Modelling Mathematical Methods and Scientific Computation

Modelling Mathematical Methods and Scientific Computation PDF Author: Nicola Bellomo
Publisher: CRC Press
ISBN: 9780849383311
Category : Mathematics
Languages : en
Pages : 516

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Book Description
Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

Modelling Mathematical Methods and Scientific Computation

Modelling Mathematical Methods and Scientific Computation PDF Author: Nicola Bellomo
Publisher: CRC Press
ISBN: 9780849383311
Category : Mathematics
Languages : en
Pages : 516

Get Book Here

Book Description
Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

Data-Driven Modeling & Scientific Computation

Data-Driven Modeling & Scientific Computation PDF 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.

Computational Mathematical Modeling

Computational Mathematical Modeling PDF Author: Daniela Calvetti
Publisher: SIAM
ISBN: 1611972477
Category : Mathematics
Languages : en
Pages : 229

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Book Description
Interesting real-world mathematical modelling problems are complex and can usually be studied at different scales. The scale at which the investigation is carried out is one of the factors that determines the type of mathematics most appropriate to describe the problem. The book concentrates on two modelling paradigms: the macroscopic, in which phenomena are described in terms of time evolution via ordinary differential equations; and the microscopic, which requires knowledge of random events and probability. The exposition is based on this unorthodox combination of deterministic and probabilistic methodologies, and emphasizes the development of computational skills to construct predictive models. To elucidate the concepts, a wealth of examples, self-study problems, and portions of MATLAB code used by the authors are included. This book, which has been extensively tested by the authors for classroom use, is intended for students in mathematics and the physical sciences at the advanced undergraduate level and above.

Mathematical Modelling and Scientific Computing with Applications

Mathematical Modelling and Scientific Computing with Applications PDF Author: Santanu Manna
Publisher: Springer Nature
ISBN: 9811513384
Category : Mathematics
Languages : en
Pages : 467

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Book Description
This book contains original research papers presented at the International Conference on Mathematical Modelling and Scientific Computing, held at the Indian Institute of Technology Indore, India, on 19–21 July 2018. Organized into 30 chapters, the book presents the recent progress and the most advanced innovations, trends, and real-world challenges encountered and solutions embraced in the applications of mathematics and scientific computing. The book will be of interests to a wide variety of researchers, students and the practicing engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics, vibration problem, computer science, and numerical optimization to physics, chemistry, biology, electrical, civil, mechanical, chemical, seismology, aerospace, and medical sciences. The aim of the conference is to bring together leading academicians, scientists, researchers, engineers, and industry partners from all over the globe to exchange and share their experiences and research results on various aspects of applied mathematics and scientific computation, like, differential equation, modeling, simulation, dynamical systems, numerical analysis, matrix theory, inverse problems, and solid and fluid mechanics, computational engineering.

Large Scale Scientific Computing

Large Scale Scientific Computing PDF Author: Deuflhard
Publisher: Springer Science & Business Media
ISBN: 1468467549
Category : Mathematics
Languages : en
Pages : 390

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Book Description
In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.

Scientific Computing with Case Studies

Scientific Computing with Case Studies PDF 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.

Numerical Computing with MATLAB

Numerical Computing with MATLAB PDF Author: Cleve B. Moler
Publisher: SIAM
ISBN: 0898716608
Category : Computers
Languages : en
Pages : 340

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Book Description
A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

Scientific Computing with Case Studies

Scientific Computing with Case Studies PDF Author: Dianne P. O'Leary
Publisher: SIAM
ISBN: 0898717728
Category : Mathematics
Languages : en
Pages : 377

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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.

Fundamentals of Scientific Computing

Fundamentals of Scientific Computing PDF Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3642194958
Category : Mathematics
Languages : en
Pages : 317

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Book Description
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Numerical Analysis and Optimization

Numerical Analysis and Optimization PDF Author: Grégoire Allaire
Publisher: OUP Oxford
ISBN: 0191525529
Category : Mathematics
Languages : en
Pages : 472

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Book Description
This text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences.