1. Course Title: Calculus I 6501104))Course Code:

2. Course Description Introduction Definition of functions
1. Topics to be Covered
List of Topics
No. of
Weeks
Contact Hours
Introduction
Definition of functions
Domain and range of functions
Types of functions and drawing curves. 2 6
Definition and calculation of limits of function
Calculation of limits of function using the general law
Limits of trigonometric functions.
Derivatives from first principle
Derivatives using general law
Derivatives of trigonometric functions
Chain rule
Implicit function differentiation 3 9
Differentiation of Exponential functions
Differentiation of Logarithmic functions
Differentiation of inverse trigonometric functions
Higher order derivatives
Maxima and Minima of the function
Applications on Maxima and Minima of the function

3. Course Components
2. Course components (total contact hours and credits per semester): contact hours: 45 credit hours:3
Lecture
Tutorial
Laboratory
Practical
Office hours
Total
Contact Hours 45
Credit 3

4. 5 1 Midterm Written Exams 20% 2 Participation and attendance 10% 3
Assessment task (Tutorials, test, group discussion and presentation, examination.)
Proportion of Total Assessment 1
Midterm Written Exams
20% 2
Participation and attendance
10% 3
Assignment and presentation
30% 4
Final Written Exam
40% 5
Total
100%

5. Umm Al-Qura University
بسم الله الرحمن الرحيم
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (1)

6. Functions and Graphs

7. Objectives:
1/ The course will Provide students with basics of differential calculus and methods to apply them to mathematical relations related to the health sciences .
2/ Know Definition of functions.
3/ Define and Calculate Domain and range of functions.
4/ Show Types of functions and drawing curves.

8. 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

9. 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

10. Cartesian Coordinate System
Objective: Graph ordered pairs of a relation
Cartesian Coordinate System

11. Quadrant I
X>0, y>0
Quadrant II
X<0, y>0
Origin (0,0)
Quadrant III
X<0, y<0
Quadrant IV
X>0, y<0

12. Graph the points (-3,3), (1,1), (3,1), (4,-2)

13. (-3,3)
(1,1)
(3,1)
(4,-2)

14. 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.

15. 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

16. 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

17. A function relates each element of a set with exactly one element of another set

18. 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.

19. 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.

20. 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}

21. Example
If we have the function
f(x) = 2x + 1
Then
f(1) = 2(1) + 1 = 3
f(2) = 2(2) + 1 = 5
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 { 3 , 5 , 7, 11} are the range

22. 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 2
Assume the values of x are { 0 , -2 , 3 , -5 , 7}

23. Types of funtions:
1- Linear function :
f(x) = mx + b

24. Square Function
f(x) = x2

25. 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)

26. Natural Exponential Function:
f(x) = ex
Where e is "Eulers Number" =   (and more ...)

27. Trigonometric functions
Sine Function
Y = sin (X)

28. Trigonometric functions
Sine Function
Y = Cos (X)

29. Thanks Radia