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A Compendium of Partial Differential Equation Models

2009-03-16 Computers
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Release : 2009-03-16
Genre : Computers
Kind : eBook
Book Rating : 861/5 ( reviews)

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Book Synopsis A Compendium of Partial Differential Equation Models by : William E. Schiesser

Download or read book A Compendium of Partial Differential Equation Models written by William E. Schiesser. This book was released on 2009-03-16. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

A Compendium of Partial Differential Equation Models

2009-03-16 Mathematics
Download A Compendium of Partial Differential Equation Models PDF Online Free

Author :
Release : 2009-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 854/5 ( reviews)

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Book Synopsis A Compendium of Partial Differential Equation Models by : William E. Schiesser

Download or read book A Compendium of Partial Differential Equation Models written by William E. Schiesser. This book was released on 2009-03-16. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.

Partial Differential Equations

2014-08-21 Mathematics
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Release : 2014-08-21
Genre : Mathematics
Kind : eBook
Book Rating : 434/5 ( reviews)

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Book Synopsis Partial Differential Equations by : Thomas Hillen

Download or read book Partial Differential Equations written by Thomas Hillen. This book was released on 2014-08-21. Available in PDF, EPUB and Kindle. Book excerpt: Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

Partial Differential Equations in Action

2022-12-08 Mathematics
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Release : 2022-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 531/5 ( reviews)

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Book Synopsis Partial Differential Equations in Action by : Sandro Salsa

Download or read book Partial Differential Equations in Action written by Sandro Salsa. This book was released on 2022-12-08. Available in PDF, EPUB and Kindle. Book excerpt: This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.

Partial Differential Equations: Modeling, Analysis and Numerical Approximation

2016-02-11 Mathematics
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Release : 2016-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 672/5 ( reviews)

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Book Synopsis Partial Differential Equations: Modeling, Analysis and Numerical Approximation by : Hervé Le Dret

Download or read book Partial Differential Equations: Modeling, Analysis and Numerical Approximation written by Hervé Le Dret. This book was released on 2016-02-11. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

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