| 1. |
- Gerlee, Philip, 1980, et al.
(författare)
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Scientific Models : Red Atoms, White Lies and Black Boxes in a Yellow Book
- 2016
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 2. |
- Gerlee, Philip, 1980, et al.
(författare)
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Scientific Models
- 2016
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 5. |
- Rosén, Andreas, 1974
(författare)
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Geometric multivector analysis
- 2019
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.
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| 6. |
- Jansson, Patrik, 1972, et al.
(författare)
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Domain-Specific Languages of Mathematics
- 2022
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- The main idea behind this book is to encourage readers to approach mathematical domains from a functional programming perspective: to identify the main functions and types involved and, when necessary, to introduce new abstractions; to give calculational proofs; to pay attention to the syntax of the mathematical expressions; and, finally, to organize the resulting functions and types in domain-specific languages. The book is recommended for developers who are learning mathematics and would like to use Haskell to make sense of definitions and theorems. It is also a book for the mathematically interested who wants to explore functional programming and domain-specific languages. The book helps put into perspective the domains of Mathematics and Functional Programming and shows how Computer Science and Mathematics are usefully taught together.
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| 7. |
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| 8. |
- Ibragimov, Nail H., et al.
(författare)
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Approximate and renormgroup symmetries
- 2009
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Approximate and Renormgroup Symmetries deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self contained introduction to basic concepts and methods of Lie group analysis, and provides an easy to follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics --mathematicians and nonmathematicians--interested in methods of applied group analysis for investigating nonlinear problems in physical, engineering and natural sciences.
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| 9. |
- Ibragimov, Nail H., et al.
(författare)
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Approximate groups and renormgroup symmetries
- 2008
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- The book deals with so-called renormalization group symmetries considered in the framework of approximate transformation groups. Renormgroup symmetries provide a basis for the renormgroup algorithm for improving solutions to boundary value problems by converting "less applicable solutions" into "more applicable solutions". the algorithm is particularly useful for improving approximate solutions given by the perturbation theory.
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| 10. |
- Ibragimov, Nail H.
(författare)
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Approximate transformation groups
- 2008
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- These notes provide an easy to follow introduction to the topic and are based on my talks at various conferences, in particular on the plenary lecture at the International Workshop on ``Differential equations and chaos" (University of Witwatersrand, Johannesburg, South Africa, January 1996). The book is prepared for the new graduate course ``Approximate transformation groups" that will be given at Blekinge Institute of Technology during January-March, 2009.
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