MATH 120: Honors Differential Calculus,
Winter term, 2016.
Instructor: Joshua Zahl.
Where and when : MTWF 10-11, in Math 102.
My office: Math 238.
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 DescriptionThis 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 policyThe 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 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. Avg: 64%
- Homework 5, Due Oct 21, 2016. [LaTeX source] [Solutions] Total: /29. Avg: 77%
- Homework 6, Due Oct 28, 2016. [LaTeX source] [Solutions] Total: /39. Avg: 79%
- Homework 7, Due Nov 4, 2016. [LaTeX source] [Solutions]Total: /25 + 12 bonus. Avg: 100%
- Midterm 2 practice [Solutions]
- Homework 8, Due Nov 21, 2016. [LaTeX source] [Solutions] Total: /23. Avg: 68%
- Homework 9, Due Nov 28, 2016. [LaTeX source] [Solutions] Total: /35. Avg: 85%
- Homework 10 [LaTeX source] [Solutions]
- Practice final [Solutions]
AnnouncementsJack and Phillip have made a (unofficial) sheet summarizing the theorems discussed in class. It is available here.
(Approximate) Course outlineHere 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 1
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
Oct 24: Functional equation for log(x)
Oct 25: Properties of log(x)
Oct 26: inverse functions
Oct 28: Properties of e^x
Oct 31: Derivatives of trigometric functions
Nov 1: Derivatives of trigometric functions cont'd
Nov 2: hyperbolic trig functions, inverse trig functions
Nov 4: Inverse trig functions cont'd, implicit differentiation
Nov 7: Implicit differentiation cont'd, logarithmic differentiation
Nov 8: L'Hopital's rule
Nov 9: Midterm 2
Nov 11: Remembrance day
Nov 14: L'Hopital's rule cont'd
Nov 15: Applications of L'Hopital's rule, anti-derivatives
Nov 16: First order differential equations, y' = ky
Nov 18: Homogeneous first order differential equations and initial value problems
Nov 21: Non-homogeneous first order differential equations
Nov 22: Non-linear first order differential equations, existence and uniqueness, second order equations
Nov 23: Linear second order homogeneous differential equations
Nov 25: Linear second order homogeneous differential equations cont'd, complex numbers
Nov 28: Logistic growth, harmonic motion
Nov 29: Review
Nov 30: Review
Dec 2: Review