LEADER 05408nam 2200709 a 450 001 9910788961303321 005 20230725052637.0 010 $a1-283-23461-0 010 $a9786613234612 010 $a981-4289-71-X 035 $a(CKB)3400000000016487 035 $a(EBL)840589 035 $a(SSID)ssj0000538986 035 $a(PQKBManifestationID)12224521 035 $a(PQKBTitleCode)TC0000538986 035 $a(PQKBWorkID)10559842 035 $a(PQKB)11220574 035 $a(MiAaPQ)EBC840589 035 $a(WSP)00007520 035 $a(Au-PeEL)EBL840589 035 $a(CaPaEBR)ebr10493536 035 $a(CaONFJC)MIL323461 035 $a(OCoLC)748215442 035 $a(EXLCZ)993400000000016487 100 $a20110712d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical mechanics$b[electronic resource] $efrom particle to muscle /$fby Ellis D. Cooper 210 $aSingapore ;$aHackensack, N. J. $cWorld Scientific$dc2011 215 $a1 online resource (390 p.) 225 1 $aWorld Scientific series on nonlinear science. Series A, Monographs and treatises ;$vv. 77 300 $aDescription based upon print version of record. 311 $a981-4289-70-1 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a2.3 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 327 $a2.5.3 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 327 $a3.8.8 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 327 $a4.3.7 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 327 $a4.5.8 The Vector Space of Matrices 330 $aThis unprecedented book offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. T 410 0$aWorld Scientific series on nonlinear science.$nSeries A,$pMonographs and treatises ;$vv. 77. 606 $aMechanics, Analytic 606 $aDynamics of a particle$xMathematical models 606 $aMuscle contraction$xMathematical models 606 $aMathematical physics 615 0$aMechanics, Analytic. 615 0$aDynamics of a particle$xMathematical models. 615 0$aMuscle contraction$xMathematical models. 615 0$aMathematical physics. 676 $a510.2457 700 $aCooper$b Ellis D$0516915 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788961303321 996 $aMathematical mechanics$93850263 997 $aUNINA