Calculus: An Introduction

Calculus refers to the mathematical study of continuous change. The major branches of calculus are differential calculus and integral calculus. Differential calculus is concerned with the immediate rate of change and the slopes of curves. Integral calculus focuses on the accumulation of quantities and the areas under and between curves. Both branches are connected by the fundamental theorem of calculus. They utilize the fundamental concepts of convergence of infinite sequences and infinite series to a well-defined limit. Calculus is used in various branches of physical sciences, computer science, statistics, engineering, economics, business, actuarial science and demography. It is also used in various other fields where a problem is capable of being mathematically modeled and where an optimal solution is required. This textbook outlines the processes and applications of calculus in detail. It presents this complex subject in the most comprehensible and easy to understand language. The book will serve as a reference to a broad spectrum of readers.