Detailed objectives for MATH 243.
At the end of MATH 243 the student will be able to perform the following tasks. Ability
to perform these tasks will be measured using tests, homework, and projects. Objectives
are segmented to correspond to the main focus of the examinations as outlined in the
general syllabus. The overlap in the objectives between different segments of the course
is to emphasize that some topics will be the focus of several tests. As a general rule,
every examination should be considered cumulative. References in parentheses are to the
global objectives presented at the end of this document.
1. Classify improper integrals as convergent or divergent. (2,4)
2. Calculate the value of a convergent improper integral. (2,4)
3. Calculate integrals numerically using the midpoint, trapezoidal or Simpson’s rule.
(1,4)
4. Estimate the error in the numerical computation of an integral. (1,4)
5. Determine the number of partitions needed to approximate an integral to a certain
accuracy. (1)
6. Distinguish between the cumulative distribution function and the probability density
function. (2)
7. Calibrate nonnegative functions so they become probability density functions. (2)
8. Calculate probabilities of events in random phenomena given the cumulative
distribution function or the probability density function. (2)
9. Model random phenomena using the uniform, and exponential distributions. (2)
10. Determine parameters of a probability density function to fit given specifications. (2)
11. Calculate probabilities of events in random phenomena given the cumulative
distribution function or the probability density function. (2)
12. Model random phenomena using the uniform, exponential and normal distributions.
(2)
13. Determine parameters of a probability density function to fit given specifications. (2)
14. Calculate mean and standard deviation of a given distribution. (2)
15. Calculate the center of mass of a linearly distributed mass. (2,4)
16. Apply the central limit theorem to estimate the reliability of data gathered through a
sample of a given size. (2)
17. Apply the central limit theorem to calculate the number of samples needed to achieve
a certain confidence level for a measurement. [This data can be used to design
measurements.] (1,2)
18. Calculate confidence intervals for normally distributed phenomena. (1)
19. Design a pseudorandom number generator for a given distribution. (2)
20. Calculate scalar and vector products in 3-space, (3)
21. Calculate areas and volumes using scalar and vector products, (3)
22. Calculate any of the forms of the equation of a straight line in 3-space when given
a) Two points,
b) A point and a direction. (3)
23. Calculate any of the forms of the equation of a straight line in 3-space when given
a) Two points,
b) A point and a direction. (3)
24. Calculate any of the forms of the equation of a plane in 3-space when given
a) Three points,
b) A point and two directions,
c) A point and a normal vector. (3)
25. Calculate the intersection of a line with a plane or the intersection of two lines. (3)
26. Calculate the distance from a point to a line or a plane. (3)
27. Translate points and equations between rectangular, cylindrical and spherical
coordinates. (3,4)
28. Calculate limits of functions of several variables. (3,4)
29. Calculate double integrals by solving iterated integrals. (4)
30. Apply Fubini’s Theorem. (4)
31. Calculate double integrals in rectangular or polar coordinates. (4)
32. Determine which coordinate system to use when solving a multiple integral. (4)
33. Model solids (not necessarily with constant density) as regions in two and threedimensional space. (4)
34. For a given solid, calculate the volume, mass, center of mass and the first and second
moments about a given axis. (4)
Primary course objectives. The framework for our course objectives is given by the
ABET2000 engineering criteria, which list the following desired outcomes for
engineering graduates.
Engineering programs must demonstrate that their graduates have:
1) An ability to apply knowledge of mathematics, science, and engineering,
2) An ability to design and conduct experiments, as well as to analyze and interpret
data,
3) An ability to design a system, component, or process to meet desired needs,
4) An ability to function on multi-disciplinary teams,
5) An ability to identify, formulate, and solve engineering problems,
6) An understanding of professional and ethical responsibility,
7) An ability to communicate effectively,
8) The broad education necessary to understand the impact of engineering solutions in a
global and societal context,
9) A recognition of the need for, and an ability to engage in life-long learning,
10) A knowledge of contemporary issues,
11) An ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice.
This course focuses mainly on outcomes 1, 2, 3, 4, 5, 7 and 11. The primary course
objectives for this class as they relate to the above are as follows.
Objective 1. The student will be able to analyze/predict the error in a numerical
integration or the uncertainty in a statistical evaluation of data. (1,2,3)
Objective 2. The student will be able to model and interpret phenomena influenced by
randomness. (1,2,3,5,6)
Objective 3. The student will be able to analyze the relationship between given points,
lines, planes, and 2-dimensional surfaces in 3-space. (1,5,7)
Objective 4. The student will be able to compute the volume, mass, center of mass of
solid bodies by representing the body as a sum of differential objects or by modeling the
surface of the body with two-dimensional functions. (1,5,7)
Achievement of the objectives will mainly be demonstrated by satisfactorily completing a
series of exams and homework assignments.