Dror Bar-Natan: Classes: 2004-05: | FEEDBACK |
Agenda: Understand calculus and its rigorous foundations.
Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Sidney Smith 5016G, 416-946-5438. Office hours: Thursdays 12:30-1:30.
Classes: Tuesdays 10-11 and Thursdays 9-11 at Sidney Smith 2117.
Tutorials: Mondays at 2-4, in three groups divided by the last non-zero digit of your student number:
digit | tutor | place | |
1-3 | Shay Fuchs, s.fuchs@utoronto.ca, SS6027, 8-2095 | WB 342 | |
4-6 | Derek Krepski, dkrepski@math.toronto.edu, SP209, 8-3201 | GB 412 (fall) / BA 2175 (spring) | |
7-9 | Brian Pigott, bpigott@math.toronto.edu, SP209, 8-3201 | GB 405 (fall) / GB 404 (spring) |
# | Week of ... | |
Fall Semester: | ||
1 | September 6 |
Classes begin on Thursday September 9.
Handout: About This Class Class notes for Thursday September 9, 2004 (degrees and radians, the basic trigonometric functions, basic identities, rotating pixels, sin and cos of sums of angles) |
2 | September 13 |
Monday's tutorials will end at 3PM instead of the usual 4PM.
Homework Assignment 1 Handout: The 13 Postulates Class notes for Tuesday September 14, 2004 (trigonometry and AM modulation, a word about the 13 postulates) Putnam Contest Announcement Class notes for Thursday September 16, 2004 (the first 12 postulates and their basic consequences) |
3 | September 20 |
Homework Assignment 2
Class notes for Tuesday September 21, 2004 (the absolute value and the triangle inequality, the natural numbers and property I) Thursday's class was cancelled. |
4 | September 27 |
Homework Assignment 3
JHU's Zucker on Math Courses Class notes for Tuesday September 28, 2004 (induction) History of the Theory of Irrational Numbers Class notes for Thursday September 30, 2004 (the integers, even/odd numbers, the rationals, irrationality of root 2, every non-empty set of natural numbers has a least member, recursive definitions) We took our Class Photo this Thursday! |
5 | October 4 |
Monday: Makeup class at tutorial time, 2-4 at LM162.
Handout: Visualization. Class notes for Monday October 4, 2004 (final words about induction and P1-12, functions, compositions and the identity, graphs) Homework Assignment 4 Class notes for Tuesday October 5, 2004 (more graphs) Class notes for Thursday October 7, 2004 (distances and circles, limits imprecise and precise, uniqueness of the limit, limit of a sum) |
6 | October 11 |
Monday is Thanksgiving.
Office hours this week: Thursday 6-8 with Derek Krepski, Friday 10-12 with Shay Fuchs and 3-5 with Dror Bar-Natan, all at the Math Aid Centre, SS 1071. Homework Assignment 5 Handout: Math 137's "How to Solve Problems" Class notes for Tuesday October 12, 2004 (existence and non-existence of limits) Class notes for Thursday October 14, 2004 (sums, products and quotients of limits, continuity, compositions) Friday October 15 is the last date to drop down to Math 133 or Math 135. |
7 | October 18 |
Monday: Term Exam 1
took place in the tutorials. See the
Solution of Term Exam 1.
Homework Assignment 6 Class notes for Tuesday October 19, 2004 (funny examples for continuity, compositions, the first fun theorem) Handouts: Monsters, Evariste Galois. Class notes for Thursday October 21, 2004 (the three fun theorems and corollaries, zeros of polynomials, beginning of a proof) Friday October 22 is the last date to drop down to Math 137. |
8 | October 25 |
Homework Assignment 7
Class notes for Tuesday October 26, 2004 (P13, equivalent form, boundedness of N) Thursday: Dror was away giving two talks, class was taught by Brian Pigott. Class notes for Thursday October 28, 2004 (Brian Pigott: proofs of the three fun theorems) |
9 | November 1 |
Homework Assignment 8
Class notes for Tuesday November 2, 2004 (differentiability and the derivative, differentiability and continuity) Class notes for Thursday November 4, 2004 (derivatives for approximations, finding derivatives is cool and easy, the chain rule) |
10 | November 8 |
Homework Assignment 9
Class notes for Tuesday November 9, 2004 (proof of the chain rule, other notations) Class notes for Thursday November 11, 2004 (the geometric signifcance of the derivative: local extrema and critical points, increasing/decreasing functions and the sign of the derivative, Rolle's theorem and the mean value theorem) |
11 | November 15 |
Homework Assignment 10
Handout: Newton vs. Leibniz. Class notes for Tuesday November 16, 2004 (sufficient condition for min/max, graphing) Handout: A Little on Convexity. Class notes for Thursday November 18, 2004 (plotting the hard (and complete) way, convexity, the Cauchy mean value theorem and L'Hopital's law) |
12 | November 22 |
Homework Assignment 11
Class notes for Tuesday November 23, 2004 (L'Hopital's law) Class notes for Thursday November 25, 2004 (inverse functions, fractional powers, monotonicity for continuous 1-1 functions) |
13 | November 29 |
Monday: Term Exam 2
took place in the tutorials. See the
Solution of Term Exam 2.
Homework Assignment 12 Class notes for Tuesday November 30, 2004 (end of monotonicity proof, proofs of continuity and differentiability of inverse functions) Transparency: Some problems with Areas. Class notes for Thursday December 2, 2004 (first class on integration) |
14 | December 6 |
Monday tutorials as follows: Shay's group at SF
1101, Derek's at BA
1190 and Brian's at BA
1130.
Web only: What Went Wrong with Term Exam 2? Class notes for Tuesday December 7, 2004 (the "one partition for every epsilon" criterion for integrability) Classes end December 8 (no Thursday class). |
Winter Semester: | ||
15 | January 3 |
No tutorials this week!
Homework Assignment 12a Handout: Integration. Class notes for Tuesday January 4, 2005 (reminders on integration, refining partitions) Class notes for Thursday January 6, 2005 (end of L(f,P1)<=U(f,P2), continuity and uniform continuity, uniform continuity and integrability, hard theorem 4) |
16 | January 10 |
Homework Assignment 13
Handout: epsilon and delta. Class notes for Tuesday January 11, 2005 (proof of hard theorem 4, f <= g => \int f <= \int g) Class notes for Thursday January 13, 2005 (integration lite theorems, HW12a in class review, the first fundamental theorem and its proof) Thursday: Dror's office hours 11:30-12:30 (this week only). |
17 | January 17 |
Homework Assignment 14
Handout: On Maps, Machines and Roaches. Class notes for Tuesday January 18, 2005 (more on the Fundamental Theorem of calculus, HW13 in class review) Transparency: A Differentiable Function with a Non-Continuous Derivative Class notes for Thursday January 20, 2005 (the second fundamental theorem of calculus, HW14 in class review, π) |
18 | January 24 |
Tutorial handout (Krepski): The Devil is in the Details
Homework Assignment 15 Handout: Pi, approximately Class notes for Tuesday January 25, 2005 (the definition of cos and sin) Class notes for Thursday January 27, 2005 (the extension of sin and cos to R, f''=-f and sin and cos, sin and cos of a sum of angles) |
19 | January 31 |
Homework Assignment 16
Transparency: Plots of the trigonometric functions Class notes for Tuesday February 1, 2005 (the inverse trigonometric functions and a word about exponentials and logarithms) Class notes for Thursday February 3, 2005 (exp and log and their basic properties) |
20 | February 7 |
Monday: Term Exam 3
took place in the tutorials. See the
Solution of Term Exam 3.
Homework Assignment 17 Class notes for Tuesday February 8, 2005 (minor properties of log and exp, their growth rate relative to polynomials and their graphs) Transparency: The Khovanov Homology of T(9,5) Class notes for Thursday February 10, 2005 (ordering by size, reverse-dictionary integration, integration by parts) Sunday February 13: last chance to drop this course. |
Reading | February 14 | |
21 | February 21 |
Homework Assignment 18
Handout: π is Irrational. Class notes for Tuesday February 22, 2005 (integration by substitution) Class notes for Thursday February 24, 2005 (substitution tricks, rational functions, arc length) |
22 | February 28 |
Homework Assignment 19
Class notes for Tuesday March 1, 2005 (arc length) Class notes for Thursday March 3, 2005 (volumes and surface areas, existence and uniqueness of Taylor polynomials) Thursday: Dror's office hour is 1-2PM. |
23 | March 7 |
Homework Assignment 20
Class notes for Tuesday March 8, 2005 (Taylor's hard to believe, examples, mins and maxs) Class notes for Thursday March 10, 2005 (proofs of the local property of Taylor polynomials, proof of the min/max theorem, the remainder formula: applications and proof, irrationality of π) |
24 | March 14 |
Homework Assignment 21
Class notes for Tuesday March 15, 2005 (the Schwarz derivative, sequences) Class notes for Thursday March 17, 2005 (sequences: the goals, limits, the relation with continuity, increasing sequences) |
25 | March 21 |
Monday: Term Exam 4 took
place in the tutorials. See the
Solution of Term Exam 4.
Homework Assignment 22 Class notes for Tuesday March 22, 2005 (vista points, increasing/decreasing subsequences, Bolzano-Weierstrass, Cauchy sequences) Handout: Series Class notes for Thursday March 24, 2005 (Cauchy's criterion, series, the sum of two series, Cauchy for series, the vanishing criterion, comparison tests, the ratio test) |
26 | March 28 |
Homework Assignment 23
Class notes for Tuesday March 29, 2005 (the ratio test, the integral test, Leibnitz's theorem, rearranging series) Class notes for Thursday March 31, 2005 (proofs of the integral test, Leibnitz's theorem and the Cauchy condensation test, the fine line between convergence and divergence, absolute convergence and reaaranging absolutely convergent series) |
27 | April 4 |
No homework assignment assigned this week!
Class notes for Tuesday April 5, 2005 (absolute convergence and the distributive law for series) Last Handout. Class notes for Thursday April 7, 2005 (things we'd had done if had more time: complex numbers and Euler's formula, the Fibonnaci sequence, more on uniform convergence) |
Study | April 11 | Absolutely all homework is due Friday April 15, 2PM, at the Math Aid Centre (SS 1071). |
Study | April 18 | |
Study | April 25 | |
Final | May 2 |
Pre-final office hours: Monday and Tuesday May 2nd and 3rd, from
10AM until 1PM (or even later, if there's demand), at the Math Aid
Centre, SS 1071.
Wednesday May 4: The Final Exam took place at 7-10PM (late!). The average grade was 81.66 of 120 (or 68.05/100), the median was 82 (68.33/100) and the standard deviation was 21.9 (18.25/100). |
Further resources: