## MATH 120: Honors Differential Calculus,

Winter term, 2017.

####
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: Th 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] Solutions
- Homework 3, Due Sept 29, 2017. [LaTeX source] Solutions
- Practice midterm 1
- Homework 4, Due Oct 13, 2017. [LaTeX source] Solutions
- Homework 5, Due Oct 20, 2017. [LaTeX source] Solutions
- Homework 6, Due Oct 27, 2017. [LaTeX source] Solutions
- Homework 7, Due Nov 3, 2017. [LaTeX source] Solutions
- Practice midterm 2 Solutions
- Homework 8, Due Nov 17, 2017. [LaTeX source] Solutions
- Homework 9, Due Nov 24, 2017. [LaTeX source] Solutions
- Practice problems Solutions

### Announcements

The final exam will be on Friday, Dec 8 at 3:30pm in mathx 1100 (the math annex building). The exam is 2.5 hours, closed book, no notes, calculators, etc. Be sure to bring your student ID to the exam.I will be holding an additional office hours on Thursday, Dec 7 from 2-3:30pm in my office, Math 117.

Thomas Rud will be holding an additional office hours on Tuesday, Dec 5 from 1:30-2:30 in LSK 300C.

Please fill out the course evaluation survey at https://eval.ctlt.ubc.ca/science

### (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.

Sept 22: Infinite limits, limits of rational functions

Sept 25: Continuity

Sept 26: The intermediate value theorem

Sept 27: The extreme value theorem

Sept 29: Derivatives

Oct 2: One-sided derivatives, product rule, intro to induction

Oct 3: Induction cont'd, power rule, quotient rule, f

^{*}theorem

Oct 4: Midterm 1

Oct 6: Chain rule

Oct 9: Thanksgiving

Oct 10: Positive derivative -> increasing function, local max/min

Oct 11: Newton's method, Rolle's theorem

Oct 13: Mean value theorem, higher derivatives

Oct 16: Taylor's theorem

Oct 17 Taylor's theorem cont'd

Oct 17 Taylor's theorem cont'd, Newton'd method revisited

Oct 20: sufficient conditions for Newton's method

Oct 23: logarithms

Oct 24: Properties of log(x), inverse functions

Oct 25: Properties of e

^{x}

Oct 27: e is irrational, properties of e

^{x}cont'd.

Oct 30: More induction

Oct 31: More induction cont'd

Nov 1: Trigonometric functions

Nov 3: Trigonometric functions cont'd

Nov 6: sinh and cosh, inverse Trigonometric functions

Nov 7: Inverse Trigonometric functions cont'd, implicit differentiation

Nov 8: Midterm 2

Nov 10: implicit differentiation cont'd

Nov 13: Remembrance day

Nov 14: logarithmic differentiation, L'Hopital's rule for 0/0

Nov 15: L'Hopital's rule for 0/0 cont'd

Nov 17: L'Hopital's rule for 0/0 cont'd

Nov 20: L'Hopital's rule for ∞ / ∞

Nov 21: Applications of L'Hopital's rule, antiderivatives

Nov 22: Antiderivatives cont'd, first order differential equations, y' = ky

Nov 24: Homogeneous first order differential equations and initial value problems

Nov 27: first order differential equations and initial value problem

Nov 28: Existence and uniqueness of first order initial value problems, secord order equations

Nov 29: Linear second order homogeneous differential equations

Dec 1: Linear second order homogeneous differential equations cont'd, Logistic growth