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Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur only at critical points. For single-variable functions
Chapter 2 Deformation and Strain
In this chapter we explain how deformation is described precisely. This gives us the framework to model the deformation of a metal beam for example, which is holding up a building (although we wont do this problem here).
2
Chapter 3 Balance Laws
In this chapter we explore the governing eld equations: the conservation of mass and linear momentum, the balance of angular momentum, and the conservation of energy. Although we refer to these principles as laws, they are postulate
Chapter 4 Introduction to Thermodynamics
In this chapter we introduce the topic of thermodynamics which are needed to develop governing equations (specically constitutive equations) for a continuous medium. The development of constitutive equations will b
Chapter 5 The Entropy Inequality and Constitutive Equations
In the 1950s and 1960s, thermodynamics was combined with classical continuum mechanics to form a rational method for developing constitutive equations. These methods were pioneered by A. C. Ering
Chapter 6 Miscellaneous Topics
6.1 Boundary Conditions
After determining the governing equations one must determine appropriate boundary and initial conditions which make the problem physically meaningful and mathematically possible to solve. Mathematical
Project Information
Continuum Mechanics, Spring 2008 Due 4pm, Friday May 9, 2008 The project for this course consists of two parts: the written report and the oral report. The written report (worth 80% of the project grade) may be hand written or typed an
Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur only at critical points. For single-variable functions