Differential equations: a modeling approach, Ledder
Автор: Strang Название: Differential Equations and Linear Algebra ISBN: 0980232791 ISBN-13(EAN): 9780980232790 Издательство: Cambridge Academ Рейтинг: Цена: 5203 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Описание: The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a ``random noise,'' also known as a ``generalized random field.'' At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals a la Norbert Wiener, an infinite-dimensional Ito-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts.There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation.
Описание: This monograph presents the latest advances of fuzzy logic and soft computing in reservoir characterization and modeling. It proposes for the first time that future develoments require perception-based information processing. The book presents important steps in this direction by introducing fuzzy partial differential equations and relational equations. It provides a unique opportunity for soft computing researchers and oil industry practitioners to understand the significance of the changes in the fields by presenting recent accomplishments and new directions.
Описание: Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained. Modeling with ItГґ Stochastic Differential Equations is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming.
Описание: This book provides a unified view of numerical analysis, mathematical modeling in applications, and programming, which is known as scientific computing or computational science. The integrated science of solving a problem with mathematical, numerical, and programming tools makes this book quite unique among related books since it covers a wide array of topics from mathematical modeling to implementing a working computer program. The book describes: how models are set up; how they are preprocessed mathematically with scaling, classification, and approximation; and how a problem is solved numerically with suitable numerical methods. All results are shown appropriately with visualization. The examples in the book are taken from scientific and engineering applications, such as mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic filed theory, control theory, etc. The numerical methods are demonstrated on simple model problems and programmed in MATLAB. The author also highlights the ideas behind some well-known methods, such as finite differences and finite elements. Both MATLAB and the interactive scientific computing program Comsol Multiphysics are used to solve real-world problems found throughout the book.
Описание: A First Course in Differential Equations, Modeling, and Simulation shows how differential equations arise from applying basic physical principles and experimental observations to engineering systems. Avoiding overly theoretical explanations, the textbook also discusses classical and Laplace transform methods for obtaining the analytical solution of differential equations. In addition, the authors explain how to solve sets of differential equations where analytical solutions cannot easily be obtained. Incorporating valuable suggestions from mathematicians and mathematics professors, the Second Edition: Expands the chapter on classical solutions of ordinary linear differential equations to include additional methods Increases coverage of response of first- and second-order systems to a full, stand-alone chapter to emphasize its importance Includes new examples of applications related to chemical reactions, environmental engineering, biomedical engineering, and biotechnology Contains new exercises that can be used as projects and answers to many of the end-of-chapter problems Features new end-of-chapter problems and updates throughout Thus, A First Course in Differential Equations, Modeling, and Simulation, Second Edition provides students with a practical understanding of how to apply differential equations in modern engineering and science.
Описание: Variational Methods Are Very Powerful Techniques In Nonlinear Analysis And Are Extensively Used In Many Disciplines Of Pure And Applied Mathematics (Including Ordinary And Partial Differential Equations, Mathematical Physics, Gauge Theory, And Geometrical Analysis).In Our First Chapter, We Gather The Basic Notions And Fundamental Theorems That Will Be Applied Throughout The Chapters. While Many Of These Items Are Easily Available In The Literature, We Gather Them Here Both For The Convenience Of The Reader And For The Purpose Of Making This Volume Somewhat Self-Contained. Subsequent Chapters Deal With How Variational Methods Can Be Used In Fourth-Order Problems, Kirchhoff Problems, Nonlinear Field Problems, Gradient Systems, And Variable Exponent Problems. A Very Extensive Bibliography Is Also Included.
Описание: Helps you work more effectively and gauge your progress along the way. This student resource manual contains worked-out solutions to approximately half of the problems in "Differential Equations, 2nd Edition". Including problem solutions, it offers graphs, suggestions for students, and additional resource material.
Описание: Designed to meet the challenges of understanding and solving interdisciplinary problems, this book presents many learning tools like step-by-step procedures (critical thinking), the concept of `math` being a language, applied examples from diverse fields, frequent recaps, flowcharts and exercises.
Описание: Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. Beyond the usual model problems, the presentation includes a number of realistic applications that illustrate the power and usefulness of the ideas behind these techniques. This complete, self-contained book includes numerous exercises and error estimates, as well as a rigorous approximation and computational tool.
Описание: This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
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