## MATH 120: Honors Differential Calculus,

Winter term, 2017.

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Instructor: Joshua Zahl.

Where and when : MTWF 10-11, in Math 102.

My office: Math 117.

e-mail: jzahl@math.ubc.ca

Office hours: M 11:00-12:00, T 13:00-14:00, W 14:00-15:00

TA office hours: R 13:00-14:00 in LSK 300C

Text: We will loosely follow *Calculus Volume 1* by Tom Apostol. The text *Calculus: Single Variable, 8th edition* by Adams and
Essex is also recommended as a useful source of practice problems. Previous editions are fine as well.

### Course Description

This is an Honours course, with an emphasis on theory. Course material will mostly be taken from Chapters I, 3, 4, 6, 7, and 8 of Apostol: 1-4 of the text: The real numbers, Limits and continuous functions, Differentiation, Elementary functions, Applications and Approximation.### Grading policy

The course mark will be based on weekly homework assignments (20%), two midterms (40%), and a final exam (40%).

There will be weekly homework assignments, which are due Friday at the beginning of class. Graded homework will be returned the following Wednesday. The lowest homework score will be dropped.

There will be two in-class midterms. These will be held on **Wednesday, October 4th** and **Wednesday, November 8th**. Please make
sure you do not make travel plans, work plans, etc., without regard to the examination schedule in this class. There will be no make-up or alternate exams. If you miss a midterm, your score will be recorded as 0, unless you have a serious documented reason (an illness, a death in the family, etc.), in which case you should discuss your circumstances with the instructor as soon as possible, and in advance of the test.

### Homework

- Homework 1, Due Sept 15, 2017. [LaTeX source] Solutions
- Homework 2, Due Sept 22, 2017. [LaTeX source]
- Homework 3, Due Sept 29, 2017. [LaTeX source]

### (Approximate) Course outline

Here I will post short summaries of each class and other relevant to our secion notes, as we go along.Sep 6: Sets and set notation, the natural numbers, integers, rationals.

Sep 8: Real numbers and their properties; the least upper bound property.

Sept 11: Number line, open, closed, half-open, and punctured intervals. Functios; domain and co-domain.

Sep 12: Graphs of functions, range, one-to-one, arithmetic of functions, composition of functions.

Sep 13: Quantifiers ∀ and ∃, limits.

Sep 15: Quantifiers and limits cont'd.

Sep 18: Examples of limits, arithmetic of limits, Limits are a local property.

Sep 19: Proof of sum and product theorem for limits.

Sept 20: One-sided limits, limits at infinity.