Mathematical mechanics: from particle to muscle
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2011
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 77 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (xv, 373 p.) |
| ISBN: | 9789814289702 9789814289719 9814289701 981428971X |
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| 490 | 0 | |a World Scientific series on nonlinear science |v v. 77 | |
| 500 | |a Includes bibliographical references (p. 353-362) and index | ||
| 500 | |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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 | ||
| 500 | |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 | ||
| 650 | 7 | |a SCIENCE / Mechanics / General |2 bisacsh | |
| 650 | 7 | |a SCIENCE / Mechanics / Solids |2 bisacsh | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Mechanics, Analytic | |
| 650 | 4 | |a Dynamics of a particle |x Mathematical models | |
| 650 | 4 | |a Muscle contraction |x Mathematical models | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Biophysik |0 (DE-588)4006891-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Muskelkontraktion |0 (DE-588)4170858-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Muskelkontraktion |0 (DE-588)4170858-1 |D s |
| 689 | 0 | 1 | |a Biophysik |0 (DE-588)4006891-2 |D s |
| 689 | 0 | 2 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804175466431512576 |
|---|---|
| any_adam_object | |
| author | Cooper, Ellis D. |
| author_facet | Cooper, Ellis D. |
| author_role | aut |
| author_sort | Cooper, Ellis D. |
| author_variant | e d c ed edc |
| building | Verbundindex |
| bvnumber | BV043077518 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)756782686 (DE-599)BVBBV043077518 |
| dewey-full | 531.01/515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.01/515 |
| dewey-search | 531.01/515 |
| dewey-sort | 3531.01 3515 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043077518 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:44Z |
| institution | BVB |
| isbn | 9789814289702 9789814289719 9814289701 981428971X |
| language | English |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xv, 373 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| series2 | World Scientific series on nonlinear science |
| spelling | Cooper, Ellis D. Verfasser aut Mathematical mechanics from particle to muscle Ellis D. Cooper Singapore World Scientific c2011 1 Online-Ressource (xv, 373 p.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 77 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 SCIENCE / Mechanics / General bisacsh SCIENCE / Mechanics / Solids bisacsh Mathematische Physik Mathematisches Modell Mechanics, Analytic Dynamics of a particle Mathematical models Muscle contraction Mathematical models Mathematical physics Biophysik (DE-588)4006891-2 gnd rswk-swf Muskelkontraktion (DE-588)4170858-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Muskelkontraktion (DE-588)4170858-1 s Biophysik (DE-588)4006891-2 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389650 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cooper, Ellis D. Mathematical mechanics from particle to muscle SCIENCE / Mechanics / General bisacsh SCIENCE / Mechanics / Solids bisacsh Mathematische Physik Mathematisches Modell Mechanics, Analytic Dynamics of a particle Mathematical models Muscle contraction Mathematical models Mathematical physics Biophysik (DE-588)4006891-2 gnd Muskelkontraktion (DE-588)4170858-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4006891-2 (DE-588)4170858-1 (DE-588)4037952-8 |
| title | Mathematical mechanics from particle to muscle |
| title_auth | Mathematical mechanics from particle to muscle |
| title_exact_search | Mathematical mechanics from particle to muscle |
| title_full | Mathematical mechanics from particle to muscle Ellis D. Cooper |
| title_fullStr | Mathematical mechanics from particle to muscle Ellis D. Cooper |
| title_full_unstemmed | Mathematical mechanics from particle to muscle Ellis D. Cooper |
| title_short | Mathematical mechanics |
| title_sort | mathematical mechanics from particle to muscle |
| title_sub | from particle to muscle |
| topic | SCIENCE / Mechanics / General bisacsh SCIENCE / Mechanics / Solids bisacsh Mathematische Physik Mathematisches Modell Mechanics, Analytic Dynamics of a particle Mathematical models Muscle contraction Mathematical models Mathematical physics Biophysik (DE-588)4006891-2 gnd Muskelkontraktion (DE-588)4170858-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | SCIENCE / Mechanics / General SCIENCE / Mechanics / Solids Mathematische Physik Mathematisches Modell Mechanics, Analytic Dynamics of a particle Mathematical models Muscle contraction Mathematical models Mathematical physics Biophysik Muskelkontraktion |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389650 |
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