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Mathematical mechanics [[electronic resource] ] : from particle to muscle / / by Ellis D. Cooper
Mathematical mechanics [[electronic resource] ] : from particle to muscle / / by Ellis D. Cooper
Autore Cooper Ellis D
Pubbl/distr/stampa Singapore ; ; Hackensack, N. J., : World Scientific, c2011
Descrizione fisica 1 online resource (390 p.)
Disciplina 510.2457
Collana World Scientific series on nonlinear science. Series A, Monographs and treatises
Soggetto topico Mechanics, Analytic
Dynamics of a particle - Mathematical models
Muscle contraction - Mathematical models
Mathematical physics
Soggetto genere / forma Electronic books.
ISBN 1-283-23461-0
9786613234612
981-4289-71-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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
Record Nr. UNINA-9910464521503321
Cooper Ellis D  
Singapore ; ; Hackensack, N. J., : World Scientific, c2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Mathematical mechanics [[electronic resource] ] : from particle to muscle / / by Ellis D. Cooper
Mathematical mechanics [[electronic resource] ] : from particle to muscle / / by Ellis D. Cooper
Autore Cooper Ellis D
Pubbl/distr/stampa Singapore ; ; Hackensack, N. J., : World Scientific, c2011
Descrizione fisica 1 online resource (390 p.)
Disciplina 510.2457
Collana World Scientific series on nonlinear science. Series A, Monographs and treatises
Soggetto topico Mechanics, Analytic
Dynamics of a particle - Mathematical models
Muscle contraction - Mathematical models
Mathematical physics
ISBN 1-283-23461-0
9786613234612
981-4289-71-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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
Record Nr. UNINA-9910788961303321
Cooper Ellis D  
Singapore ; ; Hackensack, N. J., : World Scientific, c2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui