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Continuous Nowhere Differentiable Functions
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions....
Hölder and locally Hölder Continuous Functions, and Open Sets of Class C^k, C^{k,lambda}
This book offers a systematic treatment of a classic topic in Analysis. It fills a gap in the existing literature by presenting in detail the classic λ-Hölder condition and introducing the notion of locally Hölder-continuous function in an open set Ω in Rn. Further, it provides the essential notions of multidimensional geometry applied to analysis. Written in an accessible style and with proofs given as clearly as possible, it is a valuable resource for graduate students in Mathematical Analysis and researchers dealing with Hölder-continuous functions and their applications.
Spaces of Continuous Functions
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
Rings of Continuous Functions
Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.
An Introduction to Analytic Functions
When first published in 1959, this book was the basis of a two-semester course in complex analysis for upper undergraduate and graduate students. J. S. Mac Nerney was a proponent of the Socratic, or “do-it-yourself” method of learning mathematics, in which students are encouraged to engage in mathematical problem solving, including theorems at every level which are often regarded as “too difficult” for students to prove for themselves. Accordingly, Mac Nerney provides no proofs. What he does instead is to compose and arrange the investigation in his own unique style, so that a contextual proof is always available to the persistent student who enjoys a challenge. The central idea is t...
Topological Properties of Spaces of Continuous Functions
This book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies studied are the set-open topologies and the uniform topologies. Where appropriate, the analogous theorems for the two major classes of topologies are studied together, so that a comparison can be made. A chapter on cardinal functions puts characterizations of a number of topological properties of function spaces into a more general setting: some of these results are new, others are generalizations of known theorems. Excercises are included at the end of each chapter, covering other kinds of function space topologies. Thus the book should be appropriate for use in a classroom setting as well as for functional analysis and general topology. The only background needed is some basic knowledge of general topology.
Continuous Functions of Vector Variables
This is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. The author covers boundedness, extreme values, and uniform continuity of functions, along with connections between continuity and topological concepts such as connectedness and compactness. The order of topics mimics the order of development in elementary calculus, with analogies and generalizations from such familiar ideas as the Pythagorean theorem.
Nonsmooth Vector Functions and Continuous Optimization
Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.
Go To Guide for CUET (UG) Mathematics with 14 Previous Year Solved Papers & 10 Practice Sets 4th Edition | NCERT Coverage with PYQs & Practice Question Bank | MCQs, AR, MSQs & Passage based Questions
Disha’s updated 4th edition of the book ‘Go To Guide for CUET (UG) Mathematics with 10 Practice Sets & 14 Previous Year Solved Papers’ has been prepared as per the changed pattern of CUET. # The Book is divided into 2 Parts – A: Study Material; B – 10 Practice Mock Tests # Part A covers well explained theory in a ONE-LINER format which is easy to remember. # The complete syllabus is divided into 15 Chapters as per NCERT. # More than 1800+ questions are provided for practice with Hints & Solutions # 2 Sets of 2024, 4 Sets of CUET 2023 & 3 of 2022 solved papers are also added to the book chapter-wise. # 2017 - 2021 Previous Paper of past 5 Years of CUCET have been included chapter-wise for better understanding and to know the nature of actual paper. # Part B provides 10 Mock Tests on the 2024 pattern of 50 MCQs (40 to be attempted). # Detailed solutions are provided for all the Questions. # The Book is strictly based on the Class 12 syllabus and follows NCERT Books.
