This document provides an introduction to calculus, including its definition, classification, and key concepts. Calculus is the branch of mathematics dealing with finding derivatives and integrals of functions, based on infinitesimal differences. It has two main types: differential calculus concerns rates of change, while integral calculus involves the theory and applications of integrals and integration, such as determining lengths, areas, and volumes. The document defines differentiation as finding derivatives and integration as evaluating indefinite or definite integrals. It provides formulas and examples of differentiation and integration.

1. CALCULUS

2. INTRODUCTION
Definition of Calculus
Classification of Calculus
Differentiation
Formulas of Differentiation
Example of Differentiation
Integration
Formulas of Integration
Example of Integration

3. DEFINATION OF CALCULUS
The branch of
mathematics that deals
with the finding and
properties of derivatives
and integrals of
functions, by methods
originally based on the
summation of
infinitesimal differences.

4. CLASSIFICATION OF CALCULUS
 Differential Calculus :
A branch of
mathematics
concerned chiefly
with the study of the
rate of change of
functions with respect
to their variables
especially through
the use of derivatives
and differentials.
 Integral Calculus:
A branch of
mathematics
concerned with the
theory and
applications (as in
the determination of
lengths, areas, and
volumes and in the
solution of
differential
equations) of
integrals and
integration
The two main types of Calculus:

5. DIFFERENTIATION:
 The process of finding a derivative is called
differentiation. The reverse process is called
anti-differentiation. The fundamental
theorem of calculus states that anti-
differentiation is the same as integration.
Differentiation and integration constitute
the two fundamental operations in single-
variable calculus.

6. FORMULAS OF DIFFERENTIATION

7. EXAMPLE :
1. 2.

8. EXAMPLE :
3. 4.

9. INTEGRATION :
 The process of evaluating an
indefinite integral or a definite
Integral.
 The indefinite integral ∫f(x)dx is defined as a
function g such as its derivative D.[g(x)]=f(x).
 The definite integral is a number
whose value depends on the function f and the
numbers a and b, and it is defined as the limit
of Riemann sum.
 the arbitrary constant c is called a
constant of integration .

10. FORMULAS OF INTEGRATION

11. EXAMPLE :
1. 2.

12. EXAMPLE:
3.
4.

13. THANK YOU