Mathematical Mechanics: From Particle to Muscle (World Scientific Nonlinear Science Series a)

This unprecedented book offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of latest mathematical technologies -- Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory -- to explicate Particle Mechanics, The Theory of Substances (categorical thermodynamics), and computer simulation using a diagram-based parallel programming language (stochastic timing machinery). Proofs rely almost entirely on algebraic calculations without set theory. Metaphors and analogies, and distinctions between representational pictures, mental model drawings, and mathematical diagrams are offered. AP level high school calculus students, high school science teachers, undergraduates and graduate college students, and researchers in mathematics, physics, chemistry, and biology may use this integrated publication to broaden their perspective on science, and to experience the precision that mathematical mechanics brings to understanding the molecular mechanism vital for nearly all animal behavior Cover 1 Front_Matter 2 Copyright 5 Contents 8 Acknowledgments 16 Chapter 1 Introduction 17 PART 2 Mathematics 35 Chapter 2 Ground & Foundation of Mathematics 36 Chapter 3 Calculus as an Algebra of Infinitesimals 88 Chapter 4 Algebra of Vectors 123 9789814289719_others02 157 PART 3 Particle Mechanics 157 Chapter 5 Particle Universe 158 PART 4 Timing Machinery 183 Chapter 6 Introduction to Timing Machinery 184 Chapter 7 Stochastic Timing Machinery 195 PART 5 Theory of Substances 210 Chapter 8 Algebraic Thermodynamics 211 Chapter 9 Clausius, Gibbs & Duhem 247 Chapter 10 Experiments & Measurements 253 Chapter 11 Chemical Reaction 281 PART 6 Muscle Contraction ResearchThis 297 Chapter 12 Muscle Contraction 298 9789814289719_bmatter 331 Appendix A Exponential & Logarithm Functions 331 Appendix B Recursive Definition of Stochastic Timing Machinery 333 Appendix C MATLAB Code 337 Appendix D Fundamental Theorem of Elastic Bodies 349 Bibliography 355 Index 365 Offers the details of the mathematical mechanics for the modeling of skeletal muscle contraction. This work examines a succession of distinguishable universes of particles, and continuous, thermodynamic, chemical, and molecular bodies, with a focus on proofs by algebraic calculation without set theory. This title offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding