Introduction to Differential Calculus Systematic Studies with Engineering Applications - Hardcover

Jai Rathod

Hardcover

ISBN 10: 1681171848 ISBN 13: 9781681171845

Publisher: Scitus Academics LLC, 2016

Synopsis

Differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus. In differential calculus, primary objects of study are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point. Differential calculus and integral calculus are associated by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration. Differentiation has applications to nearly all quantitative disciplines. Derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena. Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory and abstract algebra. Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners presents the fundamental theories and methods of differential calculus and shows how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. The book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications.

About this title

Review

The book is addressed mainly to students studying non–mathematical subjects. It will be also helpful for those who want to understand why it is important to study Calculus and how to apply it.   (Zentralblatt MATH, 1 December 2012)

From the Back Cover

Enables readers to apply the fundamentals of differential calculus to solve real–life problems in engineering and the physical sciences

Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real–world problems in engineering and the physical sciences. With its easy–to–follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications.

The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including:

• Concepts of function, continuity, and derivative

• Properties of exponential and logarithmic function

• Inverse trigonometric functions and their properties

• Derivatives of higher order

• Methods to find maximum and minimum values of a function

• Hyperbolic functions and their properties

Readers are equipped with the necessary tools to quickly learn how to understand a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine–tuning of various calculus skills. Introduction to Differential Calculus is an excellent book for upper–undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.

Edition details

• Publisher: Scitus Academics LLC
• Publication date: 2016
• Language: English
• ISBN 10: 1681171848
• ISBN 13: 9781681171845
• Binding: Hardcover
• Number of pages: 260