Mathematics: Frontiers and Perspectives

Mathematics: Frontiers and Perspectives

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 476

ISBN-13: 9780821826973

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A celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians.


Frontiers of Applied Mathematics

Frontiers of Applied Mathematics

Author: Din-Yu Hsieh

Publisher: World Scientific

Published: 2007

Total Pages: 236

ISBN-13: 9812770453

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This volume brings together articles on the mathematical aspects of life sciences, astrophysics, and nonlinear wave problems. It covers theoretical problems associated with the nervous system, drosophila embryos, protein folding, biopolymers, protoplanetary disks and extrasolar planets, gaseous disks, spiral galaxies, dark matter dynamics, star formation, solitary waves, photonics, and nonlinear light propagation in periodic media. The contributions are written for a general audience, and the authors have included references for further reading.


Frontiers Of Applied Mathematics - Proceedings Of The 2nd International Symposium

Frontiers Of Applied Mathematics - Proceedings Of The 2nd International Symposium

Author: Din-yu Hsieh

Publisher: World Scientific

Published: 2007-04-24

Total Pages: 236

ISBN-13: 9814476269

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This volume brings together articles on the mathematical aspects of life sciences, astrophysics, and nonlinear wave problems. It covers theoretical problems associated with the nervous system, drosophila embryos, protein folding, biopolymers, protoplanetary disks and extrasolar planets, gaseous disks, spiral galaxies, dark matter dynamics, star formation, solitary waves, photonics, and nonlinear light propagation in periodic media. The contributions are written for a general audience, and the authors have included references for further reading.


Engineering—An Endless Frontier

Engineering—An Endless Frontier

Author: Sunny Y. AUYANG

Publisher: Harvard University Press

Published: 2009-06-30

Total Pages: 353

ISBN-13: 0674020324

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Genetic engineering, nanotechnology, astrophysics, particle physics: We live in an engineered world, one where the distinctions between science and engineering, technology and research, are fast disappearing. This book shows how, at the dawn of the twenty-first century, the goals of natural scientists--to discover what was not known--and that of engineers--to create what did not exist--are undergoing an unprecedented convergence. Sunny Y. Auyang ranges widely in demonstrating that engineering today is not only a collaborator with science but its equal. In concise accounts of the emergence of industrial laboratories and chemical and electrical engineering, and in whirlwind histories of the machine tools and automobile industries and the rise of nuclear energy and information technology, her book presents a broad picture of modern engineering: its history, structure, technological achievements, and social responsibilities; its relation to natural science, business administration, and public policies. Auyang uses case studies such as the development of the F-117A Nighthawk and Boeing 777 aircraft, as well as the experiences of engineer-scientists such as Oliver Heaviside, engineer-entrepreneurs such as Henry Ford and Bill Gates, and engineer-managers such as Alfred Sloan and Jack Welch to give readers a clear sense of engineering's essential role in the future of scientific research. Table of Contents: Preface 1. Introduction 2 . Technology Takes Off 2.1 From Practical Art to Technology 2.2 Construction Becomes Mathematical 2.3 Experimenting with Machines 2.4 Science and Chemical Industries 2.5 Power and Communication 3. Engineering for Information 3.1 From Microelectronics to Nanotechnology 3.2 Computer Hardware and Software 3.3 Wireless, Satellites, and the Internet 4. Engineering in Society 4.1 Social Ascent and Images of Engineers 4.2 Partnership in Research and Development 4.3 Contributions to Sectors of the Economy 5. Innovation by Design 5.1 Inventive Thinking in Negative Feedback 5.2 Design Processes in Systems Engineering 5.3 “Working Together� in Aircraft Development 5.4 From Onboard Computers to Door Hinges 6. Sciences of Useful Systems 6.1 Mathematics in Engineering and Science 6.2 Information and Control Theories 6.3 Wind Tunnels and Internet Simulation 6.4 Integrative Materials Engineering 6.5 Biological Engineering Frontiers 7. Leaders Who Are Engineers 7.1 Business Leaders in the Car Industry 7.2 Public Policies and Nuclear Power 7.3 Managing Technological Risks Appendix A. Statistical Profiles of Engineers Appendix B. U.S. Research and Development Notes Index I am impressed by the scope of Engineering - An Endless Frontier, and fascinated by Sunny Auyang's comprehensive knowledge of the subject. This is just the kind of book the National Academy of Engineering has been encouraging to promote the importance of engineering to the public. It will have a long shelf-life in that it pulls together material that is not readily accessible, and will serve as a reference for anyone interested in engineering as a profession. Engineering needs this book! --John Hutchinson, Harvard University Engineering - An Endless Frontier is extraordinary in scope. Sunny Auyang describes the different kinds of contemporary engineering practices and productions, attempts to provide historical background, explains the scientific basis for engineering innovation in different fields, and addresses the broad, systems level managerial, entrepreneurial, and design activities of professionals. It's rare to find a single author who can grasp and explain the essential features of modern technologies across such an array of industrial sectors and engineering disciplines and explain how they work, why they work they way they do, and what is required for their innovation, development and, yes, even maintenance. --Louis L. Bucciarelli, Professor Emeritus of Engineering and Technology Studies, MIT


Extremum Problems for Eigenvalues of Elliptic Operators

Extremum Problems for Eigenvalues of Elliptic Operators

Author: Antoine Henrot

Publisher: Springer Science & Business Media

Published: 2006-08-29

Total Pages: 205

ISBN-13: 3764377062

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This book focuses on extremal problems. For instance, it seeks a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. Also considered is the case of functions of eigenvalues. The text probes similar questions for other elliptic operators, such as Schrodinger, and explores optimal composites and optimal insulation problems in terms of eigenvalues.


Frontiers in Fractional Calculus

Frontiers in Fractional Calculus

Author: Sachin Bhalekar

Publisher: Bentham Science Publishers

Published: 2018-03-21

Total Pages: 381

ISBN-13: 1681085992

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This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.


Nonlinear Dispersive Waves and Fluids

Nonlinear Dispersive Waves and Fluids

Author: Avy Soffer

Publisher: American Mathematical Soc.

Published: 2019-03-12

Total Pages: 290

ISBN-13: 1470441098

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This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics. The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.


Hamiltonian Reduction by Stages

Hamiltonian Reduction by Stages

Author: Jerrold E. Marsden

Publisher: Springer

Published: 2007-06-05

Total Pages: 527

ISBN-13: 3540724702

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This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.