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homework1 - Math 20F Lecture C(Winter 2008 Homework 1(Due...

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Unformatted text preview: Math 20F - Lecture C (Winter 2008) Homework 1 (Due on Wednesday, January 23rd by 3pm) *Please drop your homework off into the box on the 6th floor in the APM building. Note that there are separate boxes for the homeworks and Matlab assignments. Make sure to return it into the box for the homeworks and not for the Matlab assignments. *This homework covers sections 1.1-7 from your textbook. Some of the homework ques- tions may require the knowledge of variety of topics and the ability to put them together. Ideally before attempting these questions, you should first practice with some of the suggested questions listed on the course homework page. 1. (Sections 1.1, 1.2) In your physics lab you are given a T-shaped object illustrated below. You measure the temperatures at the left and right end-points as T l = 0 ◦ C and T r = 40 ◦ C , respectively. You are asked to approximate the temperatures at the internal nodes by the average of the adjacent nodes. Note that there are three nodes adjacent to the 2nd node, so T 2 is the average of T 1 , T 3 and T 4 . All other nodes have two adjacent nodes. T d T 1 T 2 T 3 T 4 T l = 0 ◦ C T r = 40 ◦ C (a) Suppose you can also measure the temperature at the bottom as T d = 50 ◦ C . Set up a system of four linear equations in four unknowns. Solve it by row reducing the associated augmented matrix into the reduced echelon form to determine T 1 , T 2 , T 3 , T 4 . (b) Suppose your instrument breaks and you cannot measure the temperature at the bot- tom. Find all possible set of temperatures for the internal nodes. You can view T d as a free variable; the temperatures at the internal nodes are basic variables that can be uniquely determined if T d was given....
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This note was uploaded on 07/01/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

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homework1 - Math 20F Lecture C(Winter 2008 Homework 1(Due...

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