Calculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. Underlying all of these topics is the concept of a limit, which consists of analyzing the behaviour of a function at points ever closer to a particular point, but without ever actually reaching that point. Calculus has two basic applications: differential calculus and integral calculus. The main purpose of this volume is to provide an introduction to calculus in its many forms. Give some presentations to illustrate how powerful calculus is as a mathematical tool for solving a variety of scientific problems, introduce concepts from a variety of application areas, such as biology, chemistry, economics, physics and engineering, to demonstrate applications of calculus. This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This book emphasizes the fundamental concepts from calculus and analytic geometry and the application of these concepts to selected areas of science and engineering. Topics covered includes: Sets, Functions, Graphs and Limits, Differential Calculus, Integral Calculus, Sequences, Summations and Products and Applications of Calculus. In this book, much emphasis is put on explanations of concepts and solutions to examples. By reading the book carefully, students should be able to understand the concepts introduced and know how to answer questions with justification. Students should bear in mind that the main purpose of learning calculus is not just knowing how to perform differentiation and integration but also knowing how to apply differentiation and integration to solve problems. For that, one must understand the concepts.
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