A Friendly Approach To Functional Analysis

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A Friendly Approach To Functional Analysis

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Author : Amol Sasane
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-02-20

A Friendly Approach To Functional Analysis written by Amol Sasane and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.

'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.

Friendly Approach To Functional Analysis A

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Author : Amol Sasane
language : en
Publisher:
Release Date : 2017

Friendly Approach To Functional Analysis A written by Amol Sasane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

A Friendly Approach To Functional Analysis

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Author : A. Sasane
language : en
Publisher: Essential Textbooks in Mathema
Release Date : 2017

A Friendly Approach To Functional Analysis written by A. Sasane and has been published by Essential Textbooks in Mathema this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Branch spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimisation, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study. A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics. Book jacket.

Analysis In Euclidean Space

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Author : Joaquim Bruna
language : en
Publisher: World Scientific
Release Date : 2022-10-04

Analysis In Euclidean Space written by Joaquim Bruna and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-04 with Mathematics categories.

Based on notes written during the author's many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves, geometric measure theory, integral geometry, and others.With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid footing in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work through independently.Analysis in Euclidean Space comprises 21 chapters, each with an introduction summarizing its contents, and an additional chapter containing miscellaneous exercises. Lecturers may use the varied chapters of this book for different undergraduate courses in analysis. The only prerequisites are a basic course in linear algebra and a standard first-year calculus course in differentiation and integration. As the book progresses, the difficulty increases such that some of the later sections may be appropriate for graduate study.

Ordinary Differential Equations And Applications

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Author : Enrique Fernandez-cara
language : en
Publisher: World Scientific
Release Date : 2023-07-26

Ordinary Differential Equations And Applications written by Enrique Fernandez-cara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-26 with Mathematics categories.

Differential equations can bring mathematics to life, describing phenomena originating in physics, chemistry, biology, economics, and more. Used by scientists and engineers alike, differential equations are also the starting point of much purely mathematical activity. They also play a role in the formulation and resolution of problems in harmonic analysis, differential geometry, and probability calculus. A large part of functional analysis has therefore been motivated by the need to solve questions in the analysis of differential systems, as with numerical analysis.Differential equations are doubly relevant, then: as significant in many areas of mathematics, and as important machinery for applying mathematics to real-world problems. This book therefore aims to provide a rigorous introduction to the theoretical study of differential equations, and to demonstrate their utility with applications in many fields.Ordinary Differential Equations and Applications originates from several courses given by the author for decades at the University of Seville. It aims to bring together rigorous mathematical theory and the rich variety of applications for differential equations. The book examines many aspects of differential equations: their existence, uniqueness, and regularity, alongside their continuous dependence on data and parameters. Delving into permanent interpretation of the laws of differential equations, we also look at the role of data and how their solutions behave. Each chapter finishes with a collection of exercises, many of which also contain useful hints.

Standard And Non Standard Methods For Solving Elementary Algebra Problems

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Author : Vladimir G Chirskii
language : en
Publisher: World Scientific
Release Date : 2024-11-07

Standard And Non Standard Methods For Solving Elementary Algebra Problems written by Vladimir G Chirskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Mathematics categories.

Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.

A First Course In Algebraic Geometry And Algebraic Varieties

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Author : Flaminio Flamini
language : en
Publisher: World Scientific
Release Date : 2023-02-13

A First Course In Algebraic Geometry And Algebraic Varieties written by Flaminio Flamini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.

This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material.

Introduction To Number Theory

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Author : Richard Michael Hill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-12-04

Introduction To Number Theory written by Richard Michael Hill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Mathematics categories.

'Probably its most significant distinguishing feature is that this book is more algebraically oriented than most undergraduate number theory texts.'MAA ReviewsIntroduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.

Mathematical Introduction To General Relativity A Second Edition

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Author : Amol Sasane
language : en
Publisher: World Scientific
Release Date : 2024-12-20

Mathematical Introduction To General Relativity A Second Edition written by Amol Sasane and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Science categories.

The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe. Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to all the 283 exercises are included.The second edition corrects errors from the first edition, and includes 60 new exercises, 10 new remarks, 29 new figures, some of which cover auxiliary topics that were omitted in the first edition.

Keynesian Sraffian Computable And Dynamic Economics

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Author : Kumaraswamy Velupillai
language : en
Publisher: Springer Nature
Release Date : 2021-03-08

Keynesian Sraffian Computable And Dynamic Economics written by Kumaraswamy Velupillai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-08 with Business & Economics categories.

This book explores an alternative approach to the conventional, market-based, view of economic theory and economic policy, at theoretical, numerical and applicable levels. The chapters provide a theoretical, empirical, and algorithmic approach to marcodynamics, Sraffian economics, and current policy issues. Post-Keynesian macroeconomics, business cycle theory, the trade cycle, microfoundations, and the Philips Machine are also covered. This book aims to challenge orthodox ideas and provide a lens through which to honour the work of Stefano Zambelli. It will be of relevant to students and academics interested in economics.