Introduction to Differential Calculus

Systematic Studies with Engineering Applications for Beginners

Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9781118117750
• eBook ISBN: 9781118130148
• Edition: 1
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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.

Table of contents

• Cover
• Title Page
• Copyright
• Foreword
• Preface
• Biographies
• Introduction
• Acknowledgments
• Chapter 1: From Arithmetic to Algebra
• Chapter 2: The Concept of a Function
• Chapter 3: Discovery of Real Numbers: Through Traditional Algebra
• Chapter 4: From Geometry to Coordinate Geometry
• Chapter 5: Trigonometry and Trigonometric Functions
• Chapter 6: More About Functions
• Chapter 7a: The Concept of Limit of a Function
• Chapter 7b: Methods for Computing Limits of Algebraic Functions
• Chapter 8: The Concept of Continuity of a Function, and Points of Discontinuity
• Chapter 9: The Idea of a Derivative of a Function
• Chapter 10: Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions
• Chapter 11a: Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions
• Chapter 11b: Methods of Computing Limits of Trigonometric Functions
• Chapter 12: Exponential Form(s) of a Positive Real Number and its Logarithm(s): Pre-Requisite for Understanding Exponential and Logarithmic Functions
• Chapter 13a: Exponential and Logarithmic Functions and Their Derivatives
• Chapter 13b: Methods for Computing Limits of Exponential and Logarithmic Functions
• Chapter 14: Inverse Trigonometric Functions and Their Derivatives
• Chapter 15a: Implicit Functions and Their Differentiation
• Chapter 15b: Parametric Functions and Their Differentiation
• Chapter 16: Differentials “dy” and “dx”: Meanings and Applications
• Chapter 17: Derivatives and Differentials of Higher Order
• Chapter 18: Applications of Derivatives in Studying Motion in a Straight Line
• Chapter 19a: Increasing and Decreasing Functions and the Sign of the First Derivative
• Chapter 19b: Maximum and Minimum Values of a Function
• Chapter 20: Rolle's Theorem and the Mean Value Theorem (MVT)
• Chapter 21: The Generalized Mean Value Theorem (Cauchy's MVT), L' Hospital's Rule, and their Applications
• Chapter 22: Extending the Mean Value Theorem to Taylor's Formula: Taylor Polynomials for Certain Functions
• Chapter 23: Hyperbolic Functions and Their Properties
• Appendix A: (Related To Chapter-2) Elementary Set Theory
• Appendix B: (Related To Chapter-4)
• Appendix C: (Related To Chapter-20)
• Index