MATH1052 Semester 1 2001

Practical Exercise 6

This practical exercise is to be done during Week 10. During the practical sessions for Weeks 8 and 9 you can spend time working on the project to be submitted in Week 9.

 

The graphics capabilities provided in MATLAB are useful for viewing the approximation to a surface given by the Taylor series form.

Assignment

  1. Consider the surface given by the function

    2. .

    Use MATLAB to draw the surface over the region 0 < x <2 and 0 < y < 2.

  2. Construct the tangent plane approximation

    3. about the point x0 = 1 and y0 = 1 by hand. Then use MATLAB to code the formulas and to plot the approximation g on the same figure as the surface f from the previous question. Remember to use the hold on command in order to plot more than one surface on the same set of axes.

  3. Construct the quadratic approximation

about the point x0 = 1 and y0 = 1 by hand (g is given by the expression above). Then use MATLAB to plot the approximation h on top of the previous two surfaces. You should observe that h is a better fit to the surface than g.