Mathematical mechanics : from particle to muscle /
Saved in:
Author / Creator: | Cooper, Ellis D. |
---|---|
Imprint: | Singapore ; Hackensack, NJ : World Scientific, ©2011. |
Description: | 1 online resource (xv, 373 pages) : illustrations (some color). |
Language: | English |
Series: | World Scientific series on nonlinear science. Series A ; v. 77 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 77. |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11279004 |
Table of Contents:
- 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.