Course Syllabus
MSIS4523: Data Communication Systems
Course Details
Course:
Section:
Meeting Time:
Meeting Location:
Course URL:
MSIS 4523 Data Communication Systems
001
TR 12:30 PM 1:45 PM
Classroom Building 321 and Gunderson Small Lab (101)
D2L
Instruct
Course Schedule
MSIS4523: Data Communication Systems
Tentative Schedule
NOTE: This schedule is tentative and is subject to change. Make sure you frequent the course website and class for any
updates and announcements.
Due
Week Date
Topic
Reading/Assignmen
Limits Unit Overview
Tangent Lines
Finding the slope of a tangent line, at a given point a:
f (a + h) f (a)
h0
h
1
Ex. Find the equation of the tangent line of f (x) =
at x = 2 = a = 2.
2x
1. Find f (a) and f (a + h)
2. Find slope of tangent
3. Use point
MCV4UW
15 Oct 2015
Product Rule and Power of a Function Rule
Product Rule:
Let u, v be different functions, then
(uv) = u v + uv
Ex. Differentiate.
f (x) = (3x2 + 2x 5) (4x2 + 3x 1)

cfw_z

cfw_z
u
v
f (x) = (6x + 2) (4x2 + 3x 1) + (3x2 + 2x 5 (8x + 3
MCV4UW
23 Sept 2015
The Limit of a Function continued
Limit Rules
Suppose that lim f (x) and lim g(x) both exist. Let a, c R.
xa
xa
1. lim [f (x) g(x)] = lim f (x) lim g(x)
xa
xa
xa
2. lim cf (x) = c lim f (x)
xa
xa
3. lim f (x)g(x) = lim f (x) lim g(x)
x
MCV4UW
8 Oct 2015
Derivatives
Recall that the slope of a tangent line to f (x) is given by
mT = lim
h0
f (a + h) f (a)
h
This process happens so often that it is given a name. It is called the derivative of f (x) at x = a, and is
written as
f (a + h) f (a
MCV4UW
9 Oct 2015
Differentiation Rules
Recall that the derivative of a function is given by
f (x + h) f (x)
h0
h
f (x) = lim
This can lead to very difficult limits to evaluate.
Ex. Determine the derivative of
v
v
u
v
u
u
u
u
u
u
3
u
u
1
+
x
t
t
Yikes!
f
MCV4UW
15 Sept 2015
The Tangent Problem
A tangent line is a line that locally touches a function at y = f (x) at just one point and is parallel to the
function at that point.
f (x)
secant
y = f (x)
(a, f (a)
tangent
x
A secant line is a line that intersec
MCV4UW
21 Sept 2015
The Limit of a Function
The limit of a function is a generalisation of function evaluation.
x3
. Evaluate f (x) at x = 3.
x2 4x + 3
33
0
f (3) = 2
=
what happens now?
3 4(3) + 3
0
Consider f (x) =
What is happening near x = 3?
x<3
2.5
MCV4UW
17 Sept 2015
The Tangent Problem continued
Ex. Find the slope of the tangent line of f (x) =
x 2, x = 3 a = 3
f (a + h) f (a)
h0
h
1+h1
= lim
h0
h
1+h1
1+h+1
= lim
rationalise*
h0
h
1+h+1
1+h1
= lim
h0 h( 1 + h + 1)
1
= lim
h0 1 + h + 1
1
=
1+0+