Calculus Prerequisite for Math Stat I and II
Students in this mathematical statistics course are expected to be able to use many calculus techniques skillfully. Following is a list of most of the calculus topics used during this course.
- Find the derivative of any function covered in calculus classes, including exponential, logarithmic, and trigonometric functions.
- Use basic techniques of integration including substitution and integration by parts. Also be able to use integral tables.
- Be able to use the Fundamental Theorem of Calculus to do problems such as
- Find improper integrals (and be able to find when they do not converge.)
- Use L'Hospital's rule.
- Use Taylor approximations to functions and recognize sums as Taylor approximations for many basic functions such as .
- Use standard techniques for finding the sum of an infinite series, including recognizing geometric series.
- Find local and absolute extrema and points of inflection of functions.
- Use mathematical software to graph functions and find local and absolute extrema of functions that are analytically intractable. (It is possible to learn to do this quickly, on free software. More information is available.)
- Carry out all the calculus techniques on functions with parameters. (For example, find the local extrema and points of inflection of the probability density function of a normal distribution with parameters and .)
- Compute double integrals.
- Find local and absolute extrema of functions of two variables.