## MATH 120: Honors Differential Calculus,

Winter term, 2016.

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Instructor: Joshua Zahl.

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

My office: Math 238.

e-mail: jzahl@math.ubc.ca

Office hours: M 16:00-17:00, T 14:30-15:30, W 11:00-12:00

Text: We will loosely follow *Calculus Single Variable 8th edition* by Adams and Essex. Previous editions should be fine as well.

### Course Description

This is an Honours course. Emphasis will be on both computation and theory. Course material will mostly be taken from Chapters 1-4 of the text: Limits, 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 at the end of class. The lowest homework score will be dropped.

There will be two in-class midterms. These will be held on **Wednesday, October 5th** and **Wednesday, November 9th**. 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 16, 2016. [LaTeX source] Total: /38, Avg: 80.1%.

Comment: all students received +2 on #3, since I thought it was graded too harshly. - Homework 2, Due Sept 23, 2016. [LaTeX source] [Solutions] Total: /29. Avg: 60%.
- Homework 3, Due Sept 30, 2016. [LaTeX source] [Solutions] Total: /26. Avg: 54%.

Comment: I made problem 5b a bonus problem (i.e. the HW total is 26 instead of 30) - Midterm 1 practice [Solutions]
- Midterm 1. Total: /40. Avg: 61%
- Homework 4, Due Oct 14, 2016. [LaTeX source] [Solutions] Total: /30
- Homework 5, Due Oct 21, 2016. [LaTeX source] Total: /29
- Homework 6, Due Oct 21, 2016. [LaTeX source] Total: /39

### Announcements

### (Approximate) Course outline

Here I will post short summaries of each class and other relevant to our secion notes, as we go along.Sep 7: Sets and set notation, the natural numbers, integers, rationals, real numbers. Properties of the real numbers.

Sep 9: The real numbers; Least upper bound property, number line, open intervals.

Sep 12: Closed intervals, functions: domain, co-domain, graphs of functions, range, one-to-one

Sep 13: arithmetic of functions, composition of functions, into to limits

Sep 14: examples of limits, arithmetic of limits

Sep 16: Limits are a local property, squeeze theorem

Sep 19: One-sided limits, limits at infinity

Sep 20: Limits at infinity of rational functions

Sep 21: Limits at infinity of rational functions cont'd

Sep 23: Infinite limits, continuity

Sep 26: The intermediate value theorem

Sep 27: The extreme value theorem, types of discontinuities, arithmetic of continuous functions

Sep 28: differentiability

Sept 30: differentiability

Oct 3: differentiability implies continuity, one-sided derivatives diffrentiability rules, proof by induction

Oct 4: Reciprocal rule, quotient rule, f^* theorem

Oct 5: midterm

Oct 7: chain rule

Oct 10: Thanksgiving

Oct 11: Positive derivative -> increasing function, local max/min

Oct 12: local max/min, Newton's method

Oct 14: Rolle's theorem, mean value theorem

Oct 17: mean value theorem cont'd, higher derivatives, alternate notation for derivatives

Oct 18: Taylor's theorem, summation notation, telescoping sums, Landau's big-O notation

Oct 19: Big-O and Taylor's theorem, cont'd

Oct 21: Taylor's theorem cont'd, proof of Newton's method