Bøger i Cornerstones serien

This book presents the principles of functional analysis. It includes recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis.

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The ¿Problems and Complements¿ sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students.Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework.Key features:¿ Many examples, exercises, hints, and solutions guide the reader throughout the text.¿ Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties.¿ Original proofs, which may be difficult to locate elsewhere, are given for many well-known results.¿ The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results.¿ The systematic use of pullback and pushforward introduces concise notation.¿ Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations.Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields.

The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class. This second edition contains a significant amount of new material, including a new chapter dedicated to the CR geometry of the unit sphere.

How should we think about Christian apologetics in a society where people are encouraged to discover, determine, and live their own truth?In this short book, Joe Boot explains that Christ-centred gospel witness is about getting to the heart of a person, for the root of unbelief is a heart condition, not a lack of evidence or convincing arguments. Sin has a profound impact on the heart and human understanding.Dr Boot considers some of the prevailing worldviews in the West today, demonstrating that their foundational problem is a refusal to acknowledge Jesus Christ as Lord and King. As we think about and engage in witnessing to the gospel of the Kingdom, the heart and its attachment to cherished lies must be taken into account.

How should we think about Christian apologetics in a society where people are encouraged to discover, determine and live their own truth? In this short book, Joe Boot explains that Christ-centred gospel witness is about getting to the heart of a person, for the root of unbelief is a heart condition, not a lack of evidence or convincing arguments. Dr. Boot considers some of the prevailing worldviews in the West today, demonstrating that their foundational problem is a refusal to acknowledge Jesus Christ as Lord and King. As we engage in witnessing to the gospel of the Kingdom, the heart and its attachment to cherished lies must be taken into account. Gospel Witness is part of the Cornerstones series of short books for Christians wishing to strengthen their understanding of the scope and implications of the gospel in the twenty-first century.

Culture is something we build, something we do with creation; it is the outward expression of a people's worship, in terms of which they cultivate their society, including its law, education, arts and customs and much more besides. Whether we realize it or not, we all participate daily in culture-building of one form or another. The gospel of the kingdom is the good news that Jesus Christ is King of kings and Lord of lords, and that he is at work to redeem this fallen world, remaking it in accordance with his good purposes. To speak of gospel culture, then, is to speak of a total meaning for the cosmos, a design plan. The gospel has something to say about the way we go about all our cultural activities. God's Word is a total structuration of life and thought. If we would see Jesus Christ honoured and worshipped, if we would see our Lord's will done on earth as it is in heaven, then we must faithfully consider the scriptural view of the gospel and its implications for culture. ';Dr. Joseph Bootis a rigorous thinker, uncompromisingly committed to biblical truth and unafraid to articulate it in the boldest way. He is a cultural theologianof the highest order.'P. Andrew Sandlin, Founder and President, Center forCultural Leadership, Coulterville, California, U.S.A.

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research* Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

This integrated book begins by discussing Fourier series, Hilbert spaces and the Fourier transform on the real line, and then turns to the heart of the text, geometric considerations. The concept of orthogonality weaves the material into a coherent whole.

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method.

Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or establishedA comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematicsIncluded throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Following Lagrangrian principles, this book employs mathematics not only as a unifying language, but also to exemplify its role as a catalyst in such new concepts and discoveries as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics.

* Presents a comprehensive treatment with a global view of the subject* Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis.