Review:
1. Mathematics of finance (5.1 - 5.5)
k - the number of interest compounded a year
t - the number of years.
r - annual rate
n = kt and rp = r/k.
kt
Compound amount
r
S = P 1 +
k
Effective rate
r
re = 1 + 1
k
k
Compound amount under continuous

2. Mathematics of Finance
2.1 Compound interest
Example 2.1: Suppose that $1000 is invested at the rate of 8% compounded annually.
Notes:
1. annual rate nominal rate annual percentage rate
interest rate
2.
compound amount S
The periodic rate rp
The compou

4. Differentiation
4.1 The derivative
The slope of the segment line of a graph y = f(x)
f ( a + h) f ( a )
h
In fact as h 0,
f ( a + h) f ( a )
h
Let y = f(x). f is _ if lim
h 0
f ( a + h) f ( a )
exists, and the limit is called the
h
_, denoted f(a), or

3.Limits & Continuity
3.1 Limits
Consider function f ( x) =
x3 1
. Note f(x) is not defined at x = 1.
x 1
Left of 1 ( x < 1 )
x
f ( x) =
Right of 1 (x > 1 )
x 1
x 1
3
0
0.5
0.9
0.99
0.999
x
f ( x) =
x3 1
x 1
2
1.5
1.1
1.01
1.001
The limit of f(x) as x app

1
functions
1.1 Functions
Example 1.1: Suppose that you are planning to buy apples and their cost is $1.47
per pound ($3.14/kg) in your local shop.
A function f is a rule or process that assigns to each input a corresponding output.
Input
Output
f
1
Examp

MATA32F
Calculus for Management I
Fall 2014
Course Syllabus and Lecture Schedule
For the rst two weeks of MATA32F we study Mathematics of Finance (part of Chapter 5). Then
we spend about 4 5 weeks each on Limits and Dierential Calculus (parts of Chapters

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 11
Fall 2014
This is the last posted assignment for MATA32F.
Study: Sections 14.6, 14.7, 14.9, and 14.10. Remember that we omit sections 14.1 and 14.8 f

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 10
Fall 2014
Please see the note below concerning Quiz 5.
Study: Sections 14.4, 14.5, 15.1, and 14.6 for this assignment. Read ahead in sections 14.7, 1

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 7
Fall 2014
Quiz 3 on Assignment 7 (and Assignments 5 and 6, only up to and including Chapter 12 problems)
is written in Week 7 by all students in MATA3

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 9
Fall 2014
Study: Sections 13.6 and 14.2 - 14.4 for this assignment. Read ahead in sections 14.5, 14.6 and
15.1 for future lectures and assignments. Re

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 8
Fall 2014
This Assignment 8 is quite long and somewhat dicult. It deals with the applications of derivatives
in analyzing functions, monotonicity, con

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 6
Fall 2014
Study: Sections 12.1 - 12.3 for this assignment. Read ahead in sections 12.4 - 12.7 for upcoming
lectures and future assignments. Assignment

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 4
Fall 2014
Study: Sections 5.5 (only page 228), 10.1 - 10.3, 11.1, and 11.2 for this assignment. Some material
to re-study in this assignment is intent

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA32F
Assignment 5
Fall 2014
This Assignment 5 has two pages.
Study: Sections 11.3 - 11.5 for this current assignment. Read ahead in sections 12.1 - 12.7 for
upcoming le

5. Differentiation (Conti.)
5.1 Elasticity of Demand
Let p be the price per unit of a product and q be the quantity of units demanded.
Percentage change in quantity is
Percentage change in change is
Let the demand function p = f(q) be differentiable.
If q

Course Syllabus and Lecture Schedule
2015 Winter
(This schedule is a guideline and it is possible that there may be small changes to the ordering or
duration of course topics as the course proceeds. All chapter and section references are in the
textbook,

6. Curve sketching
6.1 Increasing and decreasing
f is a _ function on an
interval I if whenever a, b I and
a < b then f(a) > f(b).
f is a _ function on an
interval I if whenever a, b I and
a < b then f(a) < f(b).
If f is continuous and differentiable on a

*x* Sorry.No solutions will be postedxx*
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
FINAL EXAMINATION
MATA32 - Calculus for Management I
Examiners: R. Grinnell
Date: Apri127,2177
Time: 2:00 pm
Duration: 3 horrs
P

IJniversity of Toronto at Scarborough
Department of Computer and Mathematical Sciences
FINAL EXAMINATION
MATAS2S - Calculus for Management I
cfw_<'<*Solutions are not provided'(x*
Date: April 29,2013
Time: 2:00 pm
Duration: 3 hours
Examiner: R. Grinnell
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I-Jniversity of Toronto at Scarborough
Department of Computer and Mathematical Sciences
FINAL EXAMINATION
MATAS2F - Calculus for Management f
Examiners: R. Grinnell
B.Pike
P; ct9 Vog'on ,
Date: December ll