Essential Calculus with Applications (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Richard A. Silverman

• Language: English

• Edition: Reprint Edition

• ISBN: 9780486660974

• Pages: 320

• Cover: Paperback

• Dimensions: 9.1 x 6.1 x 0.7 inches

About The Book

Calculus by Richard A. Silverman is a rigorous yet accessible introduction to the essential problem-solving techniques that make calculus an indispensable tool in mathematics, physics, biology, economics, and many other fields. Written for undergraduate students, this text takes a comprehensive approach to introducing the core concepts of differential and integral calculus, making it suitable as a primary textbook or a refresher for those looking to review fundamental calculus principles.

The book begins with necessary precalculus material such as sets, inequalities, and mathematical induction, building a solid foundation for the study of calculus. In Chapter Two, the study of differential calculus begins with a detailed discussion of functions, derivatives, and limits, followed by applications of differentiation, including velocity, continuous functions, optimization problems, and more in Chapter Three. Chapter Four then delves into integral calculus, covering the Riemann integral, integration techniques, and improper integrals. The book also briefly introduces differential equations, exploring applications related to growth, decay, and motion. The final chapter extends the concepts to functions of several variables, completing the study of differential calculus.

To reinforce understanding, the book includes numerous problems with solutions and a newly added section of "Supplementary Hints and Answers," providing students with opportunities to test their comprehension before progressing. Silverman’s concise, well-written approach makes this book an ideal resource for anyone wishing to master the essentials of calculus.