This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilities of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Angewandte Mathematik: Body & Soul" ist ein neuer Grundkurs in der Mathematikausbildung für Studienanfänger in den Naturwissenschaften, der Technik, und der Mathematik, der an der Chalmers Tekniska Högskola in Göteborg entwickelt wurde. Er besteht aus drei Bänden sowie Computer-Software. Das Projekt ist begründet in der Computerrevolution, die ihrerseits völlig neue Möglichkeiten des wissenschaftlichen Rechnens in der Mathematik, den Naturwissenschaften und im Ingenieurwesen eröffnet hat. Es besteht aus einer Synthese der mathematischen Analysis (Soul) mit der numerischen Berechnung (Body) sowie den Anwendungen. Die Bände I-III geben eine moderne Version der Analysis und der linearen Algebra wieder, einschließlich konstruktiver numerischer Techniken und Anwendungen, zugeschnitten auf Anfängerprogramme im Maschinenbau und den Naturwissenschaften. Weitere Bände behandeln Themen wie z.B. dynamische Systeme, Strömungsdynamik, Festkörpermechanik und Elektromagnetismus. Dieser Band entwickelt das Riemann-Integral, um eine Funktion zu einer gegebenen Ableitung zu bestimmen. Darauf aufbauend werden Differentialgleichungen und Anfangswertprobleme mit einer Vielzahl anschaulicher Anwendungen behandelt. Die lineare Algebra wird auf n-dimensionale Räume verallgemeinert, wobei wiederum dem praktischen Umgang und numerischen Lösungstechniken besonderer Platz eingeräumt wird. Die Autoren sind führende Experten im Gebiet des wissenschaftlichen Rechnens und haben schon mehrere erfolgreiche Bücher geschrieben. "[......] Oh, by the way, I suggest immediate purchase of all three volumes!" The Mathematical Association of America Online, 7.7.04
This is Volume 4 of the book series of the Body and Soul mathematics education reform program. It presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2) up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. This is an outstanding textbook presenting plenty of new material with an excellent pedagogical approach.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
This is Volume 4 of the book series of the Body and Soul mathematics education reform program. It presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2) up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. This is an outstanding textbook presenting plenty of new material with an excellent pedagogical approach.
It is no coincidence that Donald Robertson, known as @drawbertson to his hundreds of thousands of followers on social media, has become the fashion world’s favorite art bomber of the Instagram era.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. The authors outline, analyze and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally.
Donald Judd Interviews presents sixty interviews with the artist over the course of four decades, and is the first compilation of its kind. It is the companion volume to the critically acclaimed and bestselling Donald Judd Writings. This collection of interviews engages a diverse range of topics, from philosophy and politics to Judd’s insightful critiques of his own work and the work of others such as Mark di Suvero, Edward Hopper, Yayoi Kusama, Barnett Newman, and Jackson Pollock. The opening discussion of the volume between Judd, Dan Flavin, and Frank Stella provides the foundation for many of the succeeding conversations, focusing on the nature and material conditions of the new art developing in the 1960s. The publication also gathers a substantial body of unpublished material across a range of mediums including extensive interviews with art historians Lucy R. Lippard and Barbara Rose. Judd’s contributions in interviews, panels, and extemporaneous conversations are marked by his forthright manner and rigorous thinking, whether in dialogue with art critics, art historians, or his contemporaries. In one of the last interviews, he observed, “Generally expensive art is in expensive, chic circumstances; it’s a falsification. The society is basically not interested in art. And most people who are artists do that because they like the work; they like to do that [make art]. Art has an integrity of its own and a purpose of its own, and it’s not to serve the society. That’s been tried now, in the Soviet Union and lots of places, and it doesn’t work. The only role I can think of, in a very general way, for the artist is that they tend to shake up the society a little bit just by their existence, in which case it helps undermine the general political stagnation and, perhaps by providing a little freedom, supports science, which requires freedom. If the artist isn’t free, you won’t have any art.” Donald Judd Interviews is co-published by Judd Foundation and David Zwirner Books. The interviews expand upon the artist’s thinking present in Donald Judd Writings (Judd Foundation/David Zwirner Books, 2016).
With hundreds of pages of new and previously unpublished essays, notes, and letters, Donald Judd Writings is the most comprehensive collection of the artist’s writings assembled to date. This timely publication includes Judd’s best-known essays, as well as little-known texts previously published in limited editions. Moreover, this new collection also includes unpublished college essays and hundreds of never-before-seen notes, a critical but unknown part of Judd’s writing practice. Judd’s earliest published writing, consisting largely of art reviews for hire, defined the terms of art criticism in the 1960s, but his essays as an undergraduate at Columbia University in New York, published here for the first time, contain the seeds of his later writing, and allow readers to trace the development of his critical style. The writings that followed Judd’s early reviews are no less significant art-historically, but have been relegated to smaller publications and have remained largely unavailable until now. The largest addition of newly available material is Judd’s unpublished notes—transcribed from his handwritten accounts of and reactions to subjects ranging from the politics of his time, to the literary texts he admired most. In these intimate reflections we see Judd’s thinking at his least mediated—a mind continuing to grapple with questions of its moment, thinking them through, changing positions, and demonstrating the intensity of thought that continues to make Judd such a formidable presence in contemporary visual art. Edited by the artist’s son, Judd Foundation curator and co-president Flavin Judd, and Judd Foundation archivist Caitlin Murray, this volume finally provides readers with the full extent of Donald Judd’s influence on contemporary art, art history, and art criticism.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
Donald Rumsfeld is one of the most valuable assets of his country. He quickly organized the military to fight the unconventional war on terrorism and claimed victory after victory. Here are his defining statements.
How a dedicated conservative perceived and used the powers of the presidency is here treated with authority, objectivity, and a dash of wit. The personal papers of William Howard Taft cast important new light on his aims and performance as chief executive. Making full use of the papers, Professor Anderson corrects previous studies of Taft that are either uncritical or unduly harsh, and offers instead a balanced and fair assessment. Taking a topical rather than a chronological approach to the Taft years, the author analyzes his accomplishments as party leader, administrator, legislator, leader of public opinion, and diplomat. The history of Taft's presidency, he concludes, illustrates many of the inherent strengths and weaknesses of a system of government that is reliant upon the will of the people for action and ultimate success. Comparing Taft with his eloquent and dynamic predecessor, Theodore Roosevelt, Anderson contrasts both their views of presidential power and their political styles. Finally, he places Taft in a larger historical context—as an apostle of constitutional democracy who valued the rule of law more than majority rule.
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