Mathematical mechanics: from particle to muscle
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2011
|
| Schriftenreihe: | World scientific series on nonlinear science
A ; 77 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 373 S. graph. Darst. |
| ISBN: | 9789814289702 9814289701 |
Internformat
MARC
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| 020 | |a 9814289701 |9 981-4289-70-1 | ||
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| 245 | 1 | 0 | |a Mathematical mechanics |b from particle to muscle |c by Ellis D. Cooper |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2011 | |
| 300 | |a XV, 373 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804143267382558720 |
|---|---|
| adam_text | Titel: Mathematical mechanics
Autor: Cooper, Ellis D.
Jahr: 2010
Contents
Acknowledgments xv
Introduction 1
1. Introduction 3
1.1 Why Would I Have Valued This Book in High School? . . 4
1.2 Who Else Would Value This Book?............. 5
1.3 Physics Biology...................... 6
1.4 Motivation .......................... 7
1.5 The Principle of Least Thought............... 10
1.6 Measurement......................... 11
1.7 Conceptual Blending..................... 11
1.8 Mental Model of Muscle Contraction............ 13
1.9 Organization......................... 15
1.10 What is Missing?....................... 18
1.11 What is Original?....................... 19
Mathematics 21
2. Ground Foundation of Mathematics 23
2.1 Introduction.......................... 23
2.2 Ground: Discourse Surface................ 26
2.2.1 Symbol Expression................ 27
2.2.2 Substitution Rearrangement........... 28
2.2.3 Diagrams Rule by Diagram Rules......... 30
viii Mathematical Mechanics: From Particle to Muscle
2.2.4 Dot Arrow..................... 30
2.3 Foundation: Category Functor.............. 36
2.3.1 Category....................... 38
2.3.2 Functor........................ 40
2.3.3 Isomorphism..................... 40
2.4 Examples of Categories Functors............. 41
2.4.1 Finite Set....................... 41
2.4.2 Set.......................... 43
2.4.3 Exponentiation of Sets............... 50
2.4.4 Pointed Set...................... 51
2.4.5 Directed Graph................... 53
2.4.6 Dynamic System................... 54
2.4.7 Initialized Dynamic System............. 56
2.4.8 Magma........................ 59
2.4.9 Semigroup...................... 60
2.4.10 Monoid........................ 61
2.4.11 Group......................... 63
2.4.12 Commutative Group ................ 63
2.4.13 Ring ......................... 64
2.4.14 Field......................... 65
2.4.15 Vector Space over a Field.............. 66
2.4.16 Ordered Field.................... 67
2.4.17 Topology....................... 68
2.5 Constructions......................... 69
2.5.1 Magma Constructed from a Set.......... 70
2.5.2 Category Constructed from a Directed Graph . . 71
2.5.3 Category Constructed from a Topological Space . 74
3. Calculus as an Algebra of Infinitesimals 75
3.1 Real Hyperreal....................... 76
3.2 Variable............................ 79
3.2.1 Computer Program Variable............ 79
3.2.2 Mathematical Variable............... 79
3.2.3 Physical Variable.................. 80
3.3 Right, Left Two-Sided Limit............... 82
3.4 Continuity........................... 83
3.5 Differentiable, Derivative Differential .......... 83
3.5.1 Partial Derivative.................. 86
3.6 Curve Sketching Reminder.................. 88
Contents ix
3.7 Integrability.......................... 89
3.8 Algebraic Rules for Calculus................. 92
3.8.1 Fundamental Rule.................. 92
3.8.2 Constant Rule.................... 92
3.8.3 Addition Rule.................... 92
3.8.4 Product Rule..................... 92
3.8.5 Scalar Product Rule................. 93
3.8.6 Chain Rule...................... 93
3.8.7 Exponential Rule.................. 94
3.8.8 Change-of-Variable Rule.............. 94
3.8.9 Increment Rule ................... 94
3.8.10 Quotient Rule.................... 94
3.8.11 Intermediate Value Rule.............. 94
3.8.12 Mean Value Rule .................. 95
3.8.13 Monotonicity Rule.................. 95
3.8.14 Inversion Rule.................... 95
3.8.15 Cyclic Rule...................... 97
3.8.16 Homogeneity Rule.................. 99
3.9 Three Gaussian Integrals .................. 99
3.10 Three Differential Equations................. 101
3.11 Legendre Transform..................... 103
3.12 Lagrange Multiplier ..................... 106
4. Algebra of Vectors 111
4.1 Introduction.......................... Ill
4.2 When is an Array a Matrix?................. 112
4.3 List Algebra.......................... 113
4.3.1 Abstract Row List.................. 114
4.3.2 Set of Row Lists................... 114
4.3.3 Inclusion of Row Lists................ 115
4.3.4 Projection of Row Lists............... 115
4.3.5 Row List Algebra.................. 115
4.3.6 Monoid Constructed from a Set.......... 117
4.3.7 Column List Algebra Natural Transformation . 119
4.3.8 Lists of Lists..................... 122
4.4 Table Algebra......................... 124
4.4.1 The Empty and Unit Tables............ 124
4.4.2 The Set of All Tables................ 124
4.4.3 Juxtaposition of Tables is a Table......... 125
x Mathematical Mechanics: From Particle to Muscle
AAA Outer Product of Two Lists is a Table ...... 126
4.5 Vector Algebra........................ 127
4.5.1 Category of Vector Spaces Vector Operators . . 128
4.5.2 Vector Space Isomorphism............. 129
4.5.3 Inner Product.................... 133
4.5.4 Vector Operator Algebra.............. 134
4.5.5 Dual Vector Space.................. 135
4.5.6 Double Dual Vector Space............. 137
4.5.7 The Unique Extension of a Vector Operator . . . 137
4.5.8 The Vector Space of Matrices ........... 139
4.5.9 The Matrix of a Vector Operator ......... 139
4.5.10 Operator Composition Matrix Multiplication . 140
4.5.11 More on Vector Operators............. 141
Particle Mechanics 145
5. Particle Universe 147
5.1 Conservation of Energy Newton s Second Law..... 149
5.2 Lagrange s Equations Newton s Second Law...... 150
5.3 The Invariance of Lagrange s Equations.......... 152
5.4 Hamilton s Principle..................... 155
5.5 Hamilton s Equations .................... 160
5.6 A Theorem of George Stokes ................ 162
5.7 A Theorem on a Series of Impulsive Forces ........ 163
5.8 Langevin s Trick....................... 164
5.9 An Argument due to Albert Einstein............ 165
5.10 An Argument due to Paul Langevin............ 167
Timing Machinery 173
6. Introduction to Timing Machinery 175
6.1 Blending Time k State Machine.............. 177
6.2 The Basic Oscillator..................... 178
6.3 Timing Machine Variable.................. 179
6.4 The Robust Low-Pass Filter................. 180
6.5 Frequency Multiplier Differential Equation....... 180
6.6 Probabilistic Timing Machine................ 181
Contents xi
6.7 Chemical Reaction System Simulation........... 182
6.8 Computer Simulation .................... 183
Stochastic Timing Machinery 187
7.1 Introduction.......................... 187
7.1.1 Syntax for Drawing Models............. 189
7.1.2 Semantics for Interpreting Models......... 190
7.2 Examples........................... 192
7.2.1 The Frequency Doubler of Brian Stromquist . . . 192
7.3 Zero-Order Chemical Reaction............... 193
7.3.1 Newton s Second Law................ 194
7.3.2 Gillespie Exact Stochastic Simulation....... 195
7.3.3 Brownian Particle in a Force Field......... 196
Theory of Substances 203
8. Algebraic Thermodynamics 205
8.1 Introduction.......................... 205
8.2 Chemical Element, Compound Mixture......... 207
8.3 Universe............................ 209
8.4 Reservoir Capacity .................... 224
8.5 Equilibrium Equipotentiality............... 225
8.6 Entropy Energy...................... 229
8.7 Fundamental Equation.................... 234
8.8 Conduction Resistance.................. 238
9. Clausius, Gibbs Duhem 241
9.1 Clausius Inequality...................... 241
9.2 Gibbs-Duhem Equation................... 244
10. Experiments Measurements 247
10.1 Experiments.......................... 247
10.1.1 Boyle, Charles Gay-Lussac Experiment..... 247
10.1.2 Rutherford-Joule Friction Experiment....... 251
10.1.3 Joule-Thomson Free Expansion of an Ideal Gas . 252
10.1.4 Iron-Lead Experiment................ 254
10.1.5 Isothermal Expansion of an Ideal Gas....... 258
10.1.6 Reaction at Constant Temperature Volume . . 260
xii Mathematical Mechanics: From Particle to Muscle
10.1.7 Reaction at Constant Pressure k Temperature . . 261
10.1.8 Theophile de Donder k Chemical Affinity .... 265
10.1.9 Gibbs Free Energy.................. 268
10.2 Measurements......................... 271
10.2.1 Balance Measurements............... 273
11. Chemical Reaction 275
11.1 Chemical Reaction Extent, Completion k Realization . . 279
11.2 Chemical Equilibrium.................... 281
11.3 Chemical Formations k Transformations.......... 285
11.4 Monoidal Category k Monoidal Functor.......... 286
11.5 Hess Monoidal Functor................... 289
Muscle Contraction Research 291
12. Muscle Contraction 293
12.1 Muscle Contraction: Chronology.............. 293
12.1.1 19th Century..................... 293
12.1.2 1930-1939...................... 293
12.1.3 1940-1949...................... 294
12.1.4 1950-1959...................... 296
12.1.5 1960-1969...................... 299
12.1.6 1970-1979...................... 301
12.1.7 1980-1989...................... 304
12.1.8 1990-1999...................... 305
12.1.9 2000-2010...................... 311
12.2 Conclusion .......................... 325
Appendices 327
Appendix A Exponential k Logarithm Functions 329
Appendix B Recursive Definition of Stochastic Timing Machinery 331
B.l Ordinary Differential Equation: Initial Value Problem . . 331
B.2 Stochastic Differential Equation:
A Langevin Equation without Inertia............ 332
Contents xiii
B.3 Gillespie Exact Stochastic Simulation:
Chemical Master Equation ................. 333
B.4 Stochastic Timing Machine: Abstract Theory....... 334
Appendix C MATLAB Code 335
C.l Stochastic Timing Machine Interpreter........... 335
C.2 MATLAB for Stochastic Timing Machinery Simulations . 338
C.3 Brownian Particle in Force Field.............. 339
C.4 Figures. Simulating Brownian Particle in Force Field . . . 344
Appendix D Fundamental Theorem of Elastic Bodies 347
Bibliography 353
Index 363
|
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| discipline | Physik Biologie |
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| id | DE-604.BV036651167 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:57Z |
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| isbn | 9789814289702 9814289701 |
| language | English |
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| spelling | Cooper, Ellis D. Verfasser (DE-588)142223859 aut Mathematical mechanics from particle to muscle by Ellis D. Cooper Singapore [u.a.] World Scientific 2011 XV, 373 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier World scientific series on nonlinear science : A 77 Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Muskelkontraktion (DE-588)4170858-1 gnd rswk-swf Biophysik (DE-588)4006891-2 gnd rswk-swf Muskelkontraktion (DE-588)4170858-1 s Biophysik (DE-588)4006891-2 s Mathematische Physik (DE-588)4037952-8 s DE-604 World scientific series on nonlinear science A ; 77 (DE-604)BV009051753 77 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020570675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cooper, Ellis D. Mathematical mechanics from particle to muscle World scientific series on nonlinear science Mathematische Physik (DE-588)4037952-8 gnd Muskelkontraktion (DE-588)4170858-1 gnd Biophysik (DE-588)4006891-2 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4170858-1 (DE-588)4006891-2 |
| 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 by Ellis D. Cooper |
| title_fullStr | Mathematical mechanics from particle to muscle by Ellis D. Cooper |
| title_full_unstemmed | Mathematical mechanics from particle to muscle by Ellis D. Cooper |
| title_short | Mathematical mechanics |
| title_sort | mathematical mechanics from particle to muscle |
| title_sub | from particle to muscle |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Muskelkontraktion (DE-588)4170858-1 gnd Biophysik (DE-588)4006891-2 gnd |
| topic_facet | Mathematische Physik Muskelkontraktion Biophysik |
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