Description
Book Synopsis: 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.
Details
Are you ready to unlock the power of calculus? Introducing Essential Calculus with Applications, a comprehensive book that will revolutionize the way you approach problem-solving. Written by a renowned mathematician, this text is designed to provide undergraduate-level students with the problem-solving techniques necessary to excel in fields like physics, biology, and economics. With its rigorous yet accessible approach, this book is an indispensable resource for any mathematician.
Chapter Two dives into the core of differential calculus, exploring the key concept of functions, derivatives, and limits. The author goes beyond theory, using differentiation as a practical tool to tackle real-world problems such as velocity, continuous and differentiable functions, optimization, and more. You'll gain a solid understanding of how differential calculus can be applied in various contexts.
But that's not all - Chapter Four extends your knowledge into integral calculus. You'll learn about the Riemann integral, mean value theorem, integration techniques, and improper integrals. With this invaluable knowledge, you'll be equipped to solve complex problems involving the calculation of areas, volumes, and more.
Looking to broaden your horizons? In Chapter Five, you'll be introduced to differential equations and their applications. From growth and decay problems to analyzing motion, this chapter opens doors to new realms of mathematical understanding.
With numerous problems and answers provided, you can put your newfound knowledge to the test. Plus, the "Supplementary Hints and Answers" section ensures that you can evaluate your grasp of the material at every step.
Don't miss out on this concise and well-written text that will serve as your ultimate guide to calculus. Whether you're a student seeking a solid foundation or a professional looking for a refresher, Essential Calculus with Applications is the perfect choice. Take the first step towards mastering calculus today.
Get your copy now and embark on a journey towards mathematical excellence!
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