CH E374 Lecture Notes - Lecture 3: Invertible Matrix, Linear Combination, Lincoln Near-Earth Asteroid Research

• School: University of Alberta
• Department: Chemical Engineering
• Course: CH E374
• Professor: Joe Mmbaga

Document Summary

Lecture notes che 374 computational methods in engineering. Based on the s. c. chapra chapter 8,9,10 and 11. Introduction & example: steady state temperature distribution in a rod. Linear algebraic equations can arise when modelling distributed systems (remember from our introductory lecture distributed systems are those systems where the dependent variable varies with position) Consider a metal rod whose ends are kept at a constant temperature, but the rod is free to lose heat to the surroundings from its sides as shown in figure 1 below. Figure 1: heat loss from a heated rod. The temperature distribution in the rod is given by the following equation (3. 1) In order to solve this equation (a mathematical model) numerically, we divide the rod into a number of nodal points as shown below and the equation is approximated at these nodes (discretization) Figure 2: node distribution for a heated rod. 22()0dthatatdx we need to find the approximation for the first derivative.