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 Fonda, Alessandro, author.
 Cham : Birkhäuser, [2023]
 Description
 Book — 1 online resource (xxi, 431 pages) : illustrations
 Summary

This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to StokesCartan Theorem. The main novelty which distinguishes this book is the choice of introducing the KurzweilHenstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics. The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.
3. Recent advances in mathematical analysis : celebrating the 70th anniversary of Francesco Altomare [2023]
 Cham, Switzerland : Birkhäuser, [2023]
 Description
 Book — 1 online resource (440 pages) : illustrations (color).
 Summary

This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (KorovkinType) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.
4. Analysis. I [2022]
 Tao, Terence, 1975 author.
 Fourth edition.  Singapore : Springer, 2022.
 Description
 Book — 1 online resource (x, 340 pages).
 Summary

 Chapter 1. Introduction
 Chapter 2. Starting at the beginning: the natural numbers
 Chapter 3. Set theory
 Chapter 4. Integers and rationals
 Chapter 5. The real numbers
 Chapter 6. Limits of sequences
 Chapter 7. Series
 Chapter 8. Infinite sets
 Chapter 9. Continuous functions on R
 Chapter 10. Differentiation of functions
 Chapter 11. The Riemann integral. .
5. Analysis. II [2022]
 Tao, Terence, 1975 author.
 Fourth edition.  Singapore : Springer, 2022.
 Description
 Book — 1 online resource (x, 210 pages)
 Summary

 Chapter 1. Metric Spaces
 Chapter 2. Continuous functions on metric spaces
 Chapter 3. Uniform convergence
 Chapter 4. Power series
 Chapter 5. Fourier series
 Chapter 6. Several variable differential calculus
 Chapter 7. Lebesgue measure
 Chapter 8. Lebesgue integration.
6. Introduction to modern analysis [2022]
 Kantorovitz, Shmuel, 1935 author.
 Second edition  Oxford ; New York, NY : Oxford University Press, [2022]
 Description
 Book — 1 online resource
 Hu, Shouchuan.
 Cham, Switzerland : Birkhäuser, 2022.
 Description
 Book — 1 online resource
 Summary

 Volume I  Theory:  Topology. Measure Theory. Banach Space Theory. Function Spaces. Multivalued Analysis. Smooth and Nonsmooth Calculus. Nonlinear Operators. Variational Analysis. References.
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8. Fundamentals of mathematical analysis [2021]
 Boules, Adel N., author.
 First edition  Oxford ; New York, NY : Oxford University Press, 2021
 Description
 Book — 1 online resource
 Summary

 1: Preliminaries
 2: Set Theory
 3: Vector Spaces
 4: The Metric Topology
 5: Essentials of General Topology
 6: Banach Spaces
 7: Hilbert Spaces
 8: Integration Theory.
 (source: Nielsen Book Data)
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9. Sharpening mathematical analysis skills [2021]
 Sîntămărian, Alina, author.
 Cham : Springer, [2021]
 Description
 Book — 1 online resource : illustrations (chiefly color) Digital: text file.PDF.
 Summary

 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 SandhamYeung Series. Solutions. References. Index.
 (source: Nielsen Book Data)
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 Rozwiązujemy zadania z analizy matematycznej. English
 Radożycki, Tomasz.
 Cham, Switzerland : Springer, [2020]
 Description
 Book — 1 online resource (386 pages)
 Summary

 Examining Curves and Surfaces. Investigating Conditional Extremes. Investigating Integrals with Parameters. Examining Unoriented Curvilinear Integrals. Examining Differential Forms. Examining Oriented Curvilinear Integrals. Studying Functions of Complex Variable. Investigating Singularities of Complex Functions. Dealing with MultiValued Functions. Studying Fourier Series.
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11. Introduction to real analysis [2019]
 Heil, Christopher, 1960 author.
 Cham, Switzerland : Springer, [2019]
 Description
 Book — xvii, 400 pages : illustrations ; 25 cm.
 Summary

 Preliminaries
 Metric and Normed Spaces
 Metric Spaces
 Convergence and Completeness
 Topology in Metric Spaces
 Compact Sets in Metric Spaces
 Continuity for Functions on Metric Spaces
 Normed Spaces
 Vector Spaces
 Seminorms and Norms
 Infinite Series in Normed Spaces
 Equivalent Norms
 The Uniform Norm
 Some Function Spaces
 Holder and Lipschitz Continuity
 Lebesgue Measure
 Exterior Lebesgue Measure
 Boxes
 Some Facts about Boxes
 Exterior Lebesgue Measure
 The Exterior Measure of a Box
 The Cantor Set
 Regularity of Exterior Measure
 Lebesgue Measure
 Definition and Basic Properties
 Toward Countable Additivity and Closure under Complements
 Countable Additivity
 Equivalent Formulations of Measurability
 Carathéodory's Criterion
 Almost Everywhere and the Essential Supremum
 More Properties of Lebesgue Measure
 Continuity from Above and Below
 Cartesian Products
 Linear Changes of Variable
 Nonmeasurable Sets
 The Axiom of Choice
 Existence of a Nonmeasurable Set
 Further Results
 Measurable Functions
 Definition and Properties of Measurable Functions
 Extended RealValued Functions
 ComplexValued Functions
 Operations on Functions
 Sums and Products
 Compositions
 Suprema and Limits
 Simple Functions
 The Lebesgue Space L...(E)
 Convergence and Completeness in L...(E)
 Egorov's Theorem
 Convergence in Measure
 Luzin's Theorem
 The Lebesgue Integral
 The Lebesgue Integral of Nonnegative Functions
 Integration of Nonnegative Simple Functions
 Integration of Nonnegative Functions
 The Monotone Convergence Theorem and Fatou's Lemma
 The Monotone Convergence Theorem
 Fatou's Lemma
 The Lebesgue Integral of Measurable Functions
 Extended RealValued Functions
 ComplexValued Functions
 Properties of the Integral
 Integrable Functions and L1(E)
 The Lebesgue Space L1(E)
 Convergence in L1Norm
 Linearity of the Integral for Integrable Functions
 Inclusions between L1(E) and L...(E)
 The Dominated Convergence Theorem
 The Dominated Convergence Theorem
 First Applications of the DCT
 Approximation by Continuous Functions
 Approximation by Really Simple Functions
 Relation to the Riemann Integral
 Repeated Integration
 Fubini's Theorem
 Tonelli's Theorem
 Convolution
 Differentiation
 The CantorLebesgue Function
 Functions of Bounded Variation
 Definition and Examples
 Lipschitz and Holder Continuous Functions
 Indefinite Integrals and Antiderivatives
 The Jordan Decomposition
 Covering Lemmas
 The Simple Vitali Lemma
 The Vitali Covering Lemma
 Differentiability of Monotone Functions
 The Lebesgue Differentiation Theorem
 L1Convergence of Averages
 Locally Integrable Functions
 The Maximal Theorem
 The Lebesgue Differentiation Theorem
 Lebesgue Points
 Absolute Continuity and the Fundamental Theorem of Calculus
 Absolutely Continuous Functions
 Differentiability of Absolutely Continuous Functions
 Growth Lemmas
 The BanachZaretsky Theorem
 The Fundamental Theorem of Calculus
 Applications of the FTC
 Integration by Parts
 The Chain Rule and Changes of Variable
 Convex Functions and Jensen's Inequality
 The lp Spaces
 The lp Spaces
 Hölder's Inequality
 Minkowski's Inequality
 Convergence in the lp Spaces
 Completeness of the lp Spaces
 lp for p < 1
 C0 and C00
 The Lebesgue Space Lp(E)
 Seminorm Properties of II : IIp
 Identifying Functions That Are Equal Almost Everywhere
 Lp(E) for 0 < p < 1
 The Converse of Hölder's Inequality
 Convergence in Ipnorm
 Dense Subsets of Lp(E)
 Separability of Lp(E)
 Hilbert Spaces and L2(E)
 Inner Products and Hilbert Spaces
 The Definition of an Inner Product
 Properties of an Inner Product
 Hilbert Spaces
 Orthogonality
 Orthogonal Complements
 Orthogonal Projections
 Characterizations of the Orthogonal Projection
 The Closed Span
 The Complement of the Complement
 Complete Sequences
 Orthonormal Sequences and Orthonormal Bases
 Orthonormal Sequences
 Unconditional Convergence
 Orthogonal Projections Revisited
 Orthonormal Bases
 Existence of an Orthonormal Basis
 The Legendre Polynomials
 The Haar System
 Unitary Operators
 The Trigonometric System
 Convolution and the Fourier Transform
 Convolution
 The Definition of Convolution
 Existence
 Convolution as Averaging
 Approximate Identities
 Young's Inequality
 The Fourier Transform
 The Inversion Formula
 Smoothness and Decay
 Fourier Series
 Periodic Functions
 Decay of Fourier Coefficients
 Convolution of Periodic Functions
 Approximate Identities and the Inversion Formula
 Completeness of the Trigonometric System
 Convergence of Fourier Series for p ... 2
 The Fourier Transform on L2(R)
 Hints for Selected Exercises and Problems
 Index of Symbols
 References
 Index.
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .H435 2019  Unknown 
 Cham : Birkhauser, 2019.
 Description
 Book — 1 online resource.
 Summary

 FM. Ben de Pagter: Curriculum Vitae
 2Local automorphisms on AW*algebras. Orthosymmetric Archimedeanvalued vector lattices. Arens extensions for polynomials and the WoodburySchep formula. On the endpoints of De Leeuw restriction theorems. Lebesgue topologies and mixed topologies. Lattice homomorphisms in harmonic analysis. Noncommutative Boyd interpolation theorems revisited. Strict singularity: a lattice approach. Asymptotics of operator semigroups via the semigroup at infinity. Markov processes, strong Markov processes and Brownian motion in Riesz spaces. A solution to the AlSalamChihara moment problem. The Katowice problem for analysts. Onefold and twofold EllisGohberg inverse problems for scalar Wiener class functions. Relatively uniform convergence in partially ordered vector spaces revisited. Dedekind complete and order continuous Banach C(K)modules. Matrix valued Laguerre polynomials. Weighted Noncommutative Banach Function Spaces. Majorization for compact and weakly compact polynomials on Banach lattices. The UMD property for MusielakOrlicz spaces. The ls Boundedness of a Family of Integral Operators on UMD Banach Function Spaces. Backward stochastic evolution equations in UMD Banach spaces. On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics. Classes of localizable measure spaces. A residue formula for locally compact noncommutative manifolds. Regular states and the Regular Algebra Numerical Range. Bilaplace Eigenfunctions compared with Laplace Eigenfunctions in some special cases.Representations of the Dedekind completions of spaces of continuous functions. Joint representation of a Riesz space and its conjugate space. When do the regular operators between two Banach lattices form a lattice?. Lexicographic cones and the ordered projective tensor product.
 (source: Nielsen Book Data)
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 Rombaldi, JeanÉtienne.
 Les Ulis : EDP Sciences, 2019.
 Description
 Book — 1 online resource (266 pages)
 Cham : Birkhäuser, 2019.
 Description
 Book — 1 online resource (384 pages)
 Summary

 Part I Yingkang: Remembering Professor Yingkang Hu. Remembrances. On Some Properties of Moduli of Smoothness with JacobiWeights. Part II Approximation Theory, Harmonic and Complex Analysis, Splines and Classical Fourier Theory. Special Difference Operators and the Constants in the Classical JacksonType Theorems. Comparison Theorems for Completely and Multiply Monotone Functions and Their Applications. Concerning Exponential Bases on MultiRectangles of Rd. Hankel Transforms of General Monotone Functions. Univalence of a Certain Quartic Function. Finding, Stabilizing, and Verifying Cycles of Nonlinear Dynamical Systems. Finding Orbits of Functions Using Suffridge Polynomials. The Sharp RemezType Inequality for Even Trigonometric Polynomials on the Period. The Lebesgue Constants of Fourier Partial Sums. LiouvilleWeyl Derivatives of Double Trigonometric Series. Inequalities in Approximation Theory Involving Fractional Smoothness in Lp, 0 < p < 1. On de BoorFix Type Functionals for Minimal Splines. A Multidimensional HardyLittlewood Theorem. The Spurious Side of DiagonalMultipoint Pade Approximants. Spline Summability of Cardinal Sine Series and the Bernstein Class. Integral Identities for Polyanalytic Functions. Pointwise Behavior of Christoffel Function on Planar Convex Domains. Towards Best Approximations for
 (source: Nielsen Book Data)
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 Haslinger, Friedrich, author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — 1 online resource (ix, 338 pages.) :.
 Summary

In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and MittagLeffler's theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Frechet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous CauchyRiemann equations and the dbar Neumann operator. Contents Complex numbers and functions Cauchy's Theorem and Cauchy's formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Frechet spaces of holomorphic functions The complex The twisted complex and Schroedinger operators.
(source: Nielsen Book Data)
16. A first course in analysis [2018]
 Conway, John B., 1939 author.
 Cambridge, United Kingdom : Cambridge University Press, [2018]
 Description
 Book — xv, 340 pages ; 26 cm.
 Summary

 1. The real numbers
 2. Differentiation
 3. Integration
 4. Sequences of functions
 5. Metric and Euclidean spaces
 6. Differentiation in higher dimensions
 7. Integration in higher dimensions
 8. Curves and surfaces
 9. Differential forms.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .C647 2018  Unknown 
17. An introduction to real analysis [2018]
 Agarwal, Ravi P. author.
 Boca Raton, FL : CRC Press, [2018]
 Description
 Book — xiv, 277 pages ; 24 cm
 Summary

 Logic and Proof Techniques. Sets and Functions. Real Numbers. Open and Closed Sets. Cardinality. Realvalued Functions. Real Sequences. Real Sequences (Contd.). Infinite Series. Infinite Series (Contd.). Limits of Functions. Continuous Functions. Discontinuous Functions. Uniform and Absolute Continuities and Functions of Bounded Variation. Differentiable Functions. Higher Order Differentiable Functions. Convex Functions. Indeterminate Forms. Riemann Integration. Properties of the Riemann Integral. Improper Integrals. RiemannLebesgue Theorem. RiemannStieltjes Integral. Sequences of Functions. Sequences of Functions (Contd.). Series of Functions. Power and Taylor Series. Power and Taylor Series (Contd.). Metric Spaces. Metric Spaces (Contd.). Bibliography. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .A33 2018  Unknown 
18. A concrete introduction to real analysis [2017]
 Carlson, Robert, 1951 author.
 2nd.  Chapman and Hall/CRC, 2017.
 Description
 Book — 1 online resource (298 pages : 28 illustrations).
 Summary

 Real Numbers and Mathematical Proofs. Infinite Sequences. Infinite Series. Functions. Integrals. Variations on the Riemann Sums Theme. Taylor Series and Power Series. Appendix: Solutions to Select Problems.
 (source: Nielsen Book Data)
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19. Essential real analysis [2017]
 Field, Michael author.
 Cham, Switzerland : Springer, 2017.
 Description
 Book — xvii, 450 pages : illustrations ; 24 cm.
 Summary

 1 Sets, functions and the real numbers. 2 Basic properties of real numbers, sequences and continuous functions. 3 Infinite series. 4 Uniform convergence. 5 Functions.
 6. Topics from classical analysis: The Gammafunction and the EulerMaclaurin formula. 7 Metric spaces. 8 Fractals and iterated function systems. 9 Differential calculus on Rm. Bibliography. Index.
 (source: Nielsen Book Data)
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .F54 2017  Unknown 
20. Mathematical analysis [2017]
 Malik, S. C., author.
 Fifth multi colour edition.  New Delhi : New Academic Science, an imprint of New Age International (UK) Ltd., [2017]
 Description
 Book — xiv, 870 pages : illustrations (some color) ; 24 cm
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .M2846 2017  Unknown 
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