MAT 237, Quiz 2

Name
Tutorial
Quiz 2 will cover sections 1.2  1.5 as well as all the background readings (posted on the DEJA VU page of
BB). If you dont have a copy of the MAT137 textbook please pair up with someone who has taken MAT137
and has a cop
Chapter 6
INFINITE SERIES
Infinite series are sums with infinitely many terms, of which the most familiar
examples are the nonterminating decimal expansions. For instance, the equality
vr = 3.14159 . is an abbreviation of the statement that vr is the sum
Chapter 4
INTEGRAL CALCULUS
In this chapter we study the integration of functions of one and several real vari
ables. As we assume that the reader is already familiar with the standard techniques
of integration for functions of one variable, our discussio
MAT237ADVANCED CALCULUS
Amir moradifam
SUMMER 2011
amir@math.toronto.edu
1. LECTURES: Tues. Thurs. 69, PB, B250
First term (MayJune): Amir Moradifam, amir@math.toronto.edu
Oce hours: TBA
Second term (JulyAugust): S. Homayouni, soheil.homayouni.boro
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MAT 237, Quiz 4 Name TUTOlOl
Part A: (2 marks) What does it mean for a point a to be a critical point of a function f. What does it
mean for this point to be a saddle point for f?
lax
l
g.
reasoning.
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S
2.
Implicit function theorems and applications
2.1 Implicit functions
The implicit function theorem is one of the most useful single tools youll meet this
year. After a while, it will be second nature to think of this theorem when you want
to figure out h
MAT 237

Quiz 4
Week of Jan 20
Quiz 5 will cover sections 2.8 and 2.9 (and indirectly 2.7). It will be written in the last 15 to 20 min of
your tutorial. As before there will be three parts in the quiz: denition, application, and proof.
Part A: Denitions
MAT 237, Quiz 3

Name
Tutorial
Quiz 2 will cover sections 1.5  1.8 and takes place in the last 15 to 20 min of your tutorial in the week
of Oct 28. There will be three parts in the quiz: part A asks you to provide a denition or statement of a
theorem
MAT 237

Quiz 5
Week of Feb. 3
Quiz 5 will cover sections 2.10, 3.1 and 3.2. It will be written in the last 15 to 20 min of your tutorial.
As before there will be three parts in the quiz: denition, application, and proof.
Part A: Denitions and statements
Chapter 5
LINE AND SURFACE INTEGRALS;
VECTOR ANALYSIS
The themes of this chapter are (1) integrals over curves and surfaces and (2) differ
ential operations on vector fields, which combine to yield (3) a group of theorems
relating integrals over curves, s
Chapter 8
FOURIER SERIES
Fourier series are infinite series that use the trigonometric functions cos n6 and
sinnO, or, equivalently, emd and e inS, as the basic building blocks, in the same
way that power series use the monomials xn. They are a basic tool
Appendix A
SUMMARY OF LINEAR ALGEBRA
This appendix consists of a brief summary of the definitions and results from linear
algebra that are needed in the text (and a little more). Brief indications of proofs
are given where it is easy to do so, but lack of
Chapter 7
FUNCTIONS DEFINED BY SERIES
AND INTEGRALS
In this chapter we study the convergence of sequences and series whose terms are
functions of a variable x and improper integrals whose integrand contains x as a
free variable. In all these situations, t