Courses

# PPT - Differential & Integral Calculus CA Foundation Notes | EduRev

## Business Mathematics and Logical Reasoning & Statistics

Created by: Wizius Careers

## CA Foundation : PPT - Differential & Integral Calculus CA Foundation Notes | EduRev

``` Page 1

Basic Concept of
Differential and Integral Calculus

CPT Section D Quantitative Aptitude Chapter 9
Dr. Atul Kumar Srivastava

Page 2

Basic Concept of
Differential and Integral Calculus

CPT Section D Quantitative Aptitude Chapter 9
Dr. Atul Kumar Srivastava

Learning Objectives

Understand the use of this Branch of mathematics in various branches of science
and Humanities
Understand the basics of differentiation and integration
Know how to compute derivative of a function by the first principal, derivative
of a function by the use of various formulae and higher order differentiation
Make familiar with various techniques of integration
Understand the concept of definite integrals of functions and its properties.
2
Page 3

Basic Concept of
Differential and Integral Calculus

CPT Section D Quantitative Aptitude Chapter 9
Dr. Atul Kumar Srivastava

Learning Objectives

Understand the use of this Branch of mathematics in various branches of science
and Humanities
Understand the basics of differentiation and integration
Know how to compute derivative of a function by the first principal, derivative
of a function by the use of various formulae and higher order differentiation
Make familiar with various techniques of integration
Understand the concept of definite integrals of functions and its properties.
2
Differential calculus-Outlines

What is Differential Calculus – An Introduction
Derivative or Deferential Coefficient (First Principal Definition)
Basic Formulas
Laws for Differentiation (Algebra of Derivative of Functions)
Derivative of A Function of Function (Chain Rule)
.Derivative of Implicit Function
.Derivative of Function In Parametric Form
3
Page 4

Basic Concept of
Differential and Integral Calculus

CPT Section D Quantitative Aptitude Chapter 9
Dr. Atul Kumar Srivastava

Learning Objectives

Understand the use of this Branch of mathematics in various branches of science
and Humanities
Understand the basics of differentiation and integration
Know how to compute derivative of a function by the first principal, derivative
of a function by the use of various formulae and higher order differentiation
Make familiar with various techniques of integration
Understand the concept of definite integrals of functions and its properties.
2
Differential calculus-Outlines

What is Differential Calculus – An Introduction
Derivative or Deferential Coefficient (First Principal Definition)
Basic Formulas
Laws for Differentiation (Algebra of Derivative of Functions)
Derivative of A Function of Function (Chain Rule)
.Derivative of Implicit Function
.Derivative of Function In Parametric Form
3
What is differential calculus – an
introduction

One of the most fundamental operations in calculus is that of differentiation. In
the study of mathematics, there are many problems containing two quantities
such that the value of one quantity depends upon the other. A variation in the
value of any ones produces a variation in the value of the other. For example
the area of a square depends upon it's side. The area of circle and volume of
sphere depend upon their radius etc.
Differential calculus is the Branch of Mathematics which studies changes
To express the rate of change of any function we introduce concept of
derivative. The concept involves a very small change in the dependent variable
with reference to a very small change in the independent variable
4
Page 5

Basic Concept of
Differential and Integral Calculus

CPT Section D Quantitative Aptitude Chapter 9
Dr. Atul Kumar Srivastava

Learning Objectives

Understand the use of this Branch of mathematics in various branches of science
and Humanities
Understand the basics of differentiation and integration
Know how to compute derivative of a function by the first principal, derivative
of a function by the use of various formulae and higher order differentiation
Make familiar with various techniques of integration
Understand the concept of definite integrals of functions and its properties.
2
Differential calculus-Outlines

What is Differential Calculus – An Introduction
Derivative or Deferential Coefficient (First Principal Definition)
Basic Formulas
Laws for Differentiation (Algebra of Derivative of Functions)
Derivative of A Function of Function (Chain Rule)
.Derivative of Implicit Function
.Derivative of Function In Parametric Form
3
What is differential calculus – an
introduction

One of the most fundamental operations in calculus is that of differentiation. In
the study of mathematics, there are many problems containing two quantities
such that the value of one quantity depends upon the other. A variation in the
value of any ones produces a variation in the value of the other. For example
the area of a square depends upon it's side. The area of circle and volume of
sphere depend upon their radius etc.
Differential calculus is the Branch of Mathematics which studies changes
To express the rate of change of any function we introduce concept of
derivative. The concept involves a very small change in the dependent variable
with reference to a very small change in the independent variable
4
Continued

y=f(x)
•                                           x -   Independent variable
•                                           y -   Dependent Variable
Thus differentiation is a process of finding the derivative of a
continuous function. It is defined as the limiting value of the
ratio of the change in the function corresponding to small
change in the independent variable as the later tends to zero.
5
```

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;