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Calculus to Analysis : An Introductory Transition / by Arturo Portnoy.
Springer Nature - Synthesis Collection of Technology Collection 14 (2025) Available online
View online- Format:
- Book
- Author/Creator:
- Portnoy, Arturo.
- Series:
- Synthesis Lectures on Mathematics & Statistics, 1938-1751
- Language:
- English
- Subjects (All):
- Mathematical analysis.
- Fourier analysis.
- Mathematical optimization.
- Calculus of variations.
- Mathematics.
- Mathematics--Study and teaching.
- Analysis.
- Fourier Analysis.
- Calculus of Variations and Optimization.
- Applications of Mathematics.
- General Mathematics and Education.
- Mathematics Education.
- Local Subjects:
- Analysis.
- Fourier Analysis.
- Calculus of Variations and Optimization.
- Applications of Mathematics.
- General Mathematics and Education.
- Mathematics Education.
- Physical Description:
- 1 online resource (125 pages)
- Edition:
- 1st ed. 2025.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
- Summary:
- This book addresses the analysis of functions of a real variable and transitions from the standard calculus sequence to mathematical analysis. The author presents the limits and convergence of sequences of functions, illustrates the limitations of the Riemann integral, and discusses the need for a new integral: the Lebesgue integral. The fundamental concepts of the theory of calculus of one variable is presented in addition to limits, continuity, derivatives and its applications, and integrals and their applications. The tone and language of the book is kept as informal as possible along with the descriptions and examples to aid learning. The book is concise and presents single variable advanced calculus leading up to Fourier analysis. In addition, the book sets up sufficient background for a course in measure theory and Lebesgue integration. In addition, this book: Discusses mathematical analysis and provides the needed definitions, lemmas, and theorems Features a concise presentation and is driven by examples of key concepts Supplemented with online interactive activities of explorations and examples .
- Contents:
- Preface
- The Fundamentals
- Sequences, Limits, and Series
- Continuous Functions
- Differentiable Functions
- The Riemann Integral
- Sequences of Functions and their Convergence
- Fourier Series I
- Fourier Series II
- Conclusions.
- Other Format:
- Print version: Portnoy, Arturo Calculus to Analysis
- ISBN:
- 9783031696626
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