## MATH 120: Honors Differential Calculus,

Winter term, 2018.

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Instructor: Joshua Zahl.

Where and when : MTWF 10-11, in WOOD 4.

My office: Math 117.

e-mail: jzahl@math.ubc.ca

Office hours: M 11:00-12:00, T 13:00-14:00, W: 16:00-17:00

TA office hours: R: 14:00-15:00, LSK300C

Text: We will loosely follow *Calculus Volume 1* by Tom Apostol.

### 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 available for pickup at the Math Learning Center, which is open 11am - 5pm Mon-Fri. The lowest homework score will be dropped.

There will be two in-class midterms. These will be held on **Wednesday, October 3rd** and **Wednesday, November 7th**. 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.

The final exam will be held on **December 4 at 8:30 am** in SWNG 121.

### Homework

Weekly homework assignments will be posted here.

- Homework 1, Due Sept 14, 2018. [LaTeX source] [TA's comments]
- Homework 2, Due Sept 21, 2018. [LaTeX source] [TA's comments]
- Homework 3, Due Sept 28, 2018. [LaTeX source] [TA's comments]
- Midterm 1 Practice 1
- Midterm 1 Practice 2
- Midterm 1 [TA's comments]
- Homework 4, Due Oct 12, 2018. [LaTeX source] [TA's comments]
- Homework 5, Due Oct 19, 2018. [LaTeX source] [TA's comments]
- Homework 6, Due Oct 26, 2018. [LaTeX source] [TA's comments]
- Homework 7, Due Nov 2, 2018. [LaTeX source] [TA's comments]
- Midterm 2 Practice [Solutions]
- Midterm 2 [TA's comments]
- Homework 8, Due Nov 16, 2018. [LaTeX source] [TA's comments]
- Homework 9, Due Nov 23, 2018. [LaTeX source] [TA's comments]
- Homework 10, Not to be handed in. [LaTeX source]

### Announcements

Dec 1, 2018: I will be holding a final office hours on Monday, Dec 3 at the usual time of 11am.Nov 23, 2018: Adam will be holding an additional TA office hours on Tuesday, November 27 at 2pm in LSK300B.

Nov 1, 2018: Adam has prepared a set of final exam practice problems. They can be found here.

Oct 30, 2018: Midterm 2 will cover everything up to and including the end of lecture on October 29, i.e. everything up to and including the generalized mean value theorem.

Oct 5, 2018: Midterm 1 will be returned in class on October 9.

### Class summary

Here I will post short summaries of what is covered in each class as we go along.Sep 5: Sets and set notation, the natural numbers, integers, rationals.

Sept 7 Sets cont'd, proof by contradiction

Sep 10: Real numbers and their properties; the least upper bound property.

Sept 11: Real numbers cont'd, exists and forall notation, the number line, open, closed, half-open intervals

Sept 12: Functions: domain and co-domain, graphs of functions

Sept 14: range, one-to-one and onto, arithmetic of functions

Sep 17: composition of functions, limits

Sept 18: Limits cont'd

Sept 19: Limits cont'd

Sept 21: Limits cont'd

Sept 24: Limit rules

Sept 25: Limit rules cont'd

Sept 26: Proof of the chain rule

Sept 28: One-sided limits, limits at infinity

Oct 1: Limits of rational functions

Oct 2: Limits of rational functions cont'd

Oct 5: Infinite limits, continuity

Oct 9: Bolzano's theorem

Oct 10: Intermediate value theorem

Oct 12: Limit rules, the derivative

Oct 15: The derivative cont'd, examples

Oct 16: Derivative rules

Oct 17: Reciprocal rule

Oct 19: Quotient rule, f

^{*}theorem

Oct 22: Chain rule

Oct 23: Chain rule cont'd, extrema

Oct 24: Extrema cont'd, local extrema implies zero derivative

Oct 26: Newton's method

Oct 29: Secant method, Rolle's theorem, mean value theorem, generalized mean value theorem

Oct 30: Higher derivatives, Taylor's theorem

Oct 31: Proof of Taylor's theorem

Nov 2: Proof of Taylor's theorem cont'd

Nov 5: Convergence of Newton's method

Nov 6: Logarithms

Nov 7: Midterm 2

Nov 9: Logarithms cont'd

Nov 13: Inverse functions

Nov 14: The exponential function

Nov 16: e

Nov 19: Trigonometric functions

Nov 20: Trigonometric functions cont'd

Nov 21: Inverse trigonometric functions

Nov 23: Inverse trigonometric functions cont'd, implicit differentiation

Nov 26: L'Hopital's rule for 0/0

Nov 27: L'Hopital's rile cont'd

Nov 28: L'Hopital's rule for infty/infty, and applications

Nov 30: Logarithmic differentiation, intro to ODE