MAT 137Y5Y: Calculus
Instructors:
Office: SB 2110Q
TU 14:00–16:00 NE 224
TH 15:00–16:00 SE 1104
Office hrs : TU 16:00-17:00, TH 14:00–15:00 email: s.kocic@utoronto.ca
Cristobal Rojas
Office : SB 2110R
TU 13:00–14:00 CC 2130
TH 13:00–15:00 CC 2130
Office hrs : TU 14:00–15:00, TH 15:00-16:00 email: cristobal.rojas@utoronto.ca
Fall 2009 - Spring 2010
Blackboard: http://portal.utoronto.ca
All course-related materials will be posted on Blackboard. Please check the website for any updates throughout the term.
Textbook: Calculus: One Variable, 10th Ed.
, by Salas, Hille, Etgen.
Other useful references: There are excellent classic books in the literature. More references will be added later on.
1.
Calculus , by M. Spivak
2.
Calculus, Vol. 1 , by T. Apostol
3.
Differential and Integral Calculus, Vol. 1 , by R. Courant
Course Description
This is a course in Calculus of one variable. The first part of the term focuses on the notion of continuity of functions and differentiation of functions, which, roughly, describes how fast the values of functions change. The second part of the course discusses the problem of integration (related to the problem of finding the area of a planer surface) and the connection between differentiation and integration – the so-called Fundamental Theorem of Calculus.
From the MCS department :
A conceptual approach for students with a serious interest in mathematics. Geometric and physical intuition are emphasized but some attention is also given to the theoretical foundations of calculus.
Material covers first a review of trigonometric functions followed by discussion of trigonometric identities.
The basic concepts of calculus: limits and continuity, the mean value and inverse function theorem, the integral, the fundamental theorem, elementary transcendental functions, Taylor’s theorem, sequences and series, power series.

Evaluation
Calculus Assessment Test: 2%
Quizzes (6): 18%
Term tests (4): 40%
Final Exam: 40%
Important Dates
• Quiz Dates (First Semester): Sep 25, Oct 16, Nov 13.
• Term Test Dates (First Semester): Oct 30, Nov 27
Course Outline
The following is a rough outline of the material which will be covered throughout the first semester.
7
8
9
4
5
6
10
11
12
Week Dates
1
2
3
Sept. 8-10
Sept. 15-17
Sept. 22-24
Sept. 29 - Oct 1.
Oct. 6-8
Oct. 13-15
Oct. 20-22
Oct. 27-29
Nov. 3-5
Nov. 10-12
Nov. 17-19
Nov. 24-26
Sections
1.2-1.4
1.5-1.7
Topics
Review of Elementary Math, Inequalities, Geometry
Review of Functions
1.8, 2.1-2.2
Introduction to Proofs, Definition of a Limit
2.3-2.4
2.5-2.6
2.6, 11.1
3.1-3.4
3.5-3.7
4.1-4.5
4.6-4.8
4.12
Limits and Continuity
Squeeze Theorem, Theorems on Continuity
Intermediate Value Theorem, Boundedness, Least Upper Bound
Derivatives, Techniques for Differentiation
Chain Rule, Trigonometric Differentiation
3.8-3.9, 4.10
Implicit differentiation, Inverse functions, Related Rates
Mean Value Theorem, Extremum problems
Taylor approximations, Convexity
Important Information
• All quizzes and term tests will be held during the Friday practical sessions from 1-2pm.
• There will be no make-up quizzes or term tests. In the event of a missed quiz or test for medical reasons (the appropriate medical documentation will need to be provided), the percentage of the final mark assigned to that quiz or test will be assigned to the final exam. Missing a quiz or term test for an inadequate reason will result in a grade 0 for that particular test or quiz.
• A series of problem sets will be assigned throughout the course. These problem sets are designed to assist students in understanding the course material. These problem sets are not to be handed in.
However, they will serve as good practice for quizzes, term tests, and the final exam as questions on these will be on approximately the same level as questions on the problem sets. Students are encouraged to use tutorial time to work through the problem sets with a teaching assistant.
• The Academic Regulations of the University are outlined in the Code of Behaviour on Academic
Matters which can be found in the UTM Calendar or on the web at http://www.utm.utoronto.ca/regcal/WEBGEN117.html
.
• Please be aware that the latest version of the student handout ”How Not to Plagiarize” is available at http://www.utoronto.ca/writing/plagsep.html
.