An Introduction to Mathematical Modeling
A Course in Mechanics
Wiley Series in Computational Mechanics
1. Auflage November 2011
348 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
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.
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.
I. Nonlinear Continuum Mechanics.
1. Kinematics of Deformable Bodies.
2. Mass and Momentum.
3. Force and Stress in Deformable Bodies.
4. The Principles of Balance of Linear and Angular Momentum.
5. The Principle of Conservation of Energy.
6. Thermodynamics of Continua and the Second Law.
7. Constitutive Equations.
8. Examples and Applications.
II. Electromagnetic Field Theory and Quantum Mechanics.
9. Electromagnetic Waves.
10. Introduction to Quantum Mechanics.
11. Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism.
12. Applications: The Harmonic Oscillator and the Hydrogen Atom.
13. Spin and Pauli's Principle.
14. Atomic and Molecular Structure.
15. Ab Initio Methods: Approximate Methods and Density Functional Theory.
III. Statistical Mechanics.
16. Basic Concepts: Ensembles, Distribution Functions and Averages.
17. Statistical Mechanics Basis of Classical Thermodynamics.
Exercises.
References.
