ME720A
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THERMOMECHANICS OF DISSIPATING CONTINUA
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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 z-transform 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, Differential-difference equations, Discrete Mechanics, Open problems.
Lecture wise Breakup
I. Lectures 1-2:
II. Lectures 3-4:
III. Lectures 5-6:
IV. Lectures 7-10:
V. Lectures 11-13:
VI. Lectures 14-16:
VII. Lectures 17-19:
VIII. Lectures 20-23:
IX. Lectures 24-27:
X. Lectures 28-31:
XI. Lectures 32-33:
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Thermodynamics of surfaces (Gibbs concept of excess quantities, surface energy, surface tension, surface stress, capillarity)
XII. Lectures 34-35:
XIII. Lectures 36-40:
References:
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The Mechanics and Thermodynamics of Continuous Media, M. Sˇilhavy ́, Springer, 1997.
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An Introduction to Thermomechanics, H. Ziegler, North-Holland, 1983.
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The Mechanics and Thermodynamics of Continua, M. E. Gurtin, E. Fried, and L. Anand, Cambridge, 2010.
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Theory of Thermal Stresses, B. A. Boley and J. H. Weiner, Dover, 1997.
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