CSCI 3656 Course Materials:

• Logistics, Policies, Information:

  • Syllabus and Administrivia
  • A link to a page that describes the rare planetary alignment that's happening this weekend just after sunset.
  • The formula sheet. Any formulae that appear on this sheet will be provided to you if they are needed for the quizzes. (Translation: don't bother memorizing them, but make sure you know how to use them!) This document also gives some "study guide"-type hints.
  • Current ITS Scientific/Numerical Computing seminars and information (including a couple of good Mathematica tutorials).
  • Some info on the unix plotting tool gnuplot.
  • Some info on how to label plots in Mathematica .
  • A numerical analysis challenge problem posed by Nick Trefethen at Oxford.
  
  

• Recent Lecture Assignments:

  • Lecture 27 (Tuesday, 23 April):
    • Reading: ODE Notes through section 2.6, and pp462-463 of Gerald & Wheatley.
    • Problems: work on PA12.
  • Lecture 28 (Thursday, 25 April):
    • Reading: G&W section 6.5.
    • Problems: given the second-order ODE system x'' + xx' - t = 0 and the initial condition x(0)=1, x'(0)=2, find x(0.2) using the second-order Adams-Bashforth method with h=0.1. Solutions here.
  • Lecture 29 (Tuesday, 30 April):
    • Reading: none.
    • Problems: work on PA12/13.
  • Lecture 28 (Thursday, 2 May):
    • Reading: ODE Notes, section 3.
    • Problems: work on PA12/13.
  
  

  Old Lecture Assignments: click here

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  Programming Exercises:

  • 1. Plotting functions using Matlab and Mathematica, and computing Taylor series approximations : due 22 January. The CSCI 4676/4686 textbook has a good chapter on Matlab if you want to look something up or dig more deeply, and the ITS website has an nice online Mathematica plotting tutorial. If you have problems plotting or printing on a remote machine, click here for some pointers.
  • 2. Newton's method: due 5 February.
  • 3. The fixed-point method and deflation: due 12 February. Click here for some info on the gnuplot unix plotting tool. If you have problems with gnuplot, you might want to try using Mathematica's ListPlot function to plot your data: ListPlot[ {{1, 0.5}, {2, 0.45}, {3, 0.3}, ... } ]
  • 4. Linear algebra in Mathematica: due 21 February. Mathematica complains about fonts, you can try this solution .
  • 5. Solving sets of linear equations with Gauss-Jordan: due 26 February.
  • 6. Simple interpolation: due 12 March. Please use the same two-point linear interpolation code for all problems in this set.
  • 7. Splines: due 19 March. Here are the cubic Bezier curve equations.
  • 8. A real-world surface interpolation problem: due 2 April. Check out Bruce Fast's tutorial for some helpful hints. Some of the other ITS tutorials listed above may also be useful. Click here for an on-line version of the glacier data. Mathematica hint for problem 1: check out the help docs on the ListPlot3D or ScatterPlot3D commands. Note that you'll need to use Mathematica's "Graphics3D" package to use the latter:

    In[6]:= Needs["Graphics`Graphics3D`"];

    In[7]:= ScatterPlot3D[ {{33.44 87.93 105.88},{8.81 84.07 103.11}} ]

    (If you don't load the library, ScatterPlot3D will simply echo the points back at you.) Similarly, TriangularSurfacePlot "needs" DiscreteMath`ComputationalGeometry`.

  • 9. Numerical integration of data: due 9 April.
  • 10. Ordinary differential equations: due 16 April. If you didn't get a copy in class on 11 April, you should check out these notes on ordinary differential equations.
  • 11. Numerical solution of ordinary differential equations I: due 23 April. Again, you'll need the ODE notes to do this assignment.
  • 12. Numerical solution of ordinary differential equations II: Runge-Kutta and chaos: due 3 May.
  • 13. Numerical solution of PARTIAL differential equations: due at the final exam. This PA is optional. It will be used to replace one lower quiz score.

Liz's written notes:

• on Taylor series
• on error in numerical methods
• on ordinary differential equations (ODEs) and solving them numerically