ME720A

THERMOMECHANICS OF DISSIPATING CONTINUA



Consice Sylabus:
Introduction to the Course and Some Applications of Difference Equations in Engineering, Preliminaries in linear algebra and analysis, Analogies between differential and difference equations, Elementary Difference Operations: the Difference and the Shift operators, The Difference and Summation Calculus, Linear difference equations, First order equations, Higher Order Difference Equations, Linear difference equations with constant coefficients, Linear difference equations with variable coefficients, Method of undetermined coefficients and variation of parameters, Generating functions, The ztransform and its applications, Systems of Linear difference equations and applications, The Sturmian theory and Fourier techniques, Asymptotic methods, Limiting behavior of solutions, Nonlinear difference equations and boundary value problems, Stability theory and relevance to dynamical systems, Partial Difference Equations, Differentialdifference equations, Discrete Mechanics, Open problems.
Lecture wise Breakup
I. Lectures 12:
II. Lectures 34:
III. Lectures 56:
IV. Lectures 710:
V. Lectures 1113:
VI. Lectures 1416:
VII. Lectures 1719:
VIII. Lectures 2023:
IX. Lectures 2427:
X. Lectures 2831:
XI. Lectures 3233:

Thermodynamics of surfaces (Gibbs concept of excess quantities, surface energy, surface tension, surface stress, capillarity)
XII. Lectures 3435:
XIII. Lectures 3640:
References:

The Mechanics and Thermodynamics of Continuous Media, M. Sˇilhavy ́, Springer, 1997.

An Introduction to Thermomechanics, H. Ziegler, NorthHolland, 1983.

The Mechanics and Thermodynamics of Continua, M. E. Gurtin, E. Fried, and L. Anand, Cambridge, 2010.

Theory of Thermal Stresses, B. A. Boley and J. H. Weiner, Dover, 1997.
