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Unformatted text preview: CS 205a Fall 2010 Midterm 1 Please write your name on the top right of the first page. The exam is closed book and no calculators are allowed. You have 1 hour and 15 minutes to complete the exam. There are two extra pages at the end if you run out of space. Please clearly state if you use those pages. Total Points: 40. Quadrature (10 pts) 1. Given a function f ( x ) and an interval [ a, b ], state the Midpoint rule and the Trapezoidal rule that approximate R b a f ( x ) dx . (6 pts) 2. What is the relationship between local error and global error? (2 pts) Prove it. (2 pts) 1 Interpolation (10 pts) 1. Construct the basis functions for Newton Interpolations of degree 2 at sample points x = 0 , 1 , 2. (3 pts) 2. Now constuct the basis functions for the Lagrange Interpolation of degree 2 at sample points x = 0 , 1 , 2. (3 pts) 2 3. Using the results from (2) and the same sample points, construct the Lagrange interpolation polynomial of degree 2 for the function f ( x ) = x 2 . Show all the steps. (4 pts) 3 ODE/Finite Difference (10 pts)...
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This note was uploaded on 01/05/2012 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.
 Fall '07
 Fedkiw

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