By J. Tinsley Oden

A smooth method of mathematical modeling, that includes detailed functions from the sector of mechanics

An creation to Mathematical Modeling: A path in Mechanics is designed to survey the mathematical types that shape the rules of contemporary technological know-how and contains examples that illustrate how the main profitable types come up from uncomplicated rules in smooth and classical mathematical physics. Written by means of an international authority on mathematical thought and computational mechanics, the booklet offers an account of continuum mechanics, electromagnetic box conception, quantum mechanics, and statistical mechanics for readers with different backgrounds in engineering, laptop technology, arithmetic, and physics.

The writer streamlines a accomplished knowing of the subject in 3 truly geared up sections:

  • Nonlinear Continuum Mechanics introduces kinematics in addition to strength and rigidity in deformable our bodies; mass and momentum; stability of linear and angular momentum; conservation of strength; and constitutive equations

  • Electromagnetic box conception and Quantum Mechanics encompasses a short account of electromagnetic wave thought and Maxwell's equations in addition to an introductory account of quantum mechanics with similar subject matters together with ab initio equipment and Spin and Pauli's principles

  • Statistical Mechanics offers an advent to statistical mechanics of structures in thermodynamic equilibrium in addition to continuum mechanics, quantum mechanics, and molecular dynamics

Each a part of the ebook concludes with workout units that permit readers to check their figuring out of the awarded fabric. Key theorems and primary equations are highlighted all through, and an intensive bibliography outlines assets for extra study.

Extensively class-tested to make sure an available presentation, An creation to Mathematical Modeling is a superb e-book for classes on introductory mathematical modeling and statistical mechanics on the upper-undergraduate and graduate degrees. The ebook additionally serves as a worthy reference for execs operating within the components of modeling and simulation, physics, and computational engineering.

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Additional info for An introduction to mathematical modeling : a course in mechanics

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These examples show that in non equilibrium t Senior Research Associate with the National Fund for Scientific Research (Belgium). New Trends In Nonlmear Dynamlcs and Edited by P. Coullet and P. This seems also to be the case for many patterns and microstructures which form in driven or metastable materials and we expect that the methods developed for the study of instabilities and bifurcations of complex dynamical systems should be useful in the understanding of materials behavior as I will try to illustrate it briefly below.

This value is given by the strain rate, the macroscopic quantity determining the freeing of dislocations. \Valgraef, Acta (1988) 563-573. New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena Edited by P. CoulJet and P. Huerre Plenum Press, New York, 1990 ~fet. emo = g(ei) - = be, - (I) where g(e;) is the function describing the generation of the slow dislocations by the applied stress. The freeing rate b plays the role of the so--called bifurcation parameter; its magnitude determines the type of the solutions of eq.

Valgraef, Acta (1988) 563-573. New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena Edited by P. CoulJet and P. Huerre Plenum Press, New York, 1990 ~fet. emo = g(ei) - = be, - (I) where g(e;) is the function describing the generation of the slow dislocations by the applied stress. The freeing rate b plays the role of the so--called bifurcation parameter; its magnitude determines the type of the solutions of eq. (l). We limit the following discussion to one spatial dimension, the direction of primary slip, since PSB are essentially one-dimensional periodic structures.

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