Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Introduction and historical background

The concept of limit and convergence is fundamental in the study of Calculus and Analysis. The fragments of this concept are evident in ‘the method of exhaustion’ formulated by Ancient Greeks and used by Archimedes (287-212) B.C., in obtaining a formula for the area of the circular region conceived as a successive approximation of the area of inscribed polygons with an increased number of sides.

It was the genius of Bhaskaracharya (1150 A.D), who achieved a breakthrough in the invention of infinitesimal (Anantaksudra) and instantaneous velocity (Tatkalika gati) for his Astronomical calculations. Madhava (1340-1425) a talented mathematician from Cochin refined the above concepts

Fermat (1608) too dealt with the idea of the rate of change and drawing of tangents but often due to ignorance, the credit of developing these concepts goes to Newton (1642-1727) and Leibnitz (1646-1716). In fact, Newton has acknowledged and expressed his indebtedness to Fermat to further his ideas. It was mainly Cauchy (1789-1857) and Weierstrass (1815-1897) who put the limiting process on a sound foundation.

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