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math1cnotes1 - MA1C, WEEK 1: LEVEL CURVES AND LIMITS TA:...

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Unformatted text preview: MA1C, WEEK 1: LEVEL CURVES AND LIMITS TA: PADRAIC BARTLETT 1. Administrivia and Announcements So, before we begin, heres a series of random administrative things: These notes, like all future notes, can be found on my website . The easiest way to contact me if you have questions on the HW is via email! My address is padraic@caltech.edu. I have an office hour! From 8-9pm, on Sunday, in 155 Sloan (though if quite a few people show up, well just occupy a random nearby room.) The late HW policy has changed from last quarter. I.e. you are no longer allowed to turn in late HW . In the event that you become sick/calamities befall you/other such things, we need you to contact us by 10pm the night before the HW is due; furthermore, please only attempt this under fairly dire circumstances, as we have very little leeway to be merciful. If this is confusing, look at the course webpage, or contact any of us for further clarification! (as evidenced by the fact that Ive messed the details of this policy up twice by attempting to go from memory, this is possible.) Draw all of your pictures for this HW by hand. 2. Random Questions So: notice that if you glue together the sides of a square as depicted below, you get a doughnut (i.e. a torus). Question 2.1. Can you come up with a way to glue together a hexagon to get a torus? How about a way to glue together a octagon to get a 2-hole torus (i.e. a torus with two holes?) What other shapes can you make? 3. Level Curves So, the idea behind level curves is pretty simple: given a function f ( x,y ), we can come up with a 3-dimensional graph for f by drawing the curves C ( a ) = { ( x,y ) : f ( x,y ) = a } , and putting those curves on the plane z = a in the xyz-plane. If youve ever seen an elevation map or topographical map for a mountain range, 1 2 TA: PADRAIC BARTLETT this is exactly what were doing, (except our functions here are not necessarily representing mountain ranges. but you get the idea.) We work one explicit example here to give the idea of how these things go: Example 3.1. Draw the level curves of the function f ( x,y...
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This note was uploaded on 03/01/2011 for the course MA 01c taught by Professor Marsden during the Spring '10 term at Caltech.

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math1cnotes1 - MA1C, WEEK 1: LEVEL CURVES AND LIMITS TA:...

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