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Theoretical and Numerical aspects for incompressible fluids
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View Preview. Learn more Check out. Other disciplines such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions.
As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. The corresponding spread of numerical software represents an enrichment for the scientific community.
However, the user has to make the correct choice of the method or the algorithm which best suits the problem at hand. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties stability, accuracy, computational complexity , and demonstrate their performances on examples and counterexamples which outline their pros and cons. This choice satisfies the two fundamental needs of user-friendliness and wide-spread diffusion, making it available on virtually every computer.
Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. VI Preface make the right choice among the numerical methodologies and make use of the related computer programs. This book is primarily addressed to undergraduate students, with particular focus on the degree courses in Engineering, Mathematics, Physics and Computer Science. The attention which is paid to the applications and the related development of software makes it valuable also for graduate students, researchers and users of scientific computing in the most widespread professional fields.
The content of the volume is organized into four Parts and 13 chapters. Part I comprises two chapters in which we review basic linear algebra and introduce the general concepts of consistency, stability and convergence of a numerical method as well as the basic elements of computer arithmetic. Part II is on numerical linear algebra, and is devoted to the solution of linear systems Chapters 3 and 4 and eigenvalues and eigenvectors computation Chapter 5.
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We continue with Part III where we face several issues about functions and their approximation. Specifically, we are interested in the solution of nonlinear equations Chapter 6 , solution of nonlinear systems and optimization problems Chapter 7 , polynomial approximation Chapter 8 and numerical integration Chapter 9. Part IV, which demands a mathematical background, is concerned with approximation, integration and transforms based on orthogonal polynomials Chapter 10 , solution of initial value problems Chapter 11 , boundary value problems Chapter 12 and initial-boundary value problems for parabolic and hyperbolic equations Chapter Part I provides the indispensable background.
Each of the remaining Parts has a size and a content that make it well suited for a semester course. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering.
But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. Skip to main content Skip to table of contents.
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