Question

Please give me some Calculus notes.

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Answer 1

ANSWERS:-

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. The two main types are differential calculus and integral calculus.

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Answer 2

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DEFINITION :-

Calculus is the branch of mathematics that deals with continuous change. In this article, let us discuss the calculus definition, problems and the application of calculus in detail. Also, we are going to discuss what advanced calculus is along with the concepts involved in the basic calculus.

INTRODUCED BY :-

Newton and Leibniz

BASICS :-

Basic Calculus is the study of differentiation and integration. Both concepts are based on the idea of limits and functions. Some concepts, like continuity, exponents, are the foundation of advanced calculus. Basic calculus explains about the two different types of calculus called “Differential Calculus” and “Integral Calculus”. Differential Calculus helps to find the rate of change of a quantity, whereas integral calculus helps to find the quantity when the rate of change is known.

FORMULA :-

The degree of closeness to any value or the approaching term. A limit is normally expressed using the limit formula as-

lim x → c f(x)=A

It is read as “the limit of f of x as x approaches c equals A”.

FORMULA DERIVATION :-

Instantaneous rate of change of a quantity with respect to the other. The derivative of a function is represented as:

lim x → h f(x+h) − f(x)h = A

A function f(x) is said to be continuous at a particular point x = a, if the following three conditions are satisfied –

f(a) is defined

lim x → a f(x) exists

lim x → a − f(x)=lim x → a + f(x) = f(a)

QUOTIENT RULE :-

The Quotient rule is a method for determining the derivative (differentiation) of a function which is in fractional form.

CHAIN RULE :-

The rule applied for finding the derivative of the composition of a function is basically known as the chain rule.

INTEGRATION :-

Integration is the reciprocal of differentiation. As differentiation can be understood as dividing a part into many small parts, integration can be said as a collection of small parts in order to form a whole. It is generally used for calculating areas.

DEFINITE INTEGRAL :-

A definite integral has a specific boundary within which function needs to be calculated. The lower limit and upper limit of the independent variable of a function is specified; its integration is described using definite integrals. A definite integral is denoted as:

∫ b/a f(x). dx = F(x)

INDEFINITE INTEGRAL :-

An indefinite integral does not have a specific boundary, i.e. no upper and lower limit is defined. Thus the integration value is always accompanied by a constant value (C). It is denoted as:

∫ f(x). dx = F(x) + C