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1. A Course in Calculus and Real Analysis
by Sudhir R. Ghorpade, Balmohan V. Limaye
出版情報: New York, NY : Springer Science+Business Media, LLC, 2006
シリーズ名: Undergraduate Texts in Mathematics ;
オンライン: http://dx.doi.org/10.1007/0-387-36425-0
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2. The Real Numbers and Real Analysis
by Ethan D. Bloch
出版情報: New York, NY : Springer Science+Businees Media, LLC, 2011
オンライン: http://dx.doi.org/10.1007/978-0-387-72177-4
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3. Introduction to Mathematical Analysis
by Igor Kriz, Aleš Pultr
出版情報: Basel : Springer Basel : Imprint: Birkhäuser, 2013
オンライン: http://dx.doi.org/10.1007/978-3-0348-0636-7
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Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
1. Preliminaries
2. Metric and Topological Spaces I
3. Multivariable Differential Calculus
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
6. Systems of Ordinary Differential Equations
7. System of Linear Differential Equations
8. Line Integrals and Green's Theorem
Part 2. Analysis and Geometry
9. An Introduction to Complex Analysis
10. Metric and Topological Spaces II
11. Multilinear Algebra
12. Smooth Manifolds, Differential Forms and Stokes' Theorem
13. Calculus of Variations and the Geodesic Equation
14. Tensor Calculus and Riemannian Geometry
15. Hilbert Spaces I: Definitions and Basic Properties
16. Hilbert Spaces II: Examples and Applications
Appendix A. Linear Algebra I: Vector Spaces
Appendix B. Linear Algebra II: More about Matrices
Bibliography
Index of Symbols
Index.
Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
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4. Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
edited by Michael Ruzhansky, Ville Turunen
出版情報: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014
シリーズ名: Trends in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-3-319-02550-6
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Preface
Contributions by N. Bez, M. Sugimoto, Tang Bao Ngoc Bui, M. Reissig, F. Colombini, D. Del Santo, F. Fanelli, G. Metivier, E. Cordero, F. Nicola, L. Rodino, S. Coriasco, K. Johansson, J. Toft, V. Fischer, M. Ruzhansky, G. Garello, A. Morando, D. Grieser, E. Hunsicker, N. Habal, W. Rungrottheera, B
W. Schulze, C. Iwasaki, B. Kanguzhin, N. Tokmagambetov, S. Katayama, H. Kubo, M. Lassas, T. Zhou, T. Matsuyama, T. Nishitani, S. Serovajsky, K. Shakenov, S. Tikhonov, M. Zeltser, Y. Wakasugi, K. Yagdjian.
Preface
Contributions by N. Bez, M. Sugimoto, Tang Bao Ngoc Bui, M. Reissig, F. Colombini, D. Del Santo, F. Fanelli, G. Metivier, E. Cordero, F. Nicola, L. Rodino, S. Coriasco, K. Johansson, J. Toft, V. Fischer, M. Ruzhansky, G. Garello, A. Morando, D. Grieser, E. Hunsicker, N. Habal, W. Rungrottheera, B
W. Schulze, C. Iwasaki, B. Kanguzhin, N. Tokmagambetov, S. Katayama, H. Kubo, M. Lassas, T. Zhou, T. Matsuyama, T. Nishitani, S. Serovajsky, K. Shakenov, S. Tikhonov, M. Zeltser, Y. Wakasugi, K. Yagdjian.
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5. Real Analysis via Sequences and Series
by Charles H.C. Little, Kee L. Teo, Bruce van Brunt
出版情報: New York, NY : Springer New York : Imprint: Springer, 2015
シリーズ名: Undergraduate Texts in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4939-2651-0
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Preface
1. Introduction
2. Sequences
3. Series
4. Limits of Functions
5. Continuity
6. Differentiability
7. The Riemann Integral
8. Taylor Polynomials and Taylor Series
9. The Fixed Point Problem
10. Sequences of Functions
Bibliography
Index
Preface
1. Introduction
2. Sequences
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6. The Rise and Development of the Theory of Series up to the Early 1820s
by Giovanni Ferraro
出版情報: New York, NY : Springer Science+Business Media, LLC, 2008
シリーズ名: Sources and Studies in the History of Mathematics and Physical Sciences ;
オンライン: http://dx.doi.org/10.1007/978-0-387-73468-2
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7. Fundamental Mathematical Analysis. 1st ed. 2020
by Robert Magnus
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: Springer Undergraduate Mathematics Series ;
オンライン: https://doi.org/10.1007/978-3-030-46321-2
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1 Introduction
2 Real Numbers
3 Sequences and Series
4 Functions and Continuity
5 Derivatives and Differentiation
6 Integrals and Integration
7 The Elementary Transcendental Functions
8 The Techniques of Integration
9 Complex Numbers
10 Complex Sequences and Series
11 Function Sequences and Function Series
12 Improper Integrals
Index
1 Introduction
2 Real Numbers
3 Sequences and Series
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8. Sharpening Mathematical Analysis Skills. 1st ed. 2021
by Alina Sîntămărian, Ovidiu Furdui
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Problem Books in Mathematics ;
オンライン: https://doi.org/10.1007/978-3-030-77139-3
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Preface
Notations
Sequences of Real Numbers
Series of Real Numbers
Power Series
Derivatives and Applications
Partial Derivatives and Applications
Implicit Functions
Challenges, Gems, and Mathematical Beauties
An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series
Solutions
References
Index
Preface
Notations
Sequences of Real Numbers
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9. Real Analysis: Foundations. 1st ed. 2021
by Sergei Ovchinnikov
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Universitext ;
オンライン: https://doi.org/10.1007/978-3-030-64701-8
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1 Rational Numbers
2 Real Numbers
3 Continuous Functions
4 Differentiation
5 Integration
6 Infinite Series
A Natural Numbers and Integers
B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields
1 Rational Numbers
2 Real Numbers
3 Continuous Functions
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10. Calculus off the Beaten Path : A Journey Through Its Fundamental Ideas. 1st ed. 2022
by Ignacio Zalduendo
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2022
シリーズ名: SUMS Readings ;
オンライン: https://doi.org/10.1007/978-3-031-15765-3
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Chapter. 1. The Real Numbers
Chapter. 2. Sequences and Series
Chapter. 3. Functions
Chapter. 4. The Derivative
Chapter. 5. The Integral
Chapter. 6. More Derivatives
Chapter. 7. Convexity and The Isoperimetric Inequality
Chapter. 8. More Integrals
Chapter. 9. The Gamma Function
Chapter. 1. The Real Numbers
Chapter. 2. Sequences and Series
Chapter. 3. Functions