Continuum Mechanics Using Mathematica(r): Fundamentals, Methods, and Applications

ISBN-13: 9781493916030 / Angielski / Twarda / 2014 / 480 str.

Antonio Romano; Addolorata Marasco

Opis

This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica(R) provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhauser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica(R) Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

Recenzje

"[The authors] bring a fresh quality to this subject. Their book of 11 chapters rigorously and clearly introduces various attributes often lacking in other books. Starting with basic linear algebra, the book migrates smoothly to curvilinear coordinates. There, the authors analyze different coordinates and introduce singular surfaces important in porous media analysis. From that point onward the authors present balance and constitutive equations common to other classical books. However, this book resourcefully goes a step further by applying Mathematica in order to clarify key concepts; this attractive feature is one of the book's strengths. In each Mathematica case, the authors define the aim of the program, description of the problem, and relative algorithm. All chapters are well written, particularly the last four on wave propagation, linear elasticity, and other topics including shock waves, Rayleigh waves, and SH waves. Given this book's elucidative and concise approach, the scientific community should look forward to reading the second volume, to treat mixtures, phase change, magnetoelastic bodies, and other important topics. Summing Up: Highly recommended. Graduate students through professionals."

-Choice (Review of the first edition)

"The book will be an invaluable reference for all those with active interest in the areas of continuum mechanics and its fundamental applications: balance laws, constitutive axioms, linear elasticity, fluid dynamics, waves, etc. It may serve as a supplement to any of the standard textbooks for undergraduate students, graduate students, and researchers in applied mathematics, mathematical physics, and engineering."

-Zentralblatt MATH (Review of the first edition)

Spis treści

1 Elements of Linear Algebra.- 2 Vector Analysis.- 3 Finite and Infinitesimal Deformations.- 4 Kinematics.- 5 Balance Equations.- 6 Constitutive Equations.- 7 Symmetry Groups: Solids and Fluids.- 8 Wave Propagation.- 9 Fluid Mechanics.- 10 Linear Elasticity.- 11 Other Approaches to Thermodynamics.- 12 Fluid Dynamics and Meteorology.- 13 Fluid Dynamics and Navigation.- A Brief Introduction to Weak Solutions.- References.- Index.

O autorze

Antonio Romano has been the author or co-author of numerous books on mechanics and Mathematica and he has taught courses in mechanics for 35 years at "Il Fredrico" University in Naples. Addolorata Marasco is a Professor of Mathematics at the University of Naples Federico II, Italy. She received her PhD in 2003 in Applied Mathematics and Informatics.

Blurb

This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica^® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5).

Key topics and features:
* Concise presentation strikes a balance between fundamentals and applications
* Requisite mathematical background carefully collected in two introductory chapters and one appendix
* Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity.

This second edition expands the key topics and features to include:

* Two new applications of fluid dynamics: meteorology and navigation

* New exercises at the end of the existing chapters

* The packages are rewritten for Mathematica 9

Continuum Mechanics using Mathematica^®: Fundamentals, Methods, and Applications is aimed at advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.