The mathematical study of continuous change is known as calculus. There are two major divisions of calculus, known as differential calculus and integral calculus. The instantaneous rates of change and the slope of curves is studied under differential calculus. Integral calculus deals with the accumulation of quantities and areas between and under the curves. The link between these two branches is known as the fundamental theorem of calculus. This theorem states that differentiation and integration are inverse operations. Calculus finds its application in every field where a problem can be mathematically modeled and where an optimal solution is sought. Therefore, it is used in all branches of physical science, actuarial science, computer science, statistics, engineering and a variety of other disciplines. The topics covered in this extensive book deal with the core aspects of calculus. It is appropriate for students seeking detailed information in this area as well as for experts. The book will serve as a valuable source of reference for graduate and post graduate students.