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Essential Calculus with Applications
Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician.The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables.Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.
505 pages, Kindle Edition
First published August 1, 1989
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May 7, 2020
Calculus is an essential tool for anyone interested in higher mathematics. For me, the unfortunate thing is that I never got past Calculus II. Remembering all of those Trigonometric Identities was tough. However, I digress.
Essential Calculus with Applications is written by Richard A Silverman. It delivers what it promises on the cover. It provides a mathematical background so that the reader understands what the author is talking about in later chapters. It builds on previous knowledge with the author assuming that the reader has only the basics of algebra and geometry.
There is a lot to like about this book. Since the author presumes nothing, he includes how to pronounce the symbols you encounter in the book. There are a lot of proofs in the book as well. For one thing, it includes proof that the square root of 2 is irrational. I have seen this proof before but it is nice to see it again. The book goes through Sets and how to manipulate them, the basics of graphing lines and equations, inequalities, and a smattering of trigonometry before it gets to the calculus part.
With the actual calculus part, it introduces a concept and then demonstrates a use or application for that tool. So it goes through limits, derivatives, integrals, related rates, partial derivatives, and more. There isn’t anything bad to say about this book. It was written back in the 1970s and some of the text shows this, but it is mostly through the technology.
The book contains answers to the problems at the back of the book. I liked it, even though it took a while to get through it.
Essential Calculus with Applications is written by Richard A Silverman. It delivers what it promises on the cover. It provides a mathematical background so that the reader understands what the author is talking about in later chapters. It builds on previous knowledge with the author assuming that the reader has only the basics of algebra and geometry.
There is a lot to like about this book. Since the author presumes nothing, he includes how to pronounce the symbols you encounter in the book. There are a lot of proofs in the book as well. For one thing, it includes proof that the square root of 2 is irrational. I have seen this proof before but it is nice to see it again. The book goes through Sets and how to manipulate them, the basics of graphing lines and equations, inequalities, and a smattering of trigonometry before it gets to the calculus part.
With the actual calculus part, it introduces a concept and then demonstrates a use or application for that tool. So it goes through limits, derivatives, integrals, related rates, partial derivatives, and more. There isn’t anything bad to say about this book. It was written back in the 1970s and some of the text shows this, but it is mostly through the technology.
The book contains answers to the problems at the back of the book. I liked it, even though it took a while to get through it.
Displaying 1 of 1 review