Course Title: Calculus
Course Code: )6501104)
I
Course Description
1. Topics to be Covered
List of Topics
Introduction

Definition of functions

Domain and range of functions

Types of functions and drawing curves.

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

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

No. of
Weeks
Contact Hours
2
6
2
6
2
6
3
9
2
6
2
6
2
6
Course Components
2. Course components (total contact hours and credits per semester): contact hours: 45 credit hours:3
Lectu
re
Tutorial
Laboratory
Practical
Office
hours
Total
Contact Hours
45
45
Credit
3
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%
‫بسم هللا الرحمن الرحيم‬
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (1)
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.
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 II
X<0, y>0
Quadrant I
X>0, y>0
Origin (0,0)
Quadrant III
X<0, y<0
Quadrant IV
X>0, y<0
Graph the points
(-3,3), (1,1), (3,1), (4,-2)
(-3,3)
(1,1)
(3,1)
(4,-2)
 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 = 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
 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) =
x2
Assume 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)

Thanks
Radia