2. The Concept of a Function

  1. Ulrich L. Rohde1,2,
  2. G. C. Jain3,
  3. Ajay K. Poddar2 and
  4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch2

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) The Concept of a Function, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch2

Author Information

  1. 1

    BTU Cottbus, Germany

  2. 2

    Synergy Microwave Corporation, Paterson, NJ, USA

  3. 3

    Defense Research & Development Organization, Maharashtra, India

  4. 4

    Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

Publication History

  1. Published Online: 28 DEC 2011
  2. Published Print: 9 DEC 2011

ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

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Keywords:

  • “function,” as language of sets, modes of expression;
  • function, and domain, codomain, image, range;
  • infinity and algebra of infinity

Summary

This chapter contains sections titled:

  • Introduction

  • Equality of Ordered Pairs

  • Relations and Functions

  • Definition

  • Domain, Codomain, Image, and Range of a Function

  • Distinction Between “f” and “f(x)”

  • Dependent and Independent Variables

  • Functions at a Glance

  • Modes of Expressing a Function

  • Types of Functions

  • Inverse Function f−1

  • Comparing Sets without Counting their Elements

  • The Cardinal Number of a Set

  • Equivalent Sets (Definition)

  • Finite Set (Definition)

  • Infinite Set (Definition)

  • Countable and Uncountable Sets

  • Cardinality of Countable and Uncountable Sets

  • Second Definition of an Infinity Set

  • The Notion of Infinity

  • An Important Note About the Size of Infinity

  • Algebra of Infinity (∞)