EML 5060 Analysis in Mechanical Engineering 9/16/98
Closed book Van Dommelen 11:00-11:50am

Show all reasoning and intermediate results leading to your answer. One book of mathematical tables, such as Schaum's Mathematical Handbook, may be used.

1.

A graduate student will probably spent about 12.5 hours of study outside class for each 3 credit hour class. But that does not necessarily mean that you spent 12.5 hours a week on Continuum Mechanics and 12.5 hours on Analysis in Mechanical Engineering! Assume that your grade in Analysis can be computed as

$$g_a = 1 + 3 \sqrt{t_a\over 25},$$ (1)

where t_a is the time you spent studying on Analysis each week. So, you will get 1 grade point, a D, with no study and 4 grade points, an A, if you study 25 hours per week on Analysis alone. Also assume that your grade in Continuum Mechanics is

$$g_c = 2 + 2 \sqrt{t_c\over 25},$$ (2)

where t_c is the time you spent studing on Continuum Mechanics each week. Find the maximum grade point average GPA,

$$GPA = {g_a + g_c\over 2}$$ (3)

that you can get if t_a + t_c = 25, i.e. if you study 25 hours on Analysis and Continuum Mechanics combined. How much of the 25 hours would you spent on Analysis? Solution.

2.

Oblique shock waves in supersonic flows are described by the ``shock polar"

$$(2-x) y^2 = (1-x)^2 (x - {\textstyle\frac12})$$ (4)

Draw this curve as accurately as possible. Derive all symmetries, intercepts, extents, asymptotes, and behavior at large |x|. Solution.

3.

Find the centroid of half a sphere by multiple integration. Solution.