Continuum Mechanics I

At the end of this course, the students should be able to: 1. strengthen their background in the basic prerequisites to Continuum Mechanics; 2. master vector analyses, tensor theory and kinematics; 3. develop the ability to use general models and equations that apply to all materials in solid, liquid, gaseous or any combination of forms; and 4. explain the differential and integral formulations of the governing equations.

Mathematical preliminaries for continuum mechanics. Linear Independence, basis vectors, dimensionality. The Einstein summation convention. Scaling, scalar, vector and tensor products. Cartesian and curvilinear orthogonal coordinate systems. Tensors as linear transformations. Tensor invariants. Additive and multiplicative decompositions. Differentiation of vectors and tensors. Gradient, divergence and curl. Integral theorems of stokes and gauss. Use of symbolic algebra and computed graphical illustrations. Thermodynamic laws. Prerequisite: GET 301, GET 302