Homework

First Midterm Thursday October 16

Second Midterm Tuesday December 2

Final Exam Thursday December 11 10:45 am

• Due Thursday 9/4
  • Section 1.1 5, 8, 9, 11, 12a,b&c, 14, 23, 24, 25, 29.
• Due Thursday 9/11
  • Section 1.2 1,6,11-14
  • Section 1.3 1,7, 12
• Click for exemplar assignment
  • Section 2.1 1,2,4,9,10,11
  • Figure out how to add labels and plot
    • x⁴-5x²+4 on [-3,3] and
    • x³-x²-2x+3 on [-5,5].
    Print these and turn them in. You can look at my plots but yours should be labeled with your name....e-mail me your .m files. Use the naming convention that all of your filenames begin with your first and last initials.
  • Section 2.2 1, 3, 5, 8, 9, 14, 15.
• Due Thursday 10/2
  • Right click on this link to save this file and play with it. Print graphs of a number of diffferent Euler solutions, use your textbook problems for suggestions or make up your own functions. Comment,
  • Section 2.4 9, 10.
  • section 2.5 11, 16, extra credit 17.
• Due Tuesday 10/14
  • Section 3.1 9
  • Graph the functions from problem 3 section 3.3 using either Matlab or Mathematica, use this to identify appropriate intervals using the x₀ given as one end point, for the Bisection Method. Print your graphs and comment on what you expect to find when you apply Bisection and Newton's method to them. Write programs to implement both the bisection method and Newton's method. Have your programs return all successive root approximations. Print these for the following: Complete problem 3 section 3.3. Also test your Bisection program on these functions where possible, using the same error tolerance. Did your results match your expectations?
  • Section 3.2 1-4; 6-9
  • Read section 3.3 and do problem 1
  • Read section 3.5 and do problems 6 and 7.
• Due Tuesday 11/4
  • You can find my spreadsheet from class here.
  • Complete problems 1-3, 7 from section 4.2.
  • Graph and find the roots of the polynomial p(x) = 8x⁴ - 8x² +1 (use whatever package you like for this but print your graph and comment).
  • Construct cubic polynomials to interpolate f(x) = e^x, f(x) = cube root(x) and f(x) = ln(2+x) using two different sets of interpolation points, the equally spaced points: {-1, -1/3, 1/3, 1} and the roots you found to the polynomial above (all of which are on the interval [-1,1]). plot the functions, the errors and the interpolating polynomials on the interval {-1,1]. Comment.
  • In general the maximum error for the previous examples should be smaller for the zeros of that polynomial nodes than for the equally spaced nodes. Extra credit if you find an example function where this difference is dramatic.
  • Here is my Script file and my Divided Difference function to do problem 3.
  • Here is the mathematica notebook for the tchebycheff nodes.
• Due Thursday 11/13
  • Section 4.6 1,2
  • Section 4.8 2-5, 18
  • Play with this Spline interpolation notebook and produce a few interesting interpolation graphs. Comment.
  • Find the 4th degree polynomial interpolant to f(0), f'(0), f"(0), f'"(0) and f(2) for f(x) = x⁵-x³-x²+x+1, p(x), using a generalized divided difference table. Graph f(x), p(x) on the same axes and f(x) - p(x).
  • Here is my spreadsheet for this problem and here is my notebook
• Due Thursday 11/20
  • Section 5.3 6, 7, 8
  • Section 6.1 1-6
• Due Tuesday 12/2
  • Section 6.5 6

Copyright 2012 K.M.Shannon all rights reserved.