Technical Mathematics at Volunteer State Community College
The mathematics department at Volunteer State Community College now offers a five semester hour course entitled, "Mathematics for Industrial Technology." In the past, the college has offered mathematics courses for general education, engineering, and business majors. The technical mathematics offering is a new direction.
In the fall of 1998 the college and Bosch Braking Systems joined with Nashville State Technical Institute to offer, for the first time, an 80 hour degree program for Bosch employees. Upon successful completion of the program these employees will receive an Associate’s Degree in Industrial Technology. The timing of this program and of this Education Edge grant initiative provided an opportunity to develop an excellent technical mathematics course.
An important component of this degree program is the technical mathematics course. The authors built into this grant project the objective of developing an up-to-date mathematics course. The advantage here would be that the authors could develop this course in conjunction with people in business and industry who use mathematics every day.
After interviews and consultation with industry personnel, a new technical mathematics course emerged for the fall semester, 1998. Initially, this course will serve those in the Bosch Associate’s Degree Program. However, it has the flexibility to serve the general population of students interested in a career in technology. It can also be used in other specialized programs that the college may design with other companies engaged in technological pursuits.
Appendix A provides a description of the syllabus for the new technical
mathematics course.
Appendix A:
Mathematics 165
Mathematics for Industrial Technology
Description: An integrated course in algebra, geometry,
and trigonometry. Topics
include but are not limited to: basic geometry,
elements of trigonometry, solving
systems of equations using determinants and matrices,
vectors, oblique triangles,
complex numbers, exponential and logarithmic functions,
variation, conic sections,
elementary statistics, elements of statistical process
control, and metric measurement. Designed primarily for students in an
Associates of Applied Science
program in conjunction with a particular industry.
Prerequisites: Two years of high school algebra
and an acceptable score on the
AAPP placement test, or DSM 086. The ability to use a
graphing calculator is
strongly recommended.
Instructor: ________________________ Office: ____________
Telephone Extension ______
Office Hours: Posted outside office door.
Textbooks: Basic Technical Mathematics with
Calculus (Metric Version), Allyn J.
Washington, Addison-Wesley Pub., 6th edition, (1995)
Student’s Solution Manual Basic Technical Mathematics,
Frances
Bazen Willbanks, Anne Ziegler, Addison-Wesley Pub., 6th
edition, (1995)
Graphing Calculator Lab Manual for the Allyn J. Washington
Series in
Basic Technical Mathematics, Robert E. Seaver,
Addison-Wesley
Pub., 6th edition, (1995)
General Education Goals: As a result of successfully completing
this course, the student will have
a sufficient mathematical foundation which will enable him or her to
perform correct calculations and
solve problems in an industrial setting.
Other Goals: In addition to performing mathematical operations
and becoming adept at problem
solving, the student should be able to communicate his or her solution
to a larger group in a clear and articulate manner.
Outcome Statements: Upon successful completion of this course,
the student will have
demonstrated the ability to perform each of the following operations.
1. Find the perimeter and area of the following two-dimensional figures:
square, rectangle, circle,
parallelogram, triangle, and trapezoid.
2. Measure angles in radians as well as degrees.
3. Use Simpson’s Rule to find the area of irregularly shaped figures.
4. Find the surface area and volume of the following three-dimensional
figures: cube, right circular
cylinder, right prism, right circular cone, regular
pyramid, sphere.
5. Solve contextual problems using all of the above mentioned concepts.
6. Find all of the following trigonometric ratios for any right triangle:
sine, cosine, tangent, cosecant,
secant, cotangent.
7. Given the appropriate information, be able to find any missing part
of a right triangle in the context
of an applied problem.
8. Find all of the trigonometric ratios of a general angle using the
correct sign whether the angle is
given in degrees or radians.
9. Convert any angle from radians to degrees and vice-versa.
10. Find the length of any circular arc.
11. Find the area of any circular sector.
12. Find the linear and angular velocity of any object moving in a circular motion.
13. Find the vector components of any object moving in any direction
on a two-dimensional
coordinate axis system.
14. Use the Law of Sines and the Law of Cosines to find any part of a general triangle.
15. Add, subtract, multiply, and divide complex numbers.
16. Find and simplify the product and quotient of any complex number in polar form.
17. Use DeMoivre’s Theorem to find any power or root of a complex number in polar form.
18. Use complex numbers to solve applied problems involving voltage,
current, reactance,
impedance, phase angle, capacitive reactance,
and inductive reactance.
19. Graph any exponential or logarithmic function.
20. Use the properties of exponents and the properties of logarithms
to solve logarithmic and
exponential equations.
21. Change the base of any logarithm to either base 10 or base e.
22. Interpret and create graphs of data on semi-log or log-log paper.
23. Find the any unknown part of a proportion.
24. Solve any applied problem where quantities vary directly, inversely, or jointly with each other.
25. Prove any trigonometric identity using the eight basic trigonometric
identities, the sum and
difference identities, the double-angle
identities, and the half-angle identities.
26. Solve for any angle given a trigonometric function of that angle.
27. Simplify and solve a trigonometric equation to find an unknown angle.
28. Use the distance formula to find the distance between any two points
on a coordinate axis
system.
29. Find the slope of any line and apply it to various situations such as carpentry and road building.
30. Find, in any form, the equation of a straight line given the appropriate information about it.
31. Use the equation of a straight line to write a formula expressing one variable in terms of another.
32. Find all of the forms of the equation of a straight line i.e. point-slope,
slope-intercept, and
general.
33. Find the coordinates of the center and the radius of a circle given
its equation either in standard
of general form.
34. Given the coordinates of the center and the radius of a circle,
write the equation for it in
standard form.
35. Given a set of data, arrange it into frequency distributions by
intervals, set up a frequency
distribution table, and represent the
data graphically by either a histogram or frequency polygon,
or both.
36. Given a set of data, find the measures of central tendency i.e. mean, median, mode.
37. Given a set of data, find the standard deviation.
38. Use the Method of Least Squares to find the equation of the line
that best fits a set of points
obtained by collecting two sets of data.
39. Extend the Method of Least Squares to find the equation of the nonlinear
curve which best fits a
set of points obtained by collecting
two sets of data.
40. Use the basic definitions of Statistical Process Control (SPC) to
create and correctly interpret
the following charts: X-R, np, p, c,
and u.
41. Use dimensional analysis to convert units within the metric system
as well as convert from metric
to English and vice-versa.
42. Graph and interpret equations of the forms: y = a sin x, y = a cos
x, y = a sin bx, y = a cos bx,
y = a sin (bx + c), y = a cos
(bx + c).
43. Solve problems involving phenomena described by the equations in item 42 above.
Mathematics for Industrial Technology
Topical Outline
* Coverage may be modified to accommodate particular industry needs.
Units of Measurement; the Metric System
Introduction
Reductions and Conversions
Basic Geometry
Lines and Angles
Triangles
Quadrilaterals
Circles
Measurement of Irregular Areas
Solid Geometric Figures
The Trigonometric Functions
Angles
Defining the Trigonometric Functions
Values of the Trigonometric Functions
The Right Triangle
Application of Right Triangles
Determinants and Matrices
Determinants: Expansion by Minors
Some Properties of Determinants
Matrices: Definitions and Basic Operations
Multiplication of Matrices
Finding the Inverse of a Matrix
Matrices and Linear Equations
Trigonometric Functions of Any Angle
Signs of the Trigonometric Functions
Trigonometric Functions of Any Angle
Radians
Applications of the Use of Radian Measure
Vectors and Oblique Triangles
Introduction to Vectors
Components of Vectors
Vector Addition by Components
Applications of Vectors
Oblique Triangles, the Law of Sines
The Law of Cosines
Graphs of Trigonometric Functions
Graphs of y = a sin x and y = a cos x
Graphs of y = a sin bx and y = a cos bx
Graphs of y = a sin (bx + c) and y = a cos (bx + c)
Applications of Trigonometric Graphs
Complex Numbers
Basic Definitions
Basic Operations with Complex Numbers
Graphical Representation of Complex Numbers
Polar Form of a Complex Number
Exponential Form of a Complex Number
Products, Quotients, Powers, and Roots of Complex Numbers
An Application to Alternating Current (ac) Circuits
Variation
Ratio and Proportion
Variation
Additional Topics in Trigonometry
Fundamental Trigonometric Identities
Sine and Cosine of the Sum and Difference of Two Angles
Double-Angle Formulas
Half-Angle Formulas
Solving Trigonometric Equations
The Inverse Trigonometric Functions
Plane Analytic Geometry
Basic Definitions
The Straight Line
The Circle
Introduction to Statistics and Empirical Curve Fitting
Frequency Distributions
Measures of Central Tendency
Standard Deviation
Fitting a Straight Line to a Set of Points
Fitting Nonlinear Curves to Data
Statistical Process Control
X-R Charts
p charts
c charts
np charts
u charts
Problem Solving Tools
Assessment Techniques
Outcome statements will be assessed through in-class quizzes, tests,
and problem solving. In addition, take-home assignments will be given.
These assignments will involve application of course topics to various
problem-solving situations. Homework problems will be assigned at each
class meeting and discussed at each subsequent class meeting.
Evaluation and Attendance Policies
Evaluation: There will be 5 major tests (not including the final examination)
during the semester. The
major tests will be at least one hour in length. Each major test will
count 100 points. There will also
be several announced quizzes which will be 10-20 minutes in length.
Each quiz will count 20 points.
Only the BEST FIVE quizzes will count toward the final grade in the
course.
There will also be two special project assignments to be completed outside
of class and turned in. These assignments will be worth 25 points each.
Homework will be assigned at each class meeting.
It may be done in any format desired (i.e., loose leaf notebook, spiral
notebook, folder..). It will be checked at the end of the semester for
completeness and effort. Homework will count a maximum of 50 points.
There will be a final examination which will be selectively comprehensive.
It will be worth 100
points. There is a total of 800 possible points to obtain.
Final grades will be assigned according to the following totals.
5 major tests = 500 points
5 best quizzes = 100 points
2 projects = 50 points
homework = 50 points
final exam = 100 points
720 - 800 points = A
640 - 719 points = B
560 - 639 points = C
480 - 559 points = D
0 - 479 points = F
Total = 800 points
Incomplete "I" Grade
A grade of "I" is designed only for severe emergencies such as car failure
on the day of the final
examination, death in the family, serious illness, or some life changing
event. It will not be given in
the situation where a student is merely behind in his or her work.
Inclement Weather Policy
If the College is closed due to extreme weather, this class will not
meet and any events planned, i.e.
test or quiz, will occur at the next class meeting. If the College
is open, class will be held as usual.
Also any work due to be handed in on the date of a canceled class will
be due at the next regularly
scheduled meeting.
Attendance
Prompt and regular attendance is expected. Attendance will be recorded
at every meeting. The College is required by federal law to keep attendance
records for purposes of financial aid. See
page 52 of the current catalog (1998-99).
Honesty Policy
Honorable and ethical behavior is expected regarding all course work.
In any case where cheating is
suspected, the student will be required to take an alternate test or
do an alternate assignment.
In any case where there is absolute proof of cheating on any part of
any course work, the student will receive an F in the course. Final decisions
in these matters rest solely with the instructor.
Make-Up Work
Due to the frequency of quizzes, a missed quiz will not be made up and
will be counted as a dropped grade. The first missed major test will be
replaced by the student’s grade on the final exam. If a
student misses a second major test, he or she will be allowed to take
a make-up test of significantly
greater difficulty to replace that grade. This policy is in force regardless
of the reasons why a student misses a test or a quiz.
Final Note
A mathematics class is driven by the question and answer format among
all the participants, student
and teacher alike. Therefore, everyone in the class is encouraged to
ask a question or open
discussion of a problem at any time. Some class time will be devoted
to group work and group and
individual presentations of problems and solutions. Everyone will be
expected to be an active
member of the class.
American Disabilities Act
In compliance with the American Disabilities Act, it is the student’s
responsibility to contact their
instructors concerning any special accommodations required for completion
of course requirements.
Volunteer State Community College is an equal opportunity Affirmative
Action Educational Institution. No person shall be excluded from the participation
in, be denied the benefit of,
or be subjected to discrimination under any program or activity
of the College because of
race, color, national origin, age or handicap.
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