Course Title: Calculus I 6501104))Course Code:

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

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

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%

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

Functions and Graphs

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

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

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

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) = x 2 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