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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 |
Tabla de Contenidos:
- Machine generated contents note: 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. Piola Transformation
- 1.6. Polar Decomposition Theorem
- 1.7. Principal Directions and Invariants of Deformation and Strain
- 1.8. 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. Principles of Balance of Linear and Angular Momentum
- 4.1. Cauchy's Theorem: The Cauchy Stress Tensor
- 4.2. Equations of Motion (Linear Momentum)
- 4.3. Equations of Motion Referred to the Reference Configuration: The Piola
- Kirchhoff Stress Tensors
- 4.4. Power
- 5. 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. Coleman
- Noll Method: Consistency with the Second Law of Thermodynamics
- 8. Examples and Applications
- 8.1. 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. Schrodinger's Equation
- 10.4.1. Case of a Free Particle
- 10.4.2. Superposition in Rn
- 10.4.3. Hamiltonian Form
- 10.4.4. Case of Potential Energy
- 10.4.5. Relativistic Quantum Mechanics
- 10.4.6. General Formulations of Schrodinger's Equation
- 10.4.7. Time-Independent Schrodinger 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. 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. 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. Continuous Spectrum
- 11.7. Generalized Uncertainty Principle for Dynamical Variables
- 11.7.1. Simultaneous Eigenfunctions
- 12. Applications: The Harmonic Oscillator and the Hydrogen Atom
- 12.1. Introductory Remarks
- 12.2. Ground States and Energy Quanta: The Harmonic Oscillator
- 12.3. Hydrogen Atom
- 12.3.1. Schrodinger Equation in Spherical Coordinates
- 12.3.2. Radial Equation
- 12.3.3. Angular Equation
- 12.3.4. Orbitals of the Hydrogen Atom
- 12.3.5. Spectroscopic States
- 13. Spin and Pauli's Principle
- 13.1. Angular Momentum and Spin
- 13.2. Extrinsic Angular Momentum
- 13.2.1. Ladder Property: Raising and Lowering States
- 13.3. Spin
- 13.4. Identical Particles and Pauli's Principle
- 13.5. Helium Atom
- 13.6. Variational Principle
- 14. Atomic and Molecular Structure
- 14.1. Introduction
- 14.2. Electronic Structure of Atomic Elements
- 14.3. Periodic Table
- 14.4. Atomic Bonds and Molecules
- 14.5. Examples of Molecular Structures
- 15. Ab Initio Methods: Approximate Methods and Density Functional Theory
- 15.1. Introduction
- 15.2. Born
- Oppenheimer Approximation
- 15.3. Hartree and the Hartree
- Fock Methods
- 15.3.1. Hartree Method
- 15.3.2. Hartree
- Fock Method
- 15.3.3. Roothaan Equations
- 15.4. Density Functional Theory
- 15.4.1. Electron Density
- 15.4.2. Hohenberg
- Kohn Theorem
- 15.4.3. Kohn
- Sham Theory
- III. Statistical Mechanics
- 16. Basic Concepts: Ensembles, Distribution Functions, and Averages
- 16.1. Introductory Remarks
- 16.2. Hamiltonian Mechanics
- 16.2.1. Hamiltonian and the Equations of Motion
- 16.3. Phase Functions and Time Averages
- 16.4. Ensembles, Ensemble Averages, and Ergodic Systems
- 16.5. Statistical Mechanics of Isolated Systems
- 16.6. Microcanonical Ensemble
- 16.6.1. Composite Systems
- 16.7. Canonical Ensemble
- 16.8. Grand Canonical Ensemble
- 16.9. Appendix: A Brief Account of Molecular Dynamics
- 16.9.1. Newtonian's Equations of Motion
- 16.9.2. Potential Functions
- 16.9.3. Numerical Solution of the Dynamical System
- 17. Statistical Mechanics Basis of Classical Thermodynamics
- 17.1. Introductory Remarks
- 17.2. Energy and the First Law of Thermodynamics
- 17.3. Statistical Mechanics Interpretation of the Rate of Work in Quasi-Static Processes
- 17.4. Statistical Mechanics Interpretation of the First Law of Thermodynamics
- 17.4.1. Statistical Interpretation of Q
- 17.5. Entropy and the Partition Function
- 17.6. Conjugate Hamiltonians
- 17.7. Gibbs Relations
- 17.8. Monte Carlo and Metropolis Methods
- 17.8.1. Partition Function for a Canonical Ensemble
- 17.8.2. Metropolis Method
- 17.9. Kinetic Theory: Boltzmann's Equation of Nonequilibrium Statistical Mechanics
- 17.9.1. Boltzmann's Equation
- 17.9.2. Collision Invariants
- 17.9.3. Continuum Mechanics of Compressible Fluids and Gases: The Macroscopic Balance Laws.