Mathematical mechanics [[electronic resource] ] : from particle to muscle / / by Ellis D. Cooper

• Record Nr.: UNINA9910464521503321
• Autore: Cooper Ellis D
• Pubbl/distr/stampa: Singapore ; ; Hackensack, N. J., : World Scientific, c2011
• ISBN: 1-283-23461-0; 9786613234612; 981-4289-71-X
• Descrizione fisica: 1 online resource (390 p.)
• Collana: World Scientific series on nonlinear science. Series A, Monographs and treatises ; ; v. 77
• Disciplina: 510.2457
• Soggetti: Mechanics, Analytic; Dynamics of a particle - Mathematical models; Muscle contraction - Mathematical models; Mathematical physics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents; Acknowledgments; Introduction; 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?; Mathematics; 2. Ground & Foundation of Mathematics; 2.1 Introduction; 2.2 Ground: Discourse & Surface; 2.2.1 Symbol & Expression; 2.2.2 Substitution & Rearrangement; 2.2.3 Diagrams Rule by Diagram Rules; 2.2.4 Dot & Arrow; 2.3 Foundation: Category & Functor2.3.1 Category; 2.3.2 Functor; 2.3.3 Isomorphism; 2.4 Examples of Categories & Functors; 2.4.1 Finite Set; 2.4.2 Set; 2.4.3 Exponentiation of Sets; 2.4.4 Pointed Set; 2.4.5 Directed Graph; 2.4.6 Dynamic System; 2.4.7 Initialized Dynamic System; 2.4.8 Magma; 2.4.9 Semigroup; 2.4.10 Monoid; 2.4.11 Group; 2.4.12 Commutative Group; 2.4.13 Ring; 2.4.14 Field; 2.4.15 Vector ; Space over a Field; 2.4.16 Ordered Field; 2.4.17 Topology; 2.5 Constructions; 2.5.1 Magma Constructed from a Set; 2.5.2 Category Constructed from a Directed Graph; 2.5.3 Category Constructed from a Topological Space3. Calculus as an Algebra of Infinitesimals; 3.1 Real & Hyperreal; 3.2 Variable; 3.2.1 Computer Program Variable; 3.2.2 Mathematical Variable; 3.2.3 Physical Variable; 3.3 Right, Left & Two-Sided Limit; 3.4 Continuity; 3.5 Differentiable, Derivative & Differential; 3.5.1 Partial Derivative; 3.6 Curve Sketching Reminder; 3.7 Integrability; 3.8 Algebraic Rules for Calculus; 3.8.1 Fundamental Rule; 3.8.2 Constant Rule; 3.8.3 Addition Rule; 3.8.4 Product Rule; 3.8.5 Scalar Product Rule; 3.8.6 Chain Rule; 3.8.7 Exponential Rule; 3.8.8 Change-of-Variable Rule3.8.9 Increment Rule; 3.8.10 Quotient Rule; 3.8.11 Intermediate Value Rule; 3.8.12 Mean Value Rule; 3.8.13 Monotonicity Rule; 3.8.14 Inversion Rule; 3.8.15 Cyclic Rule; 3.8.16 Homogeneity Rule; 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; 4.3.1 Abstract Row List; 4.3.2 Set of Row Lists; 4.3.3 Inclusion of Row Lists; 4.3.4 Projection of Row Lists; 4.3.5 Row List Algebra; 4.3.6 Monoid Constructed from a Set; 4.3.7 Column List Algebra & Natural Transformation4.3.8 Lists of Lists; 4.3.8.1 Rows of Columns and Columns of Rows; 4.3.8.2 Flattening of rows of rows; 4.4 Table Algebra; 4.4.1 The Empty and Unit Tables; 4.4.2 The Set of All Tables; 4.4.3 Juxtaposition of Tables is a Table; 4.4.4 Outer Product of Two Lists is a Table; 4.5 Vector Algebra; 4.5.1 Category of Vector Spaces & Vector Operators; 4.5.2 Vector Space Isomorphism; 4.5.3 Inner Product; 4.5.4 Vector Operator Algebra; 4.5.5 Dual Vector Space; 4.5.6 Double Dual Vector Space; 4.5.7 The Unique Extension of a Vector Operator; 4.5.8 The Vector Space of Matrices
• Sommario/riassunto: 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. T