Single Variable Differential and Integral Calculus: Mathematical Analysis

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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.

Author(s): Elimhan Mahmudov (auth.)
Edition: 1
Publisher: Atlantis Press
Year: 2013

Language: English
Pages: 373
Tags: Analysis; Ordinary Differential Equations

Front Matter....Pages i-xvi
Introduction to Numbers and Set Theory....Pages 1-30
Sequences and Series....Pages 31-66
Limits and Continuity of Functions....Pages 67-105
Differential Calculus....Pages 107-144
Some Basic Properties of Differentiable Functions....Pages 145-170
Polynomials and Interpolations....Pages 171-183
Applications of Differential Calculus to Limit Calculations and Extremum Problems....Pages 185-221
The Indefinite Integral....Pages 223-258
The Definite Integral....Pages 259-334
Applications of the Definite Integral....Pages 335-365
Back Matter....Pages 367-373