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Mathematical mechanics = from particle to muscle /

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	Mathematical mechanics/ Ellis D. Cooper.
其他題名:	from particle to muscle /
作者:	Cooper, Ellis D.
出版者:	Singapore ;World Scientific, : c2011.,
面頁冊數:	1 online resource (xv, 373 p.) :ill. (some col.). :
標題:	Mechanics, Analytic. -
電子資源:	http://www.worldscientific.com/worldscibooks/10.1142/7520#t=toc

Mathematical mechanics = from particle to muscle /
Cooper, Ellis D.

Mathematical mechanicsfrom particle to muscle /[electronic resource] :Ellis D. Cooper. - Singapore ;World Scientific,c2011. - 1 online resource (xv, 373 p.) :ill. (some col.). - World Scientific series on nonlinear science. Series A ;v. 77. - World Scientific series on nonlinear science.Series A,Monographs and treatises ;vol. 81..

Includes bibliographical references (p. 353-362) and index

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.

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.Subjects--Topical Terms:

134546
Mechanics, Analytic.
Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA805 / .C66 2011eb

Dewey Class. No.: 531.01/515

Mathematical mechanics = from particle to muscle /
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245 1 0 $a Mathematical mechanics $h [electronic resource] : $b from particle to muscle / $c Ellis D. Cooper.
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490 1 $a World Scientific series on nonlinear science. Series A ; $v v. 77
504 $a Includes bibliographical references (p. 353-362) and index
505 0 $a 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.
520 $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.
588 $a Description based on print version record.
650 0 $a Mechanics, Analytic. $3 134546
650 0 $a Dynamics of a particle $x Mathematical models. $3 247319
650 0 $a Muscle contraction $x Mathematical models. $3 247320
650 0 $a Mathematical physics. $3 121500
655 0 $a Electronic books. $2 local. $3 96803
830 0 $a World Scientific series on nonlinear science. $n Series A, $p Monographs and treatises ; $v vol. 81. $3 247061
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/7520#t=toc