Calculus, is a mathematical branch of higher mathematics that studies Differentiation, Integration, and related concepts and applications of functions. It is a basic subject of mathematics, including limit, differential calculus, integral calculus and its application.
LIMITS AND CONTINUITY In this chapter we develop the limit. We use limits to describe the way a function ƒ varies. Some functions vary continuously; small changes in x produce only small changes in ƒ(x). Other functions can have values that jump or vary erratically. The notion of limit gives a precise way to distinguish between these behaviors. The concept of a limit is a central idea that distinguishes calculus from algebra and trigonometry.
DIFFERENTIATION The derivative is one of the key ideas in calculus, and is used to study a wide range of problems in mathematics, science, economics, and medicine.
The derivative is a limit, measures the rate at which a function changes. In this chapter, we develop techniques to calculate derivatives easily and learn how to use derivatives to approximate complicated functions.
APPLICATIONS OF DERIVATIVES This chapter studies some of the important applications of derivatives. We learn how derivatives are used to find extreme values of functions, to determine and analyze the shapes of graphs, to calculate limits of fractions whose numerators and denominators both approach zero or infinity, and to find numerically where a function equals zero. The key to many of these accomplishments is the Mean Value Theorem, and a theorem whose corollaries provide the gateway to integral calculus in next Chapter.
INTEGRATION In this chapter, we consider the process of recovering a function from its derivative. The method we develop, called integration, is a tool for calculating much more than areas and volumes, and other more general shapes. Integration and differentiation are closely connected, The nature of their connection, contained in the Fundamental Theorem of Calculus, is one of the most important ideas in calculus.
