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8.022pset0 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 0: Math review/practice Post date: Tuesday, February 3rd Due date: Thursday, February 5th Be sure to write your name and section number on your pset Please staple multiple pages together The purpose of this assignment is to give you some inkling of the kind of math that you will be doing in 8.022. 1. Circle your recitation section: (a) R01 (b) R02 (c) R03 (d) R04 Remember your answer and write it on all 8.022 assignments (including this one!) and exams. 2. Partial derivatives and coordinate conversions (20 pts) (a) f ( x, y, z ) = 1 / x 2 + y 2 + z 2 . Compute ∂f/∂x , ∂f/∂y , and ∂f/∂z . (b) Defining the radial displacement vector ~ r = x ˆ x + y ˆ y + z ˆ z , write down a very simple form for the following quantity: ~ f ˆ x ∂f ∂x + ˆ y ∂f ∂y + ˆ z ∂f ∂z . (Note that the symbol means “is equivalent to” or “is defined as”. The symbol ~ is the gradient operator; some of you may already be familiar with it. The rest of you will be very soon!) (c) Convert to cylindrical coordinates. Put x = r c cos φ , y = r c sin φ ; leave z untouched. Compute ∂f/∂r c , ∂f/∂φ , ∂f/∂z .
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