MTH 252 Lecture Notes - Lecture 3: Hyperbola, Multivariable Calculus, Cartesian Coordinate System
7 Sep 2016
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The main questions from calc i and calc ii were: how fast is something moving? (differential, what is the average? (integral) Example: point p in oxford (say bell tower). We want to find the average daily temperature at point p during august. We could write to find the average temp. However, multivariable calculus can help us to find something broader, such as the average temperature change from a point p in all directions, or to find the average temperature of the entire northern hemisphere. A multivariable function has inputs that will be elements of r, , and. The outputs will be elements of r for now. Example: has input elements of , output of r. An example of an input of would be (this function gives the magnitude of the vector (x,y,z). We would like to see a geometric picture of these functions.
