An Introduction to Mathematical Modeling – A Course in Mechanics

John Tinsley Oden, PhD, is Associate Vice President for Research and Director of the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin. He was the founding Director of the Institute, which was created in January of 2003 as an expansion of the Texas Institute for Computational and Applied Mathematics. A member of the U.S. National Academy of Engineering, the National Academies of Engineering of Mexico and of Brazil, and The American Academy of Arts and Sciences, he serves on numerous national and international organizational, scientific, and advisory committees including the NSF Blue Ribbon Panel on Simulation-Based Engineering Science and the Task Force on Cyber Science and Grand Challenge Communities and Virtual Organizations. Dr. Oden has worked extensively on the mathematical theory and implementation of numerical methods applied to problems in solid and fluid mechanics and, particularly, nonlinear continuum mechanics and, in recent years, multi-scale modeling, stochastic systems, and uncertainty quantification.

Preface. 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.