A Primer for a Secret Shortcut to PDEs of Mathematical Physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics PDF Author: Des McGhee
Publisher: Springer Nature
ISBN: 3030473333
Category : Mathematics
Languages : en
Pages : 191

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Book Description
​This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics PDF Author: Des McGhee
Publisher: Springer Nature
ISBN: 3030473333
Category : Mathematics
Languages : en
Pages : 191

Get Book

Book Description
​This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics PDF Author: Tyn Myint U.
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 305

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Book Description


MATHEMATICS PRIMER FOR PHYSICS STUDENTS, A.

MATHEMATICS PRIMER FOR PHYSICS STUDENTS, A. PDF Author: ANDREW E. BLECHMAN
Publisher:
ISBN: 9789813238015
Category :
Languages : en
Pages :

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Book Description


The Partial Differential Equations of Mathematical Physics

The Partial Differential Equations of Mathematical Physics PDF Author: Arthur Gordon Webster
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 540

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Book Description


Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics PDF Author: Samuel James Plimpton
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 440

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Applications of Nonlinear Partial Differential Equations in Mathematical Physics

Applications of Nonlinear Partial Differential Equations in Mathematical Physics PDF Author: American Mathematical Society
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Differential Equations For Dummies

Differential Equations For Dummies PDF Author: Steven Holzner
Publisher: John Wiley & Sons
ISBN: 0470178140
Category : Mathematics
Languages : en
Pages : 381

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Book Description
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

The Fourier Transform and Its Applications

The Fourier Transform and Its Applications PDF Author: Ronald Newbold Bracewell
Publisher:
ISBN:
Category : Fourier transformations
Languages : en
Pages :

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Simulation and Learning

Simulation and Learning PDF Author: Franco Landriscina
Publisher: Springer Science & Business Media
ISBN: 1461419549
Category : Education
Languages : en
Pages : 250

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Book Description
The main idea of this book is that to comprehend the instructional potential of simulation and to design effective simulation-based learning environments, one has to consider both what happens inside the computer and inside the students' minds. The framework adopted to do this is model-centered learning, in which simulation is seen as particularly effective when learning requires a restructuring of the individual mental models of the students, as in conceptual change. Mental models are by themeselves simulations, and thus simulation models can extend our biological capacity to carry out simulative reasoning. For this reason, recent approaches in cognitive science like embodied cognition and the extended mind hypothesis are also considered in the book.. A conceptual model called the “epistemic simulation cycle” is proposed as a blueprint for the comprehension of the cognitive activies involved in simulation-based learning and for instructional design.

Information—Consciousness—Reality

Information—Consciousness—Reality PDF Author: James B. Glattfelder
Publisher: Springer
ISBN: 3030036332
Category : Science
Languages : en
Pages : 662

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Book Description
This open access book chronicles the rise of a new scientific paradigm offering novel insights into the age-old enigmas of existence. Over 300 years ago, the human mind discovered the machine code of reality: mathematics. By utilizing abstract thought systems, humans began to decode the workings of the cosmos. From this understanding, the current scientific paradigm emerged, ultimately discovering the gift of technology. Today, however, our island of knowledge is surrounded by ever longer shores of ignorance. Science appears to have hit a dead end when confronted with the nature of reality and consciousness. In this fascinating and accessible volume, James Glattfelder explores a radical paradigm shift uncovering the ontology of reality. It is found to be information-theoretic and participatory, yielding a computational and programmable universe.