Continuum Mechanics using Mathematica® Fundamentals, Applications and Scientific Computing - Romano, Antonio; Lancellotta, Renato; Marasco, Addolorata; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2006)
This book's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. The book covers essential principles and fundamental applications, and provides a solid basis for a deeper study of more challenging and specialized problems related to elasticity, fluid mechanics, plasticity, materials with memory, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes. Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and two appendices * Recent developments highlighted through coverage of more significant applications to areas such as porous media, electromagnetic fields, and phase transitions Continuum Mechanics using Mathematica® 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 the field.
Elements of Linear Algebra -- Vector Analysis -- Finite and Infinitesimal Deformations -- Kinematics -- Balance Equations -- Constitutive Equations -- Symmetry Groups: Solids and Fluids -- Wave Propagation -- Fluid Mechanics -- Linear Elasticity -- Other Approaches to Thermodynamcis.
Keywords: Mechanics; Mechanics, Applied; Applied mathematics; Engineering mathematics; Mathematical physics; Mathematical models; Classical Mechanics; Solid Mechanics; Theoretical and Applied Mechanics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics