Info
Continuum mechanics : the birthplace of mathematical models / / Myron B. Allen
| Continuum mechanics : the birthplace of mathematical models / / Myron B. Allen |
| Autore | Allen Myron B. <1954-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2016 |
| Descrizione fisica | 1 online resource (293 p.) |
| Disciplina | 531.076 |
| Soggetto topico | Continuum mechanics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-90934-8
1-118-90938-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Dedication; Preface; Contents; Chapter 1 Geometric Setting; 1.1 Vectors and Euclidean Point Space; 1.1.1 Vectors; 1.1.2 Euclidean Point Space; 1.1.3 Summary; 1.2 Tensors; 1.2.1 First-Order Tensors and Vectors; 1.2.2 Second-Order Tensors; 1.2.3 Cross Products, Triple Products, and Determinants; 1.2.4 Orthogonal Tensors; 1.2.5 Invariants of a Tensor; 1.2.6 Derivatives of Tensor-Valued Functions; 1.2.7 Summary; Chapter 2 Kinematics I: The Calculus of Motion; 2.1 Bodies, Motions, and Deformations; 2.1.1 Deformation; 2.1.2 Examples of Motions; 2.1.3 Summary
2.2 Derivatives of Motion 2.2.1 Time Derivatives; 2.2.2 Derivatives With Respect to Position; 2.2.3 The Deformation Gradient; 2.2.4 Summary; 2.3 Pathlines, Streamlines, and Streaklines; 2.3.1 Three Types of Arc; 2.3.2 An Example; 2.3.3 Summary; 2.4 Integrals Under Motion; 2.4.1 Arc, Surface, and Volume Integrals; 2.4.2 Reynolds Transport Theorem; 2.4.3 Summary; Chapter 3 Kinematics II: Strain and its Rates; 3.1 Strain; 3.1.1 Symmetric Tensors; 3.1.2 Polar Decomposition and the Deformation Gradient; 3.1.3 Examples; 3.1.4 Cauchy-Green and Strain Tensors; 3.1.5 Strain Invariants; 3.1.6 Summary 3.2 Infinitesimal Strain 3.2.1 The Infinitesimal Strain Tensor; 3.2.2 Summary; 3.3 Strain Rates; 3.3.1 Stretching and Spin Tensors; 3.3.2 Skew Tensors, Spin, and Vorticity; 3.3.3 Summary; 3.4 Vorticity and Circulation; 3.4.1 Circulation; 3.4.2 Summary; 3.5 Observer Transformations; 3.5.1 Changes in Frame of Reference; 3.5.2 Summary; Chapter 4 Balance Laws; 4.1 Mass Balance; 4.1.1 Local Forms of Mass Balance; 4.1.2 Summary; 4.2 Momentum Balance; 4.2.1 Analysis of Stress; 4.2.2 Inertial Frames of Reference; 4.2.3 Momentum Balance in Referential Coordinates; 4.2.4 Summary 4.3 Angular Momentum Balance 4.3.1 Symmetry of the Stress Tensor; 4.3.2 Summary; 4.4 Energy Balance; 4.4.1 Thermal Energy Balance; 4.4.2 Summary; 4.5 Entropy Inequality; 4.5.1 Motivation; 4.5.2 Clausius-Duhem Inequality; 4.5.3 Summary; 4.6 Jump Conditions; 4.6.1 Singular Surfaces; 4.6.2 Localization; 4.6.3 Summary; Chapter 5 Constitutive Relations: Examples of Mathematical Models; 5.1 Heat Transfer; 5.1.1 Properties of the Heat Equation; 5.1.2 Summary; 5.2 Potential Theory; 5.2.1 Motivation; 5.2.2 Boundary Conditions; 5.2.3 Uniqueness of Solutions to the Poisson Equation 5.2.4 Maximum Principle 5.2.5 Mean Value Property; 5.2.6 Summary; 5.3 Fluid Mechanics; 5.3.1 Ideal Fluids; 5.3.2 An Ideal Fluid in a Rotating Frame of Reference; 5.3.3 Acoustics; 5.3.4 Incompressible Newtonian Fluids; 5.3.5 Stokes Flow; 5.3.6 Summary; 5.4 Solid Mechanics; 5.4.1 Static Displacements; 5.4.2 Elastic Waves; 5.4.3 Summary; Chapter 6 Constitutive Theory; 6.1 Conceptual Setting; 6.1.1 The Need to Close the System; 6.1.2 Summary; 6.2 Determinism and Equipresence; 6.2.1 Determinism; 6.2.2 Equipresence; 6.2.3 Summary; 6.3 Objectivity; 6.3.1 Reducing Functional Dependencies 6.3.2 Summary |
| Record Nr. | UNINA-9910460992403321 |
Allen Myron B. <1954->
|
||
| Hoboken, New Jersey : , : Wiley, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mathematics of fluid flow through porous media / / Myron B. Allen
| The mathematics of fluid flow through porous media / / Myron B. Allen |
| Autore | Allen Myron B. <1954-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , [2021] |
| Descrizione fisica | 1 online resource (227 pages) |
| Disciplina | 620.1064 |
| Soggetto topico | Fluid dynamics - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-119-66387-3
1-119-66388-1 1-119-66386-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910555004903321 |
|
Allen Myron B. <1954->
|
||
| Hoboken, New Jersey : , : Wiley, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mathematics of fluid flow through porous media / / Myron B. Allen
| The mathematics of fluid flow through porous media / / Myron B. Allen |
| Autore | Allen Myron B. <1954-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , [2021] |
| Descrizione fisica | 1 online resource (227 pages) |
| Disciplina | 620.1064 |
| Soggetto topico | Fluid dynamics - Mathematical models |
| ISBN |
1-119-66387-3
1-119-66388-1 1-119-66386-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910831000403321 |
|
Allen Myron B. <1954->
|
||
| Hoboken, New Jersey : , : Wiley, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical analysis for applied science / / Myron B. Allen III, Eli L. Isaacson
| Numerical analysis for applied science / / Myron B. Allen III, Eli L. Isaacson |
| Autore | Allen Myron B. <1954-> |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1998 |
| Descrizione fisica | 1 online resource (512 p.) |
| Disciplina | 515 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts |
| Soggetto topico | Numerical analysis |
| ISBN |
1-118-03312-4
1-118-03027-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Numerical Analysis for Applied Science; CONTENTS; Preface; 0 Some Useful Tools; 0.1 Introduction; 0.2 Bounded Sets; 0.3 Normed Vector Spaces; 0.4 Results from Calculus; 0.5 Problems; 0.6 References; 1 Approximation of Functions; 1.1 Introduction; 1.2 Polynomial Interpolation; 1.3 Piecewise Polynomial Interpolation; 1.4 Hermite Interpolation; 1.5 Interpolation in Two Dimensions; 1.6 Splines; 1.7 Least-Squares Methods; 1.8 Trigonometric Interpolation; 1.9 Problems; 1.10 References; 2 Direct Methods for Linear Systems; 2.1 Introduction; 2.2 Gauss Elimination; 2.3 Variants of Gauss Elimination
2.4 Band Matrices2.5 Matrix Norms; 2.6 Errors and Iterative Improvement; 2.7 Problems; 2.8 References; 3 Solution of Nonlinear Equations; 3.1 Introduction; 3.2 Bisection; 3.3 Successive Substitution in One Variable; 3.4 Newton's Method in One Variable; 3.5 The Secant Method; 3.6 Successive Substitution: Several Variables; 3.7 Newton's Method: Several Variables; 3.8 Problems; 3.9 References; 4 Iterative Methods for Linear Systems; 4.1 Introduction; 4.2 Conceptual Foundations; 4.3 Matrix-Splitting Techniques; 4.4 Successive Overrelaxation; 4.5 The Conjugate-Gradient Method; 4.6 Problems 4.7 References5 Eigenvalue Problems; 5.1 Basic Facts About Eigenvalues; 5.2 Power Methods; 5.3 The QR Method: Underlying Concepts; 5.4 The QR Method Implementation; 5.5 Problems; 5.6 References; 6 Numerical Integration; 6.1 Introduction; 6.2 Newton-Cotes Formulas; 6.3 Romberg and Adaptive Quadrature; 6.4 Gauss Quadrature; 6.5 Problems; 6.6 References; 7 Ordinary Differential Equations; 7.1 Introduction; 7.2 One-Step Methods; 7.3 Multistep Methods: Consistency and Stability; 7.4 Convergence of Multistep Methods; 7.5 Problems; 7.6 References; 8 Difference Methods for PDEs; 8.1 Introduction 8.2 The Poisson Equation8.3 The Advection Equation; 8.4 Other Time-Dependent Equations; 8.5 Problems; 8.6 References; 9 Introduction to Finite Elements; 9.1 Introduction and Background; 9.2 A Steady-State Problem; 9.3 A Transient Problem; 9.4 Problems; 9.5 References; Appendix A: Divided Differences; Appendix B: Local Minima; Appendix C: Chebyshev Polynomials; Index |
| Record Nr. | UNINA-9910141239503321 |
|
Allen Myron B. <1954->
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical analysis for applied science / / Myron B. Allen III, Eli L. Isaacson
| Numerical analysis for applied science / / Myron B. Allen III, Eli L. Isaacson |
| Autore | Allen Myron B. <1954-> |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1998 |
| Descrizione fisica | 1 online resource (512 p.) |
| Disciplina | 515 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts |
| Soggetto topico | Numerical analysis |
| ISBN |
1-118-03312-4
1-118-03027-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Numerical Analysis for Applied Science; CONTENTS; Preface; 0 Some Useful Tools; 0.1 Introduction; 0.2 Bounded Sets; 0.3 Normed Vector Spaces; 0.4 Results from Calculus; 0.5 Problems; 0.6 References; 1 Approximation of Functions; 1.1 Introduction; 1.2 Polynomial Interpolation; 1.3 Piecewise Polynomial Interpolation; 1.4 Hermite Interpolation; 1.5 Interpolation in Two Dimensions; 1.6 Splines; 1.7 Least-Squares Methods; 1.8 Trigonometric Interpolation; 1.9 Problems; 1.10 References; 2 Direct Methods for Linear Systems; 2.1 Introduction; 2.2 Gauss Elimination; 2.3 Variants of Gauss Elimination
2.4 Band Matrices2.5 Matrix Norms; 2.6 Errors and Iterative Improvement; 2.7 Problems; 2.8 References; 3 Solution of Nonlinear Equations; 3.1 Introduction; 3.2 Bisection; 3.3 Successive Substitution in One Variable; 3.4 Newton's Method in One Variable; 3.5 The Secant Method; 3.6 Successive Substitution: Several Variables; 3.7 Newton's Method: Several Variables; 3.8 Problems; 3.9 References; 4 Iterative Methods for Linear Systems; 4.1 Introduction; 4.2 Conceptual Foundations; 4.3 Matrix-Splitting Techniques; 4.4 Successive Overrelaxation; 4.5 The Conjugate-Gradient Method; 4.6 Problems 4.7 References5 Eigenvalue Problems; 5.1 Basic Facts About Eigenvalues; 5.2 Power Methods; 5.3 The QR Method: Underlying Concepts; 5.4 The QR Method Implementation; 5.5 Problems; 5.6 References; 6 Numerical Integration; 6.1 Introduction; 6.2 Newton-Cotes Formulas; 6.3 Romberg and Adaptive Quadrature; 6.4 Gauss Quadrature; 6.5 Problems; 6.6 References; 7 Ordinary Differential Equations; 7.1 Introduction; 7.2 One-Step Methods; 7.3 Multistep Methods: Consistency and Stability; 7.4 Convergence of Multistep Methods; 7.5 Problems; 7.6 References; 8 Difference Methods for PDEs; 8.1 Introduction 8.2 The Poisson Equation8.3 The Advection Equation; 8.4 Other Time-Dependent Equations; 8.5 Problems; 8.6 References; 9 Introduction to Finite Elements; 9.1 Introduction and Background; 9.2 A Steady-State Problem; 9.3 A Transient Problem; 9.4 Problems; 9.5 References; Appendix A: Divided Differences; Appendix B: Local Minima; Appendix C: Chebyshev Polynomials; Index |
| Record Nr. | UNINA-9910830081103321 |
|
Allen Myron B. <1954->
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||