Treatise on Hydrodynamics, With Numberous Examples; Volume 2
Separation of Variables and Wiener-Hopf Techniques
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Modern Engineering Practice
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Junior Arithmetic-bookkeeping for Junior High Schools
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Axiomatics
The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart's history ably demonstrates, mathematics is the social activity in which styles of truth--here, abstraction--become synonymous with ways of knowing.
Iterative Learning Control for Equations with Fractional Derivatives and Impulses
1 Fractional Equations1.1 Pulse Compensation ILC1.2 PD-type ILC1.3 High Order Internal Models ILC1.4 Randomly Varying Trial Lengths ILC2 Fractional Multi-Agent Systems2.1 Linear Systems2.2 Nonlinear Systems3 Instantaneous Impulsive Equations4.1 ODE Case3.2 Stochastic Case3.3 Delay Matrix Case4 Noninstantaneous Impulsive Equations4.1 Fixed Trial Lengths ILC 4.2 Randomly Varying Trial Lengths ILC5 Noninstantaneous Impulsive Inclusions 5.1 Ordinary differential inclusion without impulses5.2 Partial differential inclusion with impulses6. Delay Equations6.1 Discrete Case6.2 Continuous Case
Artificial Intelligence Logic and Applications
This book constitutes refereed proceedings of the 2nd International Conference on Artificial Intelligence Logic and Applications 2022 held in Shanghai, China from August 26-28, 2022.The 20 full papers presented in this volume were carefully reviewed and selected from a total of 27 submissions. The papers in the volume are organised according to the following topical headings: program logic; fuzzy logic; applications; author index.
Optimal Control of Partial Differential Equations
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes ofOCPs that stand behind the advanced applications mentioned above.Starting from simple problems that allow a "hands-on" treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text.The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
A Manual of Simple Engineering Mathematics, Covering the Whole Field of Direct Current Calculations,
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Treatise on Hydrodynamics, With Numberous Examples; Volume 2
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Separation of Variables and Wiener-Hopf Techniques
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A Short Course in the Theory of Determinants
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The Substitution of Similars, the True Principle of Reasoning, Derived From a Modification of Aristo
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Intermarriage in New York City
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Conic Sections
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Mathematics for Electrical Students
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Text-Book On Geodesy and Least Squares
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Memorabilia Mathematica; or, The Philomath's Quotation-book
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Key to Algebra for the Use of Colleges and Schools
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A Short Course in the Theory of Determinants
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Intermarriage in New York City
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Memorabilia Mathematica; or, The Philomath's Quotation-book
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Napier Tercentenary Memorial Volume
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Mathematics for Electrical Students
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Key to Algebra for the Use of Colleges and Schools
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Practical Plane & Solid Geometry
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Modern Engineering Practice
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Mathematical Instruments
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Notes Upon Least Squares and Geodesy
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Secondary-School Mathematics
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A Simple Lambda-calculus Model of Programming Languages
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Principles of the Algebra of Logic
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Ordinary Differential Equations with Applications (Third Edition)
Written in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.
The Beginner's Algebra
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Landscapes of Investigation
Creating landscapes of investigation is a primary concern of critical mathematics education. It enables us to organise educational processes so that students and teachers are able to get involved in explorations guided by dialogical interactions. It attempts to address explicit or implicit forms of social injustice by means of mathematics, and also to promote a critical conception of mathematics, challenging the assumption that the subject represents objectivity and neutrality. Landscapes of Investigation provides many illustrations of how this can be done in primary, secondary, and university education. It also illustrates how exploring landscapes of investigation can contribute to mathematics teacher education programmes.This edited volume is the result of a collaboration established through the Colloquium in Research in Critical Mathematics Education, which took place in 2016, 2018, and 2019 in Brazil. Its twenty-eight contributors are young researchers from Brazil, Chile, Colombia, India, Mexico and the USA, who are dedicated to the further development of critical mathematics education.Organised in eighteen chapters, the volume presents examples of engaging students from a diversity of social and economic backgrounds, age ranges, and abilities across different countries. The chapters present original findings on the social aspects of all levels of mathematics education. Landscapes of Investigation is of particular relevance to those with an interest in the potential of mathematics education to challenge social injustices.
Advanced Calculus
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Bounded Cohomology and Simplicial Volume
Since their introduction by Gromov in the 1980s, the study of bounded cohomology and simplicial volume has developed into an active field connected to geometry and group theory. This monograph, arising from a learning seminar for young researchers working in the area, provides a collection of different perspectives on the subject, both classical and recent. The book's introduction presents the main definitions of the theories of bounded cohomology and simplicial volume, outlines their history, and explains their principal motivations and applications. Individual chapters then present different aspects of the theory, with a focus on examples. Detailed references to foundational papers and the latest research are given for readers wishing to dig deeper. The prerequisites are only basic knowledge of classical algebraic topology and of group theory, and the presentations are gentle and informal in order to be accessible to beginning graduate students wanting to enter this lively and topical field.
Elliptic Regularity Theory by Approximation Methods
Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs - such as the Krylov-Safonov and Evans-Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ - and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and H繹lder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing H繹lder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.
The Laplace Transform
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The Philosophical And Mathematical Commentaries Of Proclus On The First Book Of Euclid's Elements
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