Introductory Calculus

About the Book

Calculus is the mathematics of change, and change is an integral part of the universe. Mathematicians and scientists of all persuasions know that calculus is a cornerstone of modern science. Calculus allows us to solve a variety of problems dealing with continuously varying quantities. This development, which dates back to the seventeenth century, with the work of many great mathematicians, but in particular Isaac Newton and Gottfried Liebniz, has added tremendously to the power of our science and has allowed us to understand and master our world in ways that are nothing less than revolutionary. We should consider it to be one of the few truly great achievements of the human mind. This book explains all the basic concepts of single variable calculus through the theory and application of the derivative, the theory and application of the definite integral, and the connection between these two main parts of the subject by way of the fundamental theorem of calculus. After the discussion of differentiation and integration, I have included some of the basics of differential equations and their applications so that the student can see how important the differential and integral calculus is to many different areas. The book contains an abundance of examples at every step and many exercises to help the student learn the subject. It has been titled “Introductory Calculus” because it is mainly about the single variable part of the subject, the portion devoted to real valued functions of a single variable, which is the starting point for most of the larger treatment of calculus. So we have a compact and rigorous introduction to calculus so that the student can quickly grasp the essential concepts and get a feel for the many applications of the subject.

About the Author

Timothy C. Kearns graduated from Virginia Tech (with honors) in June of 1983, with a BS degree in statistics and mathematics. In addition, he has successfully completed additional graduate level coursework in mathematics and has been an avid reader of mathematics and science and, furthermore, a successful tutor of mathematics, statistics, and physics for more than twelve years. He is very passionate about the mathematical sciences, especially calculus and the larger subject of real analysis. He enjoys conveying his expertise in these subjects to high school and college students that are interested in a career in mathematics, engineering, and the mathematically related sciences. This book is the culmination of his many years of experience with calculus and related subjects and written for those students that are eager to learn all the fundamentals of the differential and integral calculus and many of its applications.