Differential Calculus - Study of Real Numbers

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Differential Calculus: Study of Differential calculus is always be my first choice, as more than any other branch of calculus or Mathematics I spare most of my time in solving its problem. The subject of Differential Calculus takes its stand upon the set of real numbers and concerns itself with the various properties of the same. It specially introduces and deals with what is called the Limit operation in addition to being concerned with the Algebraic operations of Addition and Multiplication and their inverses, Subtraction and Division.

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Instantaneous Rate of Change: A limit application which is different from average rate of change is very useful and applied to geometry, mechanics and other branches of theoretical physics and also to social sciences such as economics and sociology.

To study differential calculus we need to clear the concept of Real numbers:

Real Numbers their introduction, Rational numbers and their representation by points along a straight line; Natural Numbers; Fractional Numbers; Rational Numbers: Fundamental operations on rational numbers. Meaningless operation of division by zero. Representation of rational numbers by points along a line or by segments of a line.

Irrational numbers, Real numbers, Numbers and point, closed and open intervals.

Decimal representation of Real Numbers.

The Modulus of Real number.

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