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A PRESENTATION ON DIFFERENCIAL CALCULUS

PRESENTED BY

Md.Altafur Rahman Himu

INTRODUCTION

Definition of Calculus

Classification of Calculus

Differentiation

Derivative

Differential Curve

Formulas of Differentiation

DEFINATION OF DIFFERENCIAL CALCULUS

• Calculus – is that branch of mathematics that deals with growth

(development), motion (process or power of changing place or

position), maxima (greatest quantity) and minima (least

quantity).

• 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.

• Calculus - a particular method or system of calculation or

reasoning.

CLASSIFICATION OF CALCULUS

The two main types of Calculus:

1. differential calculus - a branch of mathematics concerned chiefly with thestudy of the rate of change of functions with respect to their variablesespecially through the use of derivatives and differentials.

First Branch of mathematical analysis, devised by ISAAC NEWTONand G.W.LEIBNIZ, and concerned with the problem of finding the rate ofchange of a function with respect to the variable on which it depends. Thus itinvolves calculating derivatives and using them to solve problems involvingnon-constant rates of change. Known Use of differencial calculus 1702.

•2. 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 First Known Use of INTEGRAL

CALCULUS circa 1741

•NOTE: Integral calculus Branch of CALCULUS concerned with the theory and

applications of INTEGRALs. while DIFFERENTIAL CALCULUS focuses on rates of change, such

as slopes of tangent lines and velocities, integral calculus deals with total size or value,

such as lengths, areas, and volumes.

•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.

DERIVATIVE

EXAMPLES

DIFFERENCIAL CURVE

FORMULAS OF DIFFERENTIATION