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Calculus is the study of how things change. It provides a framework for modelling systems in which there is change, and a way to deduce the predictions of such models. It provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences. With this you get the ability to find the effects of changing conditions on the system being investigated. By studying these, you can learn how to control the system to do make it do what you want it to do. Calculus, by giving engineers and you the ability to model and control systems gives them (and potentially you) extraordinary power over the material world. The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes. And this was responsible for the industrial revolution and everything that has followed from it including almost all the major advances of the last few centuries. The fundamental idea of calculus is to study change by studying "instantaneous" change, by which we mean changes over tiny intervals of time. The goal of this book is to rigorously present the fundamental concepts. This book improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts and helps them understand the connections among different topics.