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Single Variable Differential and Integral Calculus

Mathematical Analysis

  • Textbook
  • © 2013

Overview

Authors:
  1. Elimhan Mahmudov

    1. Istanbul Technical University, Istanbul, Turkey

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  • Treatment of countable and uncountable sets, the cardinality of the continuum; Dedekind completeness theorem for the set of real numbers

  • Coverage of polynomials and interpolation, Lagrange and Newton interpolation formulas

  • Inclusion of Lebesgue measure and Lebesgue integrals

  • Interesting applications: potential and kinetic energy, a body in the earth’s gravitational field, escape

  • At the end of each chapter, many of challenging of problems with answers

  • Includes supplementary material: sn.pub/extras

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction to Numbers and Set Theory

    • E. Mahmudov
    Pages 1-30

  3. Sequences and Series

    • E. Mahmudov
    Pages 31-66

  4. Limits and Continuity of Functions

    • E. Mahmudov
    Pages 67-105

  5. Differential Calculus

    • E. Mahmudov
    Pages 107-144

  6. Some Basic Properties of Differentiable Functions

    • E. Mahmudov
    Pages 145-170

  7. Polynomials and Interpolations

    • E. Mahmudov
    Pages 171-183

  8. Applications of Differential Calculus to Limit Calculations and Extremum Problems

    • E. Mahmudov
    Pages 185-221

  9. The Indefinite Integral

    • E. Mahmudov
    Pages 223-258

  10. The Definite Integral

    • E. Mahmudov
    Pages 259-334

  11. Applications of the Definite Integral

    • E. Mahmudov
    Pages 335-365

  12. Back Matter

    Pages 367-373
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Keywords

About this book

The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequences of functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems and examples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Stieltjes and Lebesque integrals are studied together and compared.

Authors and Affiliations

  • Istanbul Technical University, Istanbul, Turkey

    Elimhan Mahmudov

Bibliographic Information

  • Book Title: Single Variable Differential and Integral Calculus

  • Book Subtitle: Mathematical Analysis

  • Authors: Elimhan Mahmudov

  • DOI: https://doi.org/10.2991/978-94-91216-86-2

  • Publisher: Atlantis Press Paris

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Atlantis Press 2013

  • Hardcover ISBN: 978-94-91216-85-5Published: 04 April 2013

  • Softcover ISBN: 978-94-6239-040-9Published: 12 April 2015

  • eBook ISBN: 978-94-91216-86-2Published: 19 March 2013

  • Edition Number: 1

  • Number of Pages: XVI, 373

  • Topics: Analysis, Ordinary Differential Equations

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