across all sections, and is not written solely by your instructor. Please note that at least 50% of the mark on the final exam will be for problems that are similar to the problems in the suggested homework assignment list. Any term that occurs in Suggested Homework Problems could occur on the final exam.

After the final exam has been marked, term marks for each section will be scaled so that the distribution of term marks in the section matches the distribution of the section's final-exam marks. These adjusted term marks will be used to compute a student's final grade. This scaling is performed in order to ensure fairness of the final grades in sections whose midterm exams are harder or easier than average.

You may find it helpful to study old exams available from the department website:

http://www.math.ubc.ca/Ugrad/pastExams/index.shtml

On exams no help can be either given or received. All evaluations are closed book. No calculators, computers, or formula sheets are allowed on exams.

That being said, I would encourage you to work with others on the homework, and to discuss freely your ideas with your classmates. As iron sharpens iron, so one man (or woman!) sharpens another. However, COPYING IS NOT ALLOWED: What you turn in to me must be your own write-up. That is, it must reflect your understanding of the material (someone cannot dictate to you what to write) and must be physically written by you.

The university and I take academic dishonesty very seriously. After due investigation, students found guilty of cheating on tests and exams are usually given a final grade of 0 in the course, suspended from UBC for one year, and a notation made on their Transcript of Academic Record. For more details, see

http://students.ubc.ca/calendar/index.cfm?tree=3,54,111,960

Students with disabilities who may require special accommodations should talk to me as soon as possible. Appropriate documentation concerning disabilities may be required. For further information, please consult

https://you.ubc.ca/ubc/vancouver/disservices.ezc

Also, students who have schedule conflicts with the course due to religious observances (or other matters of equally significant weight) should come talk to me. In either case, please apprise me of the situation within the first two weeks of class (by September 20).

Outside resources (from the main MATH 100/180 site)

• Mathematics Learning Center (in LSK 100): Tutors are available, at no charge, to answer your MATH 100 questions on a drop-in basis. The current hours are 9 AM to 5 PM Mondays to Thursdays and 9 AM to 3 PM on Fridays.

• Stewart Calculus website: This website, provided by the publisher of the textbook, contains helpful supplements to the text, including reviews of high-school material.

• AMS tutoring: The UBC student society provides an assortment of tutoring services.

• Mathematics Department website: There is much available under the Undergraduates tab, including recent final exams for most undergraduate mathematics courses.

Click here to go to the main page of the math department