Some Symbols and Notations
MAT 1339
September 11, 2013
In mathematics, we make a kind of translation for some of the English
phrases just to make the sentences shorter. Some of these symbols and
notations are as follows:
1. The symbol
has been reserved f

MAT 1339, Fall 2013 Assignment 3
Due NOV8th 11:59 AM.
Late assignments will NOT be accepted. An assignment drop-o box is assigned for this
course and is located at Math department. (KED 585)
Professor: Termeh Kousha
Student Name
Student Number
By signing

MAT 1339, Fall 2013 Assignment 2
Due Oct 25th 11:59 AM.
Late assignments will NOT be accepted. An assignment drop-o box is assigned for this
course and is located at Math department. (KED 585)
Professor: Termeh Kousha
Student Name
Student Number
By signin

Vector Geometry
MAT 1339 C
Fall, 2013
1
1
Geometric Vectors
1.1
Cartesian Vectors
In the plane, coordinates are introduced as follows:
Choose a point O called the origin,
choose two perpendicular lines through O called the X -axis, and
the Y -axis, and

MAT 1339, Fall 2013 Assignment 1
Due Sep 27th 11:59 AM.
Late assignments will NOT be accepted. An assignment drop-o box is assigned for this
course and is located at Math department. (KED 585)
Professor: Termeh Kousha
Student Name
Student Number
By signin

MAT 1339, Fall 2013 Assignment 4
Due NOV29th 11:59 AM.
Late assignments will NOT be accepted. An assignment drop-o box is assigned for this
course and is located at Math department. (KED 585)
Professor: Termeh Kousha
Student Name
Student Number
By signing

Elasticity of demand
You run a business, and want to maximize revenue.
Idea #1 Raise the price
Potential Problem
You decrease the demand.
If demand decreases significantly, total revenue could decrease.
Idea #2 Decrease the price
You may not increase dema

The Derivative
MAT 1300 C
Winter 2014
1 APPROXIMATING WITH LINEAR FUNCTIONS
1
2
Approximating with Linear Functions
Ex: The sales of long distance phone time in minutes, q , depends on the
price per minute in cents, p, as follows.
q = f (p) = 5000 30p2
If

Limits, Exponentials, and Logarithms
MAT 1300 C
Winter 2014
1 LIMITS
1
2
Limits
Ex: Consider the function
f (x) =
|x2 1|
.
x1
a) What is the domain of f ?
b) As x gets really close to 1 on the left (x < 1) what happens to f ?
c) As x gets really close to

Precalculus Review
Professor: Termeh Kousha
MAT 1300 C-Winter 2014
Mathematics provides a language to precisely model a problem and then
provides tools to logically solve the problem.
Calculus is the study of functions with special emphasis on the rate of

Question 1. Simplify the following expression:
49 52
71 51
A)
221
25
B)
49
35
C)
343
5
D)
7
25
E)
25
49
Question 2.
Solve the following equation:
18
10
=
x
x4
A) x = 11
B) x =
24
13
C) x = 4
D) x =
1
11
15
E) x = 9
Question 3. Determine which of the expre

Final Examination
Math1339 (A) Calculus and Vectors
December 12, 2009
14:00-17:00
Jie Sun
Department of Mathematics and Statistics
University of Ottawa
Email: jie.sun@uottawa.ca
Final Examination
MAT 1339 A
Instructor: Jie Sun
December 12, 2009
14:00-17:0

DGD 5, Fall 2013
MAT 1339 C
Derivatives
1. Find the derivatives of the following functions:
(a) f (x) = (x2 3x)4 (x3 + 1)
(b) g (x) =
4x2 5
3x2
3
2
(c) f (x) =
(d) f (x) =
4x2 x
x x2
2
.
x3 2x2 + 5
3
(e) g (s) =
(f) h(t) =
3t1
(5t1)2
1
2x3 + 1(x 3 + 2)
2.

DGD10 - Practice Exam.
1
DGD10-Practice Midterm
Question 1. Given the vector u = [1, 1, 2], nd a unit vector v in the same direction as
u.
Question 2. Let u = [3, 1, 1] and v = [3, 4, 1]. Find (3u).(v u) and (2v u).(3)(5v ).
Question 3. Let f (x) = 3e2x2

The Derivative
MAT 1339 C
Fall 2013
1 DEFINITION OF THE DERIVATIVE
1
2
Denition of the Derivative
Let f (x) be a function. Then we dene the derivative of f at x, denoted
f (x), as
f ( x + x) f ( x)
f (x) = lim
x 0
x
if that limit exists, and if it does w

The Chain Rule
MAT 1339 C
Fall 2013
1 THE CHAIN RULE
1
2
The Chain Rule
The Chain Rule: Let f (x) and g (x) be dierentiable functions. Then
d
[f (g (x)] = f (g (x)g (x).
dx
The General Power Rule: Let g (x) be a dierentiable function and let
h(x) = [g (x)

1
Fundamentals
1.1
Real Numbers
To start, well review the numbers that make up the real number system.
1. Natural numbers (denoted N) - these are just positive whole numbers:
1, 2, 3, . . .
2. Integers (denoted Z) - all natural numbers together with their

Rate of Change
MAT 1339 C
Fall 2013
1 RATES OF CHANGE AND THE SLOPES OF CURVES
1
2
Rates of Change and the Slopes of Curves
Suppose we have a function y = f (x). If we change x from x = a to x =
a + x = a + h, for a step or dierence in x of x = h, then th

Precalculus Review
MAT 1339 C
Fall 2013
Mathematics provides a language to precisely model a problem and then
provides tools to logically solve the problem.
Calculus is the study of functions with special emphasis on the rate of change
of the function.
1

Suggested Exercises:
Throughout the semester, there will be weekly updates. You
should check this page regularly. All the exercises are from
Calculus ad Vectors 12, McGrawHill Ryserson
Suggested exerci

THE DIFFERENCE QUOTIENT
I. The ability to set up and simplify difference quotients is essential for calculus students. It is
from the difference quotient that the elementary formulas for derivatives are developed.
II. Setting up a difference quotient for

Limits and Continuity
MAT 1339 C
Fall 2013
1 LIMITS
1
2
Limits
Ex: Consider the function
f (x) =
|x2 1|
.
x1
a) What is the domain of f ?
b) As x gets really close to 1 on the left (x < 1) what happens to f ?
c) As x gets really close to 1 on the right (x