An introduction to mathematical modeling : a course in mechanics / J. Tinsley Oden.

Format:

Book

Author/Creator:

Oden, J. Tinsley (John Tinsley), 1936-

Series:

Wiley series in computational mechanics.

Wiley series in computational mechanics

Language:

English

Subjects (All):

Mechanics, Analytic.

Physical Description:

1 online resource (350 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, N.J. : Wiley, c2011.

Language Note:

English

Summary:

"An important resource, this book provides a short-course in nonlinear continuum mechanics, contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics, and presents a brief introduction to statistical mechanics of systems in thermodynamic equilibrium. Also included is information on continuum mechanics, electrodynamics, quantum mechanics, and statistical mechanics. The author approaches mechanics as the branch of physics and mathematical science concerned with describing the motion of bodies, including their deformation and temperature changes, under the action of forces, and if the study of the propagation of waves and the transformation of energy in physical systems are added, then the term mechanics does indeed apply to everything that is covered within the book. "-- Provided by publisher.

Contents:

An Introduction to Mathematical Modeling: A Course in Mechanics; Contents; Preface; I Nonlinear Continuum Mechanics; 1 Kinematics of Deformable Bodies; 1.1 Motion; 1.2 Strain and Deformation Tensors; 1.3 Rates of Motion; 1.4 Rates of Deformation; 1.5 The Piola Transformation; 1.6 The Polar Decomposition Theorem; 1.7 Principal Directions and Invariants of Deformation and Strain; 1.8 The Reynolds' Transport Theorem; 2 Mass and Momentum; 2.1 Local Forms of the Principle of Conservation of Mass; 2.2 Momentum; 3 Force and Stress in Deformable Bodies

4 The Principles of Balance of Linear and Angular Momentum 4.1 Cauchy's Theorem: The Cauchy Stress Tensor; 4.2 The Equations of Motion (Linear Momentum); 4.3 The Equations of Motion Referred to the Reference Configuration: The Piola-Kirchhoff Stress Tensors; 4.4 Power; 5 The Principle of Conservation of Energy; 5.1 Energy and the Conservation of Energy; 5.2 Local Forms of the Principle of Conservation of Energy; 6 Thermodynamics of Continua and the Second Law; 7 Constitutive Equations; 7.1 Rules and Principles for Constitutive Equations; 7.2 Principle of Material Frame Indifference

7.2.1 Solids 7.2.2 Fluids; 7.3 The Coleman-Noll Method: Consistency with the Second Law of Thermodynamics; 8 Examples and Applications; 8.1 The Navier-Stokes Equations for Incompressible Flow; 8.2 Flow of Gases and Compressible Fluids: The Compressible Navier-Stokes Equations; 8.3 Heat Conduction; 8.4 Theory of Elasticity; II Electromagnetic Field Theory and Quantum Mechanics; 9 Electromagnetic Waves; 9.1 Introduction; 9.2 Electric Fields; 9.3 Gauss's Law; 9.4 Electric Potential Energy; 9.4.1 Atom Models; 9.5 Magnetic Fields; 9.6 Some Properties of Waves; 9.7 Maxwell's Equations

9.8 Electromagnetic Waves 10 Introduction to Quantum Mechanics; 10.1 Introductory Comments; 10.2 Wave and Particle Mechanics; 10.3 Heisenberg's Uncertainty Principle; 10.4 Schrödinger's Equation; 10.4.1 The Case of a Free Particle; 10.4.2 Superposition in Rn; 10.4.3 Hamiltonian Form; 10.4.4 The Case of Potential Energy; 10.4.5 Relativistic Quantum Mechanics; 10.4.6 General Formulations of Schrödinger's Equation; 10.4.7 The Time-Independent Schrödinger Equation; 10.5 Elementary Properties of the Wave Equation; 10.5.1 Review; 10.5.2 Momentum; 10.5.3 Wave Packets and Fourier Transforms

10.6 The Wave-Momentum Duality 10.7 Appendix: A Brief Review of Probability Densities; 11 Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism; 11.1 Introductory Remarks; 11.2 The Hilbert Spaces L2(R) (or L2(Rd)) and H1(R) (or H1(Rd)); 11.3 Dynamical Variables and Hermitian Operators; 11.4 Spectral Theory of Hermitian Operators: The Discrete Spectrum; 11.5 Observables and Statistical Distributions; 11.6 The Continuous Spectrum; 11.7 The Generalized Uncertainty Principle for Dynamical Variables; 11.7.1 Simultaneous Eigenfunctions

12 Applications: The Harmonic Oscillator and the Hydrogen Atom

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613332165

9781283332163

1283332167

9781118105740

1118105745

9781118105733

1118105737

9781118105764

1118105761

OCLC:

816871863