Surveys and Tutorials in the Applied Mathematical Sciences – serie
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18 produkter
18 produkter
Del 4 - Surveys and Tutorials in the Applied Mathematical Sciences
Multiscale Finite Element Methods
Theory and Applications
Häftad, Engelska, 2009
540 kr
Skickas inom 10-15 vardagar
The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.
Häftad, Engelska, 2007
556 kr
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The book of nature, according to Galilei, is written in the language of mat- matics. The nature of mathematics is being exact, and its exactness is und- lined by the formalism used by mathematicians to write it. This formalism, characterized by theorems and proofs, and syncopated with occasional l- mas, remarks and corollaries, is so deeply ingrained that mathematicians feel uncomfortable when the pattern is broken, to the point of giving the - pression that the attitude of mathematicians towards the way mathematics should be written is almost moralistic. There is a de?nition often quoted, “A mathematician is a person who proves theorems”, and a similar, more alchemistic one, credited to Paul Erd? os, but more likely going back to Alfr´ ed R´ enyi,statingthat“Amathematicianisamachinethattransformsco?eeinto 1 theorems ”. Therefore it seems to be the form, not the content, that char- terizes mathematics, similarly to what happens in any formal moralistic code wherein form takes precedence over content. This book is deliberately written in a very di?erent manner, without a single theorem or proof. Since morality has its subjective component, to pa- phrase Manuel Vasquez Montalban, we could call it Ten Immoral Mathemat- 2 ical Recipes . Does the lack of theorems and proofs mean that the book is more inaccurate than traditional books of mathematics? Or is it possibly just a sign of lack of co?ee? This is our ?rst open question. Exactness is an interesting concept.
Häftad, Engelska, 2009
700 kr
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Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.
Del 5 - Surveys and Tutorials in the Applied Mathematical Sciences
Introduction to Fronts in Random Media
Häftad, Engelska, 2009
433 kr
Skickas inom 10-15 vardagar
This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.
Del 7 - Surveys and Tutorials in the Applied Mathematical Sciences
Modeling Information Diffusion in Online Social Networks with Partial Differential Equations
Häftad, Engelska, 2020
700 kr
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The book lies at the interface of mathematics, social media analysis, and data science. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.
Del 8 - Surveys and Tutorials in the Applied Mathematical Sciences
Kernel Mode Decomposition and the Programming of Kernels
Häftad, Engelska, 2021
807 kr
Skickas inom 10-15 vardagar
This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes.
Del 9 - Surveys and Tutorials in the Applied Mathematical Sciences
Internal Waves in the Ocean
Theory and Practice
Häftad, Engelska, 2022
807 kr
Skickas inom 10-15 vardagar
In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.
Del 10 - Surveys and Tutorials in the Applied Mathematical Sciences
Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
Häftad, Engelska, 2022
320 kr
Skickas inom 5-8 vardagar
This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains.
Del 11 - Surveys and Tutorials in the Applied Mathematical Sciences
Exploring Formalisation
A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology
Häftad, Engelska, 2022
593 kr
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This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean. After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers.
Del 12 - Surveys and Tutorials in the Applied Mathematical Sciences
Toolbox of Averaging Theorems
Ordinary and Partial Differential Equations
Häftad, Engelska, 2023
913 kr
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This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems.
Del 13 - Surveys and Tutorials in the Applied Mathematical Sciences
Continuum Modeling from Thermodynamics
Application to Complex Fluids and Soft Solids
Häftad, Engelska, 2024
860 kr
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This book presents a novel comprehensive thermodynamic framework, suitable for the design of new macroscopic models, as well as the combination of existing models. Our goal is to popularize thermodynamics for model designers. The example series of models includes very classic solid and fluid models, such as Newtonian, viscoplastic and viscoelastic materials, but also new heat effects and original combinations of existing models. The aim of the new proposed framework is to allow a clear and easy development of constitutive equations that automatically satisfy the second principle. Instead of writing directly constitutive relations, model designers are encouraged to first specify the energy. This book is primarily intended for graduate students and researchers in applied mathematics, engineering sciences, computational mechanics and physics. The reader is assumed to be familiar with classical mechanics, together with matrix and tensors algebra.
Del 14 - Surveys and Tutorials in the Applied Mathematical Sciences
Boundary Element Method for Magnetohydrodynamic Flow
2D MHD Duct Flow Problems
Häftad, Engelska, 2024
913 kr
Skickas inom 10-15 vardagar
The book secondly includes the dual reciprocity boundary element technique (DRBEM), an alternative form of BEM that expands the applicability of BEM to MHD flow and heat transfer problems as well as buoyancy MHD flow with magnetic potential and inductionless MHD flow.
Del 16 - Surveys and Tutorials in the Applied Mathematical Sciences
Concise Introduction to Classical Mechanics
Häftad, Engelska, 2025
540 kr
Skickas inom 10-15 vardagar
Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.Key features include:*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.*Numerous solved problems and real-world examples to solidify understanding.*Sample midterms and final exams to help students prepare for coursework and assessments.*Every chapter includes a ‘looking forward’ section outlining modern applications of the material.The book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.
Del 17 - Surveys and Tutorials in the Applied Mathematical Sciences
Mathematical Phyllotaxis
Häftad, Engelska, 2025
538 kr
Skickas inom 5-8 vardagar
font-family: 'Arial',sans-serif;">, and modern molecular biology.
Del 15 - Surveys and Tutorials in the Applied Mathematical Sciences
Dynamics and Control of Connected Vehicles
Inbunden, Engelska, 2025
1 811 kr
Skickas inom 5-8 vardagar
Chapter 3 focuses on longitudinal control in automated vehicles, including cruise and adaptive cruise control.
Del 6 - Surveys and Tutorials in the Applied Mathematical Sciences
Topological Crystallography
With a View Towards Discrete Geometric Analysis
Häftad, Engelska, 2012
647 kr
Skickas inom 10-15 vardagar
Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal.
Häftad, Engelska, 2026
487 kr
Skickas inom 10-15 vardagar
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Del 18 - Surveys and Tutorials in the Applied Mathematical Sciences
Billiard Problem in Nonlinear Dissipative Systems
Häftad, Engelska, 2026
1 493 kr
Skickas inom 5-8 vardagar
This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on water—a well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domain’s shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motions—even in a rectangular domain—due to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill.