Mathematical mechanics : from particle to muscle /

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 math...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cooper, Ellis D.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, NJ : World Scientific, ©2011.
Colección:World Scientific series on nonlinear science. Monographs and treatises ; v. 77.
Temas:
Mechanics, Analytic.
Particle dynamics > Mathematical models.
Muscle contraction > Mathematical models.
Mathematical physics.
Mécanique analytique.
Dynamique d'une particule > Modèles mathématiques.
Muscles > Contraction > Modèles mathématiques.
Physique mathématique.
SCIENCE > Mechanics > General.
SCIENCE > Mechanics > Solids.
Mathematical physics
Mechanics, Analytic
Muscle contraction > Mathematical models
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction. 1.1. Why would I have valued this book in high school? 1.2. Who else would value this book? 1.3. Physics & biology. 1.4. Motivation. 1.5. The principle of least thought. 1.6. Measurement. 1.7. Conceptual blending. 1.8. Mental model of muscle contraction. 1.9. Organization. 1.10. What is missing? 1.11. What is original?
  • 2. Ground & foundation of mathematics. 2.1. Introduction. 2.2. Ground : Discourse & surface. 2.3. Foundation : Category & functor. 2.4. Examples of categories & functors. 2.5. Constructions
  • 3. Calculus as an algebra of infinitesimals. 3.1. Real & hyperreal. 3.2. Variable. 3.3. Right, left & two-sided limit. 3.4. Continuity. 3.5. Differentiable, derivative & differential. 3.6. Curve sketching reminder. 3.7. Integrability. 3.8. Algebraic rules for calculus. 3.9. Three Gaussian integrals. 3.10. Three differential equations. 3.11. Legendre transform. 3.12. Lagrange multiplier
  • 4. Algebra of vectors. 4.1. Introduction. 4.2. When is an array a matrix? 4.3. List algebra. 4.4. Table algebra. 4.5. Vector algebra
  • 5. Particle universe. 5.1. Conservation of energy & Newton's second law. 5.2. Lagrange's equations & Newton's second law. 5.3. The invariance of Lagrange's equations. 5.4. Hamilton's principle. 5.5. Hamilton's equations. 5.6. A theorem of George Stokes. 5.7. A theorem on a series of impulsive forces. 5.8. Langevin's trick. 5.9. An argument due to Albert Einstein. 5.10. An argument due to Paul Langevin
  • 6. Introduction to timing machinery. 6.1. Blending time & state machine. 6.2. The basic oscillator. 6.3. Timing machine variable. 6.4. The robust low-pass filter. 6.5. Frequency multiplier & differential equation. 6.6. Probabilistic timing machine. 6.7. Chemical reaction system simulation. 6.8. Computer simulation
  • 7. Stochastic timing machinery. 7.1. Introduction. 7.2. Examples. 7.3. Zero-order chemical reaction
  • 8. Algebraic thermodynamics. 8.1. Introduction. 8.2. Chemical element, compound & mixture. 8.3. Universe. 8.4. Reservoir & capacity. 8.5. Equilibrium & equipotentiality. 8.6. Entropy & energy. 8.7. Fundamental equation. 8.8. Conduction & resistance
  • 9. Clausius, Gibbs & Duhem. 9.1. Clausius inequality. 9.2. Gibbs-Duhem equation
  • 10. Experiments & measurements. 10.1. Experiments. 10.2. Measurements
  • 11. Chemical reaction. 11.1. Chemical reaction extent, completion & realization. 11.2. Chemical equilibrium. 11.3. Chemical formations & transformations. 11.4. Monoidal category & monoidal functor. 11.5. Hess' monoidal functor
  • 12. Muscle contraction. 12.1. Muscle contraction : chronology. 12.2. Conclusion.

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