If the Mosaic account of cosmogony (the account of the creation in Genesis) is strictly correct, the sun was not created till the fourth day. And if the sun was not created till the fourth day, it could not have been the cause of the alternation of day and night for the first three days. But either the word “day” is used in Scripture in a different sense from that in which it is commonly accepted now or else the sun must have ben the cause of the alternation of day and night for the first three days. Hence it follows that either the Mosaic account of the cosmogony is not strictly correct or else the word “day” is used in Scripture in a different sense from that in which it is commonly accepted now.[...]
Posted in Calculus IV, Classes on February 12th, 2007 No Comments »
In Calculus IV on Thursday, February 8th, we covered the derivation of tangent planes. We also showed how the tangent plane for functions of 2 variables generalizes to functions of several variables, a process we call linearization.
We had no homework assignments due on Thursday, so I dove right into lecture. We proved a few more results following for our ordering of the reals. Upon completing these theorems, we were then able to do the basic sorts of solving of inequalities we teach in our lowest level of algebra. It is interesting that we get to one of final senior undergraduate courses and start doing things we do in the earliest mathematics courses, but this time, we’ve built our understanding of these rules from the ground up. Have no fear, analysis students, we will go much, much beyond those mathematical tools we used intermediate algebra.
On Wednesday, last week, we completed our material over elementary matrices, using them to derive the inverse of a matrix. Upon proving that a matrix is non-singular (i.e., invertible) if and only if it is row equivalent to the identity, we noticed that the same row operations that change a matrix A into the identity will change the identity into the inverse of A.