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An introduction to mathematical modeling : a course in mechanics /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
©2011.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Oden, J. Tinsley |q (John Tinsley), |d 1936- |1 https://id.oclc.org/worldcat/entity/E39PBJqVYC43qcvCyvqg9rbjmd | |
| 245 | 1 | 3 | |a An introduction to mathematical modeling : |b a course in mechanics / |c J. Tinsley Oden. |
| 260 | |a Hoboken, N.J. : |b Wiley, |c ©2011. | ||
| 300 | |a 1 online resource (xiv, 334 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 317-323) and index. | ||
| 520 | |a "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."-- |c Provided by publisher | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |g Machine generated contents note: |g I. |t Nonlinear Continuum Mechanics -- |g 1. |t Kinematics of Deformable Bodies -- |g 1.1. |t Motion -- |g 1.2. |t Strain and Deformation Tensors -- |g 1.3. |t Rates of Motion -- |g 1.4. |t Rates of Deformation -- |g 1.5. |t Piola Transformation -- |g 1.6. |t Polar Decomposition Theorem -- |g 1.7. |t Principal Directions and Invariants of Deformation and Strain -- |g 1.8. |t Reynolds' Transport Theorem -- |g 2. |t Mass and Momentum -- |g 2.1. |t Local Forms of the Principle of Conservation of Mass -- |g 2.2. |t Momentum -- |g 3. |t Force and Stress in Deformable Bodies -- |g 4. |t Principles of Balance of Linear and Angular Momentum -- |g 4.1. |t Cauchy's Theorem: The Cauchy Stress Tensor -- |g 4.2. |t Equations of Motion (Linear Momentum) -- |g 4.3. |t Equations of Motion Referred to the Reference Configuration: The Piola -- Kirchhoff Stress Tensors -- |g 4.4. |t Power -- |g 5. |t Principle of Conservation of Energy -- |g 5.1. |t Energy and the Conservation of Energy -- |g 5.2. |t Local Forms of the Principle of Conservation of Energy -- |g 6. |t Thermodynamics of Continua and the Second Law -- |g 7. |t Constitutive Equations -- |g 7.1. |t Rules and Principles for Constitutive Equations -- |g 7.2. |t Principle of Material Frame Indifference -- |g 7.2.1. |t Solids -- |g 7.2.2. |t Fluids -- |g 7.3. |t Coleman -- Noll Method: Consistency with the Second Law of Thermodynamics -- |g 8. |t Examples and Applications -- |g 8.1. |t Navier -- Stokes Equations for Incompressible Flow -- |g 8.2. |t Flow of Gases and Compressible Fluids: The Compressible Navier -- Stokes Equations -- |g 8.3. |t Heat Conduction -- |g 8.4. |t Theory of Elasticity -- |g II. |t Electromagnetic Field Theory and Quantum Mechanics -- |g 9. |t Electromagnetic Waves -- |g 9.1. |t Introduction -- |g 9.2. |t Electric Fields -- |g 9.3. |t Gauss's Law -- |g 9.4. |t Electric Potential Energy -- |g 9.4.1. |t Atom Models -- |g 9.5. |t Magnetic Fields -- |g 9.6. |t Some Properties of Waves -- |g 9.7. |t Maxwell's Equations -- |g 9.8. |t Electromagnetic Waves -- |g 10. |t Introduction to Quantum Mechanics -- |g 10.1. |t Introductory Comments -- |g 10.2. |t Wave and Particle Mechanics -- |g 10.3. |t Heisenberg's Uncertainty Principle -- |g 10.4. |t Schrodinger's Equation -- |g 10.4.1. |t Case of a Free Particle -- |g 10.4.2. |t Superposition in Rn -- |g 10.4.3. |t Hamiltonian Form -- |g 10.4.4. |t Case of Potential Energy -- |g 10.4.5. |t Relativistic Quantum Mechanics -- |g 10.4.6. |t General Formulations of Schrodinger's Equation -- |g 10.4.7. |t Time-Independent Schrodinger Equation -- |g 10.5. |t Elementary Properties of the Wave Equation -- |g 10.5.1. |t Review -- |g 10.5.2. |t Momentum -- |g 10.5.3. |t Wave Packets and Fourier Transforms -- |g 10.6. |t Wave -- Momentum Duality -- |g 10.7. |t Appendix: A Brief Review of Probability Densities -- |g 11. |t Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism -- |g 11.1. |t Introductory Remarks -- |g 11.2. |t Hilbert Spaces L2(R) (or L2(Rd)) and H1(R) (or H1(Rd)) -- |g 11.3. |t Dynamical Variables and Hermitian Operators -- |g 11.4. |t Spectral Theory of Hermitian Operators: The Discrete Spectrum -- |g 11.5. |t Observables and Statistical Distributions -- |g 11.6. |t Continuous Spectrum -- |g 11.7. |t Generalized Uncertainty Principle for Dynamical Variables -- |g 11.7.1. |t Simultaneous Eigenfunctions -- |g 12. |t Applications: The Harmonic Oscillator and the Hydrogen Atom -- |g 12.1. |t Introductory Remarks -- |g 12.2. |t Ground States and Energy Quanta: The Harmonic Oscillator -- |g 12.3. |t Hydrogen Atom -- |g 12.3.1. |t Schrodinger Equation in Spherical Coordinates -- |g 12.3.2. |t Radial Equation -- |g 12.3.3. |t Angular Equation -- |g 12.3.4. |t Orbitals of the Hydrogen Atom -- |g 12.3.5. |t Spectroscopic States -- |g 13. |t Spin and Pauli's Principle -- |g 13.1. |t Angular Momentum and Spin -- |g 13.2. |t Extrinsic Angular Momentum -- |g 13.2.1. |t Ladder Property: Raising and Lowering States -- |g 13.3. |t Spin -- |g 13.4. |t Identical Particles and Pauli's Principle -- |g 13.5. |t Helium Atom -- |g 13.6. |t Variational Principle -- |g 14. |t Atomic and Molecular Structure -- |g 14.1. |t Introduction -- |g 14.2. |t Electronic Structure of Atomic Elements -- |g 14.3. |t Periodic Table -- |g 14.4. |t Atomic Bonds and Molecules -- |g 14.5. |t Examples of Molecular Structures -- |g 15. |t Ab Initio Methods: Approximate Methods and Density Functional Theory -- |g 15.1. |t Introduction -- |g 15.2. |t Born -- Oppenheimer Approximation -- |g 15.3. |t Hartree and the Hartree -- Fock Methods -- |g 15.3.1. |t Hartree Method -- |g 15.3.2. |t Hartree -- Fock Method -- |g 15.3.3. |t Roothaan Equations -- |g 15.4. |t Density Functional Theory -- |g 15.4.1. |t Electron Density -- |g 15.4.2. |t Hohenberg -- Kohn Theorem -- |g 15.4.3. |t Kohn -- Sham Theory -- |g III. |t Statistical Mechanics -- |g 16. |t Basic Concepts: Ensembles, Distribution Functions, and Averages -- |g 16.1. |t Introductory Remarks -- |g 16.2. |t Hamiltonian Mechanics -- |g 16.2.1. |t Hamiltonian and the Equations of Motion -- |g 16.3. |t Phase Functions and Time Averages -- |g 16.4. |t Ensembles, Ensemble Averages, and Ergodic Systems -- |g 16.5. |t Statistical Mechanics of Isolated Systems -- |g 16.6. |t Microcanonical Ensemble -- |g 16.6.1. |t Composite Systems -- |g 16.7. |t Canonical Ensemble -- |g 16.8. |t Grand Canonical Ensemble -- |g 16.9. |t Appendix: A Brief Account of Molecular Dynamics -- |g 16.9.1. |t Newtonian's Equations of Motion -- |g 16.9.2. |t Potential Functions -- |g 16.9.3. |t Numerical Solution of the Dynamical System -- |g 17. |t Statistical Mechanics Basis of Classical Thermodynamics -- |g 17.1. |t Introductory Remarks -- |g 17.2. |t Energy and the First Law of Thermodynamics -- |g 17.3. |t Statistical Mechanics Interpretation of the Rate of Work in Quasi-Static Processes -- |g 17.4. |t Statistical Mechanics Interpretation of the First Law of Thermodynamics -- |g 17.4.1. |t Statistical Interpretation of Q -- |g 17.5. |t Entropy and the Partition Function -- |g 17.6. |t Conjugate Hamiltonians -- |g 17.7. |t Gibbs Relations -- |g 17.8. |t Monte Carlo and Metropolis Methods -- |g 17.8.1. |t Partition Function for a Canonical Ensemble -- |g 17.8.2. |t Metropolis Method -- |g 17.9. |t Kinetic Theory: Boltzmann's Equation of Nonequilibrium Statistical Mechanics -- |g 17.9.1. |t Boltzmann's Equation -- |g 17.9.2. |t Collision Invariants -- |g 17.9.3. |t Continuum Mechanics of Compressible Fluids and Gases: The Macroscopic Balance Laws. |
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