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Author: Dianne P. O'Leary
Publisher: SIAM
ISBN: 0898716667
Category : Mathematics
Languages : en
Pages : 376
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Book Description
This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
Author: Dianne P. O'Leary
Publisher: SIAM
ISBN: 0898716667
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
Author: Jose Nathan Kutz
Publisher:
ISBN: 0199660336
Category : Computers
Languages : en
Pages : 657
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Book Description
Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
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Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Author: Marco Nehmeier
Publisher: Springer
ISBN: 3319317695
Category : Computers
Languages : en
Pages : 295
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Book Description
This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.
Author: Rutherford Aris
Publisher: Courier Corporation
ISBN: 0486138895
Category : Mathematics
Languages : en
Pages : 290
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Book Description
"Engaging, elegantly written." — Applied Mathematical Modelling Mathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models. The author begins with a discussion of the term "model," followed by clearly presented examples of the different types of models (finite, statistical, stochastic, etc.). He then goes on to discuss the formulation of a model and how to manipulate it into its most responsive form. Along the way Dr. Aris develops a delightful list of useful maxims for would-be modellers. In the final chapter he deals not only with the empirical validation of models but also with the comparison of models among themselves, as well as with the extension of a model beyond its original "domain of validity." Filled with numerous examples, this book includes three appendices offering further examples treated in more detail. These concern longitudinal diffusion in a packed bed, the coated tube chromatograph with Taylor diffusion and the stirred tank reactor. Six journal articles, a useful list of references and subject and name indexes complete this indispensable, well-written guide. "A most useful, readable-and stimulating-book, to be read both for pleasure and for enlightenment." — Bulletin of the Institute of Mathematics and Its Applications
Author: Michael T. Heath
Publisher: SIAM
ISBN: 1611975573
Category : Science
Languages : en
Pages : 587
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Book Description
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
Author: Eric Lehman
Publisher:
ISBN: 9789888407064
Category : Business & Economics
Languages : en
Pages : 988
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Book Description
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Author: Faron Moller
Publisher:
ISBN:
Category :
Languages : en
Pages : 500
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Book Description
This title explores concepts of games and strategies to provide a paradigm for understanding the nature of computation and provides an elementary introduction to the mathematics and modelling of computing systems through exercises and examples, giving readers the opportunities to test their understanding and broaden their knowledge.
Author: Vladimir Mityushev
Publisher: CRC Press
ISBN: 1351998757
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.
