• 771 Pages ElementsOfMATLAB
    ElementsOfMATLAB

    School: Colorado

    f P '! a # n R G # ' G f #! # d # %R9 6 f P 9 i S(vpIpoI(78I$gemIlkhj`Sdhpi i9 R a c # d A f9 R i P9 A t P A i G f # f P T 9 he(4Ieh5gedS$u&5IUIUSWIv 7x7w (WbI5U(S3 x % f G a f H P ' P 69 P 8$@SV x R 6 a y x 77w UI5a w Pv!p(I58u"sr5qphg`

  • 1 Page Assignment12
    Assignment12

    School: Colorado

    Course: Numerical Computation

    Assignment 12 CSCI 3656 due April 21, 2011 1. (a) On your computer approximate the derivative of the function f (x) = 2.0/(x2 + 3.2) exp(1.2x) at the point x = 1.3 using a two point forward dierence formula. Use as denominators the values h = 2k for k =

  • 1 Page Assignment11
    Assignment11

    School: Colorado

    Course: Numerical Computation

    Assignment 11 CSCI 3656 due April 14, 2011 1. The following set of simulated data gives the quantity of a decaying substance at various times. The substance is composed of three isotopes with decay rates 0.0, 0.8, and 0.9. If the initial quantities are de

  • 1 Page Assignment10
    Assignment10

    School: Colorado

    Course: Numerical Computation

    Assignment 10 CSCI 3656 due April 7, 2011 1. Given data (xi , yi ) for i = 1, . . . , n, in order to compute the cubic spline coecients (bi , ci , di ), you must (i) set up the equations (3.30) on page 175, (ii) solve the tridiagonal system by Gaussian el

  • 1 Page Assignment9
    Assignment9

    School: Colorado

    Course: Numerical Computation

    Assignment 9 CSCI 3656 due March 31, 2011 1. Suppose you constuct a polynomial approximation to the function f (x) = ln(x) on the interval [1,3]. If you use n equally spaced points, give an upper bound for the interpolation error using the error bound for

  • 1 Page Assignment8
    Assignment8

    School: Colorado

    Course: Numerical Computation

    Assignment 8 CSCI 3656 due March 17, 2011 1. For the data (xi , yi ) = (0, 6.0) (1, 4.0) (2, 3.0), (4, 7.0), a) Write down the Lagrange form of the interpolating polynomial p(x). (There is no need to algebraically multiply out the polynomial. Leave it in

  • 1 Page Assignment7
    Assignment7

    School: Colorado

    Course: Numerical Computation

    Assignment 7 CSCI 3656 due March 3, 2011 1. In Matlab the command A=hilb(10) will produce an 10 10 Hilbert matrix, i.e. A(i, j ) = 1/(i+j 1). Compute the right hand side vector b = Av , where v = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]T . (a) Solve the system Ax =

  • 1 Page Assignment6
    Assignment6

    School: Colorado

    Course: Numerical Computation

    Assignment 6 CSCI 3656 due February 24, 2011 1. (a) By hand use Gaussian elimination with scaled partial pivoting to nd the P, L and U factors of the matrix A: 2 4 1 2 A= 4 4 12 10 ; 6 Verify that P A = LU (b) Now use P, L, and U to solve Ax = b, where 2

  • 1 Page Assignment5
    Assignment5

    School: Colorado

    Course: Numerical Computation

    Assignment 5 CSCI 3656 due February 17, 2011 1. Solve the following system Ax = b by Gaussian elimination with partial pivoting. Use the partial pivoting rule described in class and in Section 2.4.1 of the text. Show all the steps. 4 A= 2 2 2 6 8 3 3 ; b

  • 1 Page Assignment4
    Assignment4

    School: Colorado

    Course: Numerical Computation

    Assignment 4 CSCI 3656 due February 10, 2011 1. Given that the distance in meters fallen from rest by a skydiver is y (t) = ln(cosh(t g k )/k. compute the time taken to fall 85 meters using Newtons method. Here, gravitational acceleration g = 9.8065 m/s/s

  • 1 Page Assignment3
    Assignment3

    School: Colorado

    Course: Numerical Computation

    Assignment 3 CSCI 3656 due February 3, 2011 1. Write a program to nd a root of a given equation f (x) = 0 by the method of bisection. Specications a) It should accept as input two starting points whose function values have opposite signs and a stopping to

  • 1 Page Assignment2
    Assignment2

    School: Colorado

    Course: Numerical Computation

    Assignment 2 CSCI 3656 due January 27, 2011 1. Find a more accurate way to calculate each of the following quantities. a) (x + a)3 a3 ; x close to 0, a near 1. b) (x y ) 1/(x + 2y ) when x > y > 0 1/ c) 1 + 6h 1; h near 0. 2. The quantity Q may be compute

  • 1 Page Assignment1
    Assignment1

    School: Colorado

    Course: Numerical Computation

    Assignment 1 CSCI 3656 due January 20, 2011 1. Express the following decimal quantities in binary: 26, 3/8, 91, 39/64. Now express each as rounded normalized machine numbers with base 2 and 4 bits of precision. 2. Consider a hypothetical computer using ba

  • 54 Pages MolecularDynamics
    MolecularDynamics

    School: Colorado

    e bU 8@5 7 !v A@ Ge 87v x 9 Y yE bU H Y 7 57 7 H e t H AAa H rbU bP U P v2ye 7 ybU Cv8tgs Y W 7 P Y H T a xe w u H frqFqdigbdbG`XVT p h f eU c aUY WU R H @E7 B @ 9 5 SQPIGFDCA8764 ' 1 ' ()#320)(&% $ " #! r70Yi5 d p

  • 674 Pages IEEEArithmetic
    IEEEArithmetic

    School: Colorado

    2 r 20 2 2 4TC g g 6 2 hf 30 P T r 76 Bg 3Sy i xpA hf xC t Q C P 2 y E wC t C u t r q i g f e d C Rt pT 7q RxpT hf hE vf E Sspg 2 ph9SQ (c a `Y W VV T PQ P b%51X%$UA SR(I G EC 6 A 2 8 6 4 20 HFDB%@97531) & # ( '$%$ " ! r70Y

  • 2 Pages review1
    Review1

    School: Colorado

    February 4, 2009 3. Special matrices and what they do or what their advantages are (a) identity (b) elimination (type of elementary matrix) (c) permutation (d) tridiagonal (e) symmetric 4. P A = LU (a) Existence (can be computed for every matrix) (b

  • 1 Page Assignment13
    Assignment13

    School: Colorado

    Course: Numerical Computation

    Last Assignment CSCI 3656 due April 28, 2011 1. Consider the initial value problem y (t) = 1.0/(1.0 + t2 ) 2.0[y (t)]2 . y (0) = 0 2 The exact solution is y (t) = t/(1.0 + t ). Write a program to solve this problem on the interval [0,5] using Eulers metho

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