{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAD4401 Test1 - Name MAD 4401 Numerical Analysis Keesling...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Name MAD 4401, Numerical Analysis Keesling Test 1 9/21/11 Do all problems. Show your work and explain your answers. Each problem is worth 20 points. 1. Estimate the using Romberg Integration. Use up to 32 subdivisions in the Composite Trapezoidal Rule. Circle the best estimate of the integral. Use five digits in the first four columns. Use twelve digits for entries in the last two columns. How many digits can you expect to be correct in this answer? Explain. n = 1 n = 2 n = 4 n = 8 n = 16 n = 32 2. Give the Newton-Cotes coefficients for n = 1,2,3,4 . n = 1 a 0 = a 1 = n = 2 a 0 = a 1 = a 2 = n = 3 a 0 = a 1 = a 2 = a 3 = n = 4 a 0 = a 1 = a 2 = a 3 = a 4 = 1 1 + x 2 dx 4 4
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. The n th Legendre polynomial is given by the derivative formula. Use this to determine the polynomial formulas for the Legendre polynomials for n = 0,1,2,3,4,5 , and n = 10. 4. Find the roots of the third degree Legendre polynomial on the interval [-1,1].
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}