Continuum Mechanics : The Birthplace of Mathematical Models

• Autore: Allen Myron B
• Pubblicazione: Hoboken : , : John Wiley & Sons, Incorporated, , 2015; ©2016
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (356 pages)
• Disciplina: 531.076
• Soggetto topico: Continuum mechanics -- Textbooks; Continuum mechanics; Mathematics
• Soggetto genere / forma: Electronic books.
• Altri autori: AllenMyron B., III
• Nota di contenuto: Intro -- TITLE PAGE -- COPYRIGHT -- TABLE OF CONTENTS -- DEDICATION -- PREFACE -- CHAPTER 1: GEOMETRIC SETTING -- 1.1 VECTORS AND EUCLIDEAN POINT SPACE -- 1.2 TENSORS -- CHAPTER 2: KINEMATICS I: THE CALCULUS OF MOTION -- 2.1 BODIES, MOTIONS, AND DEFORMATIONS -- 2.2 DERIVATIVES OF MOTION -- 2.3 PATHLINES, STREAMLINES, AND STREAKLINES -- 2.4 INTEGRALS UNDER MOTION -- CHAPTER 3: KINEMATICS II: STRAIN AND ITS RATES -- 3.1 STRAIN -- 3.2 INFINITESIMAL STRAIN -- 3.3 STRAIN RATES -- 3.4 VORTICITY AND CIRCULATION -- 3.5 OBSERVER TRANSFORMATIONS -- CHAPTER 4: BALANCE LAWS -- 4.1 MASS BALANCE -- 4.2 MOMENTUM BALANCE -- 4.3 ANGULAR MOMENTUM BALANCE -- 4.4 ENERGY BALANCE -- 4.5 ENTROPY INEQUALITY -- 4.6 JUMP CONDITIONS -- CHAPTER 5: CONSTITUTIVE RELATIONS: EXAMPLES OF MATHEMATICAL MODELS -- 5.1 HEAT TRANSFER -- 5.2 POTENTIAL THEORY -- 5.3 FLUID MECHANICS -- 5.4 SOLID MECHANICS -- CHAPTER 6: CONSTITUTIVE THEORY -- 6.1 CONCEPTUAL SETTING -- 6.2 DETERMINISM AND EQUIPRESENCE -- 6.3 OBJECTIVITY -- 6.4 SYMMETRY -- 6.5 ADMISSIBILITY -- CHAPTER 7: MULTICONSTITUENT CONTINUA -- 7.1 CONSTITUENTS -- 7.2 MULTICONSTITUENT BALANCE LAWS -- 7.3 FLUID FLOW IN A POROUS SOLID -- 7.4 DIFFUSION IN A BINARY FLUID MIXTURE -- APPENDIX A: GUIDE TO NOTATION -- A.1 GENERAL CONVENTIONS -- A.2 LETTERS RESERVED FOR DEDICATED USES -- A.3 SPECIAL SYMBOLS -- APPENDIX B: VECTOR INTEGRAL THEOREMS -- B.1 STOKES'S THEOREM -- B.2 THE DIVERGENCE THEOREM -- B.3 THE CHANGEOFVARIABLES THEOREM -- APPENDIX C: HINTS AND SOLUTIONS TO EXERCISES -- CHAPTER 1 -- CHAPTER 2 -- CHAPTER 3 -- CHAPTER 4 -- CHAPTER 5 -- CHAPTER 6 -- CHAPTER 7 -- APPENDIX B -- REFERENCES -- INDEX -- End User License Agreement.
• Sommario/riassunto: Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an; excellent reference for professional mathematicians, physical scientists, and engineers.
• Titolo autorizzato: Continuum Mechanics
• ISBN: 9781118909348; 9781118909379
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910795807003321
• Lo trovi qui: Univ. Federico II