Mathematics 126 -- Calculus for Social Sciences 2

Exam 3 -- Things to Know

November 19, 2001

General Information

As announced in the course syllabus, the third full-period exam of the semester will be given in class on Friday, November 30. As on the previous exams, there will be seven or eight questions (maybe grouped together) similar to problems from the problem sets from this part of the course. You may use a graphing calculator on this exam, but calculators like the TI 89 or 92 with symbolic manipulation are not allowed on this or any other exam.

If there is interest, we could schedule a review session Tuesday evening on November 27 or Wednesday afternoon on November 28. (Other times will not work for me, unfortunately. I have orchestra rehearsals in Boston both Wednesday and Thursday evening the week of the exam, so I will not be available those evenings.) We will discuss this in class on Monday, November 26.

Material To Know

The exam will cover from the material on applications of separable differential equations (Section 9.3), through the problems dealing with maxima/minima of functions of several variables from Section 8.3 (Monday, November 19). The material on constrained max/min problems and Lagrange Multipliers (Monday, November 26 and Wednesday, November 28) will not be covered on this exam (but it may appear on the final). Specifically, you should know the following topics. (The problems listed with each will be good review problems to look at.)

• Applications of separable differential equations -- Section 9.3/1,3,8,10,11,12,13,14,15
• Probability distributions of random variables (density functions) -- problems like Section 10.1/13-29 odd numbers, 31, 35, 36, 37
• Expected value and standard deviation -- problems like Section 10.2/5,7,9,11,13,15,16,19
• Normal distributions and applications -- problems like Section 10.3/15-31. (Note: I will provide a copy of the table of values of the function F(z) = P(Z <= z) for the standard normal Z (mean 0, standard deviation 1) from pages 900-901 of the text for you to use on the exam. You should know the transformation formula for converting a normally distributed random variable with a different mean and standard deviation to the standard one.)
• Functions of several variables, level curves, etc. Problems like Section 8.1/11-24,28-31.
• Partial derivatives. Problems like Section 8.2/33-40, 43, 44, 45
• Finding maxima/minima of functions of two variables -- critical points, the second derivative test, applied story problems. Problems like Section 8.3/1-25 odd numbers. Note: Due to short time left in the semester, there will not be another individual problem set on this material. You should definitely work these problems to make sure you understand this topic!