Continuum Mechanics : The Birthplace of Mathematical Models.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.