| Acknowledgments | p. xv |
| Introduction | p. 1 |
| Introduction | p. 3 |
| Why Would I Have Valued This Book in High School? | p. 4 |
| Who Else Would Value This Book? | p. 5 |
| Physics & Biology | p. 6 |
| Motivation | p. 7 |
| The Principle of Least Thought | p. 10 |
| Measurement | p. 11 |
| Conceptual Blending | p. 11 |
| Mental Model of Muscle Contraction | p. 13 |
| Organization | p. 15 |
| What is Missing? | p. 18 |
| What is Original? | p. 19 |
| Mathematics | p. 21 |
| Ground & Foundation of Mathematics | p. 23 |
| Introduction | p. 23 |
| Ground: Discourse & Surface | p. 26 |
| Symbol & Expression | p. 27 |
| Substitution & Rearrangement | p. 28 |
| Diagrams Rule by Diagram Rules | p. 30 |
| Dot & Arrow | p. 30 |
| Foundation: Category & Functor | p. 36 |
| Category | p. 38 |
| Functor | p. 40 |
| Isomorphism | p. 40 |
| Examples of Categories & Functors | p. 41 |
| Finite Set | p. 41 |
| Set | p. 43 |
| Exponentiation of Sets | p. 50 |
| Pointed Set | p. 51 |
| Directed Graph | p. 53 |
| Dynamic System | p. 54 |
| Initialized Dynamic System | p. 56 |
| Magma | p. 59 |
| Semigroup | p. 60 |
| Monoid | p. 61 |
| Group | p. 63 |
| Commutative Group | p. 63 |
| Ring | p. 64 |
| Field | p. 65 |
| Vector Space over a Field | p. 66 |
| Ordered Field | p. 67 |
| Topology | p. 68 |
| Constructions | p. 69 |
| Magma Constructed from a Set | p. 70 |
| Category Constructed from a Directed Graph | p. 71 |
| Category Constructed from a Topological Space | p. 74 |
| Calculus as an Algebra of Infinitesimals | p. 75 |
| Real & Hyperreal | p. 76 |
| Variable | p. 79 |
| Computer Program Variable | p. 79 |
| Mathematical Variable | p. 79 |
| Physical Variable | p. 80 |
| Right, Left & Two-Sided Limit | p. 82 |
| Continuity | p. 83 |
| Differentiable, Derivative & Differential | p. 83 |
| Partial Derivative | p. 86 |
| Curve Sketching Reminder | p. 88 |
| Integrability | p. 89 |
| Algebraic Rules for Calculus | p. 92 |
| Fundamental Rule | p. 92 |
| Constant Rule | p. 92 |
| Addition Rule | p. 92 |
| Product Rule | p. 92 |
| Scalar Product Rule | p. 93 |
| Chain Rule | p. 93 |
| Exponential Rule | p. 94 |
| Change-of-Variable Rule | p. 94 |
| Increment Rule | p. 94 |
| Quotient Rule | p. 94 |
| Intermediate Value Rule | p. 94 |
| Mean Value Rule | p. 95 |
| Monotoniaty Rule | p. 95 |
| Inversion Rule | p. 95 |
| Cyclic Rule | p. 97 |
| Homogeneity Rule | p. 99 |
| Three Gaussian Integrals | p. 99 |
| Three Differential Equations | p. 101 |
| Legendre Transform | p. 103 |
| Lagrange Multiplier | p. 106 |
| Algebra of Vectors | p. 111 |
| Introduction | p. 111 |
| When is an Array a Matrix? | p. 112 |
| List Algebra | p. 113 |
| Abstract Row List | p. 114 |
| Set of Row Lists | p. 114 |
| Inclusion of Row Lists | p. 115 |
| Projection of Row Lists | p. 115 |
| Row List Algebra | p. 115 |
| Monoid Constructed from a Set | p. 117 |
| Column List Algebra & NaturalTransformation | p. 119 |
| Lists of Lists | p. 122 |
| Table Algebra | p. 124 |
| The Empty and Unit, Tables | p. 124 |
| The Set of All Tables | p. 124 |
| Juxtaposition of Tables is a Table | p. 125 |
| Outer Product of Two Lists is a Table | p. 126 |
| Vector Algebra | p. 127 |
| Category of Vector Spaces & Vector Operators | p. 128 |
| Vector Space Isomorphism | p. 129 |
| Inner Product | p. 133 |
| Vector Operator Algebra | p. 134 |
| Dual Vector Space | p. 135 |
| Double Dual Vector Space | p. 137 |
| The Unique Extension of a Vector Operator | p. 137 |
| The Vector Space of Matrices | p. 139 |
| The Matrix of a Vector Operator | p. 139 |
| Operator Composition & Matrix Multiplication | p. 140 |
| More on Vector Operators | p. 141 |
| Particle Mechanics | p. 145 |
| Particle Universe | p. 147 |
| Conservation of Energy & Newton's Second Law | p. 149 |
| Lagrange's Equations & Newton's Second Law | p. 150 |
| The Invariance of Lagrange's Equations | p. 152 |
| Hamilton's Principle | p. 155 |
| Hamilton's Equations | p. 160 |
| A Theorem of George Stokes | p. 162 |
| A Theorem on a Series of Impulsive Forces | p. 163 |
| Langevin's Trick | p. 164 |
| An Argument due to Albert Einstein | p. 165 |
| An Argument clue to Paul Langevin | p. 167 |
| Timing Machinery | p. 173 |
| Introduction to Timing Machinery | p. 175 |
| Blending Time & State Machine | p. 177 |
| The Basic Oscillator | p. 178 |
| Timing Machine Variable | p. 179 |
| The Robust Low-Pass Filter | p. 180 |
| Frequency Multiplier & Differential Equation | p. 180 |
| Probabilistic Timing Machine | p. 181 |
| Chemical Reaction System Simulation | p. 182 |
| Computer Simulation | p. 183 |
| Stochastic Timing Machinery | p. 187 |
| Introduction | p. 187 |
| Syntax for Drawing Models | p. 189 |
| Semantics for Interpreting Models | p. 190 |
| Examples | p. 192 |
| The Frequency Doubler of Brian Stromquist | p. 192 |
| Zero-Order Chemical Reaction | p. 193 |
| Newton's Second Law | p. 194 |
| Gillespie Exact Stochastic Simulation | p. 195 |
| Brownian Particle in a Force Field | p. 196 |
| Theory of Substances | p. 203 |
| Algebraic Thermodynamics | p. 205 |
| Introduction | p. 205 |
| Chemical Element, Compound & Mixture | p. 207 |
| Universe | p. 209 |
| Reservoir & Capacity | p. 224 |
| Equilibrium & Equipotentiality | p. 225 |
| Entropy & Energy | p. 229 |
| Fundamental Equation | p. 234 |
| Conduction & Resistance | p. 238 |
| Clausius, Gibbs & Duhem | p. 241 |
| Clausius Inequality | p. 241 |
| Gibbs-Duhem Equation | p. 244 |
| Experiments & Measurements | p. 247 |
| Experiments | p. 247 |
| Boyle, Charles & Gay-Lussac Experiment | p. 247 |
| Rutherford-Joule Friction Experiment | p. 251 |
| Joule-Thomson Free Expansion of an Ideal Gas | p. 252 |
| Iron-Lead Experiment | p. 254 |
| Isothermal Expansion of an Ideal Gas | p. 258 |
| Reaction at Constant Temperature & Volume | p. 260 |
| Reaction at Constant Pressure& Temperature | p. 261 |
| Théophile de Donder & Chemical Affinity | p. 265 |
| Gibbs Free Energy | p. 268 |
| Measurements | p. 271 |
| Balance Measurements | p. 273 |
| Chemical Reaction | p. 275 |
| Chemical Reaction Extent, Completion & Realization | p. 279 |
| Chemical Equilibrium | p. 281 |
| Chemical Formations & Transformations | p. 285 |
| Monoidal Category & Monoidal Functor | p. 286 |
| Hess' Monoidal Functor | p. 289 |
| Muscle Contraction Research | p. 291 |
| Muscle Contraction | p. 293 |
| Muscle Contraction: Chronology | p. 293 |
| 19th Century | p. 293 |
| 1930-1939 | p. 293 |
| 1940-1949 | p. 294 |
| 1950-1959 | p. 296 |
| 1960-1969 | p. 299 |
| 1970-1979 | p. 301 |
| 1980-1989 | p. 304 |
| 1990-1999 | p. 305 |
| 2000-2010 | p. 311 |
| Conclusion | p. 325 |
| Appendices | p. 327 |
| Exponential & Logarithm Functions | p. 329 |
| Recursive Definition of Stochastic Timing Machinery | p. 331 |
| Ordinary Differential Equation: Initial Value Problem | p. 331 |
| Stochastic Differential Equation: A Langevin Equation without Inertia | p. 332 |
| Gillespie Exact Stochastic Simulation: Chemical Master Equation | p. 333 |
| Stochastic Timing Machine: Abstract Theory | p. 334 |
| MATLAB Code | p. 335 |
| Stochastic Timing Machine Interpreter | p. 335 |
| MATLAB for Stochastic Timing Machinery Simulations | p. 338 |
| Brownian Particle in Force Field | p. 339 |
| Figures. Simulating Brownian Particle in Force Field | p. 344 |
| Fundamental Theorem of Elastic Bodies | p. 347 |
| Bibliography | p. 353 |
| Index | p. 363 |
| Table of Contents provided by Ingram. All Rights Reserved. |
