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An Introduction to Mathematical Modeling. A Course in Mechanics. Wiley Series in Computational Mechanics - Product Image

An Introduction to Mathematical Modeling. A Course in Mechanics. Wiley Series in Computational Mechanics

  • ID: 2176674
  • November 2011
  • 344 Pages
  • John Wiley and Sons Ltd

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics

An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics.

The author streamlines a comprehensive understanding of the topic in three clearly organized sections:

Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations

Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory READ MORE >

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.

“The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.” (Zentralblatt MATH, 2012)

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