1.Summary of the main learning outcomes for students enrolled in the course.
The course will Provide students with basics of differential calculus methods to apply them to mathematical relations related to the health sciences and to a variety of physical, life science, pharmaceutical, and pharmacological problems.
5. Schedule of Assessment Tasks for Students During the Semester Assessment task (Tutorials, test, group discussion and presentation,
examination.) Week Due Proportion of
Total Assessment
1 Midterm Written Exams Week 7 and
Week 12 20%
2 Participation and attendance All along 10%
3 Assignment and presentation All along 30%
4 Final Written Exam End of term 40%
Calculus I
Functions and Graphs
Numbers set
Natural numbers N
The whole numbers from 1 upwards
The set is {1,2,3,...} or {0,1,2,3,...}
Integers
The positive whole numbers, {1,2,3,...}, negative whole numbers {..., -3,-2,-1} and zero
Number Line
Rational Numbers Q
The numbers you can make by dividing one integer by another (but not dividing by zero). In other
words fractions
Real Numbers R
All Rational and Irrational numbers. They can also be positive, negative or zero.
Examples: 1.5, -12.3, 99, √2, π
Objective: Graph ordered pairs of a relation
Cartesian Coordinate System
Quadrant I X>0, y>0 Quadrant II
X<0, y>0
Quadrant IV X>0, y<0 Quadrant III
X<0, y<0
Origin (0,0 (
Graph the points
(-3,3), (1,1), (3,1), (4,-2)
-(
3,3 (
( 4 -, 2 ( ( 1,1
( (3,1(
Constant
A constant is a fixed value.
In Algebra, a constant is a number on its own, or
sometimes a letter such as a, b or c to stand for a fixed number.
Example: in "x + 5 = 9", 5 and 9 are constants
If it is not a constant it is called a variable.
Variable
A variable is a symbol for a number we don't know yet.
It is usually a letter like x or y.
Example: in x + 2 = 6, x is the variable
If it is not a variable it is called a Constant
Function
A function is a special relationship between values: Each of its input values gives back exactly one output value.
It is often written as "f(x)" where x is the value you give it.
Example:
f(x) = x/2 ("f of x is x divided by 2") is a function, because for every value of "x" you get another value "x/2", so:
* f(2) = 1
* f(16) = 8
* f(-10) = -5
A function relates each element of a set with exactly one element of another set
Function
A function is a rule or procedure for finding, from a given number, a new number.
The set of numbers x for which a function f is defined is called the domain of f.
The set of all resulting function values f(x) is called the range of f.
For any x in the domain, f(x) must be a single number.
The domain is the set of all the values of the independent variable, the x-coordinate
The range is the set of all the values of the dependent variable, the y-coordinate.
Identify the domain and range of the function below.
{ 2, 7), (4, 11), (6, 15), (8, 19)}
The domain is { 2, 4, 6, 8}
The range is { 7, 11, 15, 19}
Example
If we have the function
f(x) = 2x + 1
Then
f(1) = 2(1) + 1 = 3
f(2) = 2(2) + 1 = 4
f(3) = 2(3) + 1 = 7
F(5) = 2(5) + 1 = 11
The input values { 1 , 2 , 3 , 5} are the domain
The output values { 2 , 4 , 7, 11} are the range
Examples:
For the following functions find the domain and range
Example 1:
f(x) = 3x -2
Assume the values of x are { 1 , 5 , 7 , 9, 11}
Example 2:
f(x) =
x
2Assume the values of x are { 0 , -2 , 3 , -5 , 7}
Types of funtions:
1- Linear function :
f(x) = mx + b
Square Function
f(x) = x2
Exponential function
f(x) = ax
a is any value greater than 0
It is always greater than 0, and never crosses the x-axis
It always intersects the y-axis at y=1 ... in other words it passes through(0,1)
Natural Exponential Function:
f(x) = ex
Where e is "Eulers Number" = 2.718281828459 (and more ...)
Trigonometric functions
Sine Function
Y = sin (X)
Trigonometric functions
Sine Function
Y = Cos (X)
