TRI-COUNTY TECHNICAL COLLEGE

Pendleton, South Carolina

Catalog Course Description:  This course includes the following topics: advanced algebra; exponential and logarithmic functions; complex numbers; trigonometric identities, and graphs of trigonometric functions.  Additional topics may include statistics and discrete mathematics.  (INDUSTRIAL AND ENGINEERING TECHNOLOGY) 

Entry Level Skills: 

Prerequisites:  MAT 175 

Corequisites:  None 

Text(s): Basic Technical Mathematics with Calculus, by Allyn J. Washington (7th. edition, 2000,Addison-Wesley  publishing Co., Inc.)

Equipment: Graphing calculator (TI-83, TI-83 Plus or TI-89 recommended) 

                           Department Head                                 Division Chair

                        Dean of Instruction                              

RATIONALE

MAT 176 is the second course in mathematics for general engineering, electrical engineering, engineering graphics, and quality assurance technology majors.  The engineering technology student needs to use as well as understand more advanced algebra and trigonometry to solve problems in the technology and physics courses as well as future work.  Additionally, algebra and trig functions are learned and practiced to ensure success for calculus.

The broad categories of these ideas and techniques can be stated in competencies.  The student should be able to do as follows:

1.      Apply logarithmic and exponential functions.

2.      Graph trigonometric functions and apply complex numbers.

3.      Apply fundamental trigonometric  identities, inverses, equations as well as introductory statistics.

4.      Apply the equations and graphs of the circle, parabola, ellipse, and hyperbola as well as use polar/rectangular coordinate conversion and nonlinear equations.

5.      An optional category contains some degree three polynomial solution techniques and inequalities through degree three, including linear programming techniques.

SCHOOL-WIDE COMPETENCIES

Upon completion of this course, the student should be able to:

1.      read verbal problems and choose an appropriate strategy for solving the problem;

2.      ask and answer questions using correct English and appropriate mathematical terminology;

3.      demonstrate basic concepts, methods, techniques and applications of arithmetic, algebra, geometry, and measurement systems;

4.      demonstrate responsibility and self-discipline by meeting deadlines;

5.      demonstrate self-discipline by contributing positively in group activities;

6.      access appropriate resources such as journals, magazines, and books to accomplish skills appropriate to the course;

7.      set up and calculate the solutions to problems appropriate to the course;

8.      determine appropriate strategies for solving a problem, given certain facts and data;

9.      interpret results and determine whether the solution is realistic for a particular problem;

10.  positively function and contribute to collaborative group activities.

UNIT REQUIREMENTS AND OBJECTIVES

Unit 1 Logarithmic and Exponential Functions

This unit will deal with the concepts of exponential and logarithmic functions, their properties and their graphs. Approximately  3½ weeks, including testing should be allowed for this unit.

Upon completion of this unit the student should be able to:

1.      express given exponential equations in logarithmic form;

2.      rewrite given logarithmic equations in exponential form;

3.      solve logarithmic equations finding real number solutions for variables in any of the three positions;

4.      sketch graphs of functions of the form y = ln x  or y = log x, including applications in growth, decay, strength of materials, and chemical reaction;

5.      rewrite sums and differences of logarithms in order to manipulate pressure equations;

6.      write given expressions as the sum, difference, or multiple of logarithms and vice versa;

7.      use common logarithms to calculate ph and power supply output;

8.      find common and natural logarithms and their antilogarithms on a scientific calculator;

9.      use natural logarithms to calculate gas pressures, radio-active element behavior, angular displacement, electrical power and current;

10.  plot curves resulting from pressure/volume and pendulum period/length experiments on log-log paper;

11.  determine whether semilog or log-log paper will make the graph of a given equation a straight line and then sketch that graph.

Textbook sections and suggested homework.

This unit will cover the following sections: 13.1 (pp.351-354), 13.2 (pp.354-357), 13.3 (pp.358-361), 13.4 (pp.362-364), 13.5 (pp.365-367), 13.6 (pp.368-371), and 13.7 (pp.372-375).  Your instructor may assign specific problems for you to do; however, doing all the odd numbered problems will give you the required drill and applications necessary for you to master the material.

Unit 2 Graphs of Trigonometric Functions and Equations

This unit will cover the graphs of the sine and cosine functions with phase shifts, applications, and addition of ordinates.  In addition it will cover the solution of equations in quadratic form and solutions of radical equations.  Approximately   3 weeks including testing should be allowed for this unit.

Upon completion of this unit the student should be able to:

1. use radian measure, sketch the graphs of the functions y = a sin ( bx + c ) and y = cos ( bx + c ) for given constants a,b,and c;

2.  solve applications of the trigonometric graphs including simple harmonic motion and AC circuits;

3.  use the method of addition of ordinates to sketch given curves of sums and differences of trigonometric functions, including applications in Fourier series and current in a circuit;

4.  solve quadratic type of equations arising from applications such as in machine plate design;

5.  solve equations that include square roots arising from impedance in a circuit, solving right triangles and light refraction.

Textbook sections and suggested assignments:

This unit will cover sections :  10.1 (pp.276-280), 10.2 (pp.280-283) and 10.3 (pp.283-287). Your instructor may assign specific problems for you to do; however, doing all the odd numbered problems will give you the drill, and applications necessary to master the material.

Unit 3 Complex Numbers and Polar Coordinates

This unit deals with the concepts of polar coordinates, the transformations from polar to rectangular and vice-versa, the concepts and definitions of complex numbers, their fundamental operations in rectangular and polar, and phasors.  Approximately  2½ weeks including testing should be allowed for this unit.

Upon completion of this unit the student should be able to:

1.   plot points in polar coordinates;

2.      express polar points on rectangular form and vice versa; convert rectangular form equations to polar form and vice versa;

3.      express square roots of negative numbers in terms of imaginary numbers;

4.      locate a given number and its conjugate in the complex plane;

5.      add and/or subtract two complex numbers graphically; add, subtract, multiply, and divide complex numbers algebraically; simplify powers of imaginary numbers;

6.      write a complex number in rectangular, polar, and exponential form, given any one of the three forms;

7.      recognize which form of a complex number is the most efficient to use for a given operation, doing that operation in that form and then being able to convert it back to the original form of the complex number.

Textbook sections and suggested assignments:

This unit will cover the following sections:  12.1(pp.321-325), 12.2 (pp.325-327), 12.3 (pp.328-329), 12.4 (pp.330-332) , 12.5 (pp.333-335), and 12.6 (pp.336-341), 12.7(pp.342-347).  Your instructor may assign specific problems; however, doing all the odd problems will give you the required drill and applications to master the material.

Unit 4 Trigonometric Identities, Inverses, and Equations

This unit will cover the concepts and techniques of the fundamental trigonometric identities including the sum, difference, and double angle formulas, trigonometric equations, and trigonometric inverses.  Approximately  2½ weeks including testing should be allowed for this unit.

Upon completion of this unit the student should be able to:

1.      use fundamental trigonometric identities to simplify a given expression or to change to an equivalent expression involving only sines and cosines;

2.      simplify current and wave equations using the sine and cosine of the sum or difference of two angles;

3.      simplify given expressions using the double angle formulas;

4.      solve given trigonometric equations;

5.      evaluate arc or inverse trigonometric functions with and without using a calculator.

Textbook sections and suggested assignments:

This unit will cover  the following sections:  20.1 (pp.510-516), 20.2 (pp.517-521), 20.3 (pp.522-525), 20.4 (pp.525-528), 20.5 (pp.529-533) and 20.6 (pp.533-539).  Your instructor may assign you specific problems; however, doing all the odd problems will give you the required drill and applications necessary to master the material.

Unit 5 Introductory Statistics

This unit will cover the concepts and techniques of statistics in a SPC environment to include graphical presentations of data, measures of central tendency and measures of dispersion. Approximately  2½ weeks including testing should be allowed for this unit.

Upon completion of this unit the student should be able to do:

1.      construct stem-and-leaf displays, histograms, and frequency polygons;

2.      find the arithmetic mean, the median, and the mode of a data set;

3.      calculate the range, variance, and standard deviation of a data set;

4.      calculate the upper and lower control limits and determine the target value for a process control chart, then use sample data to determine whether the process is in or out of control.

Textbook sections and suggested assignments:

This unit will cover the following sections:  22.1 (pp.591-596), 22.2 (pp.596-600), 22.3 (pp.600-604), and 22.6 (pp.614-619). Your instructor may assign you specific problems; however, doing all the odd problems will give you the required drill and applications necessary to master the material.

INSTRUCTION METHOD

This course is taught using a variety of techniques and methods that address different learning styles.  Class notes are expected, as well as scientific calculator use.  Additional help is available in several forms as follows:

a)      Your instructor will be more than willing to give special help over problem areas.  Please do not hesitate to ask for assistance. Office hours are posted outside the instructors office in Oconee Hall.

b)      The Learning Lab ( Room OC-300) is staffed with a lab instructor trained in mathematics who will be glad to help you with whatever problems you encounter.  Also in that lab are printed and computer materials available for your help.  Some of these are listed earlier in this syllabus and the lab instructor will assist you in finding and using these materials.

c)      You may apply for one-on-one tutoring through Educational Services  in the Counseling Center.

EVALUATION

All courses taught by full-time and part-time faculty members of the mathematics department of Tri-County Technical College will be graded according to the following:

1.     Letter grades assigned for numerical averages will be:

                                   90 - 100     A

                                   80 - 89       B

                                   70 - 79       C

                                   60 - 69       D

                                   Below 60   F

2.   The course total numerical average will be calculated by averaging unit test scores, a final comprehensive examination, and, at the instructor’s discretion, a term paper/project and classwork/homework score.  The exact method of calculating your grade will be announced by your instructor at the beginning of the course.  The final exam will count no less than a unit test and no more than 20% of the final grade.

3.     Make-ups for missed tests will be given at the discretion of the instructor.  The instructor’s policy will be distributed on the first day of class.  It is the students’ responsibility to understand that policy should any questions arise. 

TRI-COUNTY TECHNICAL COLLEGE’S GRADING POLICY

The following grading system is used for credit courses:

A         Excellent                       “A” is used in GPA calculations, earns credit hours, and carries a value of 4 grade points for each credit hour.

B          Above Average            “B” is used in GPA calculations, earns credit hours, and carries a value of 3 grade points for each credit hour.

C         Average                       “C” is used in GPA calculations, earns credit hours, and carries a value of 2 grade points for each credit hour.

D         Below Average             “D” is used in GPA calculations, earns credit hours, and carries a value of 1 grade point for each credit hour.

F          Failure                          “F” is used in GPA calculations, earns no credit hours, and carries 0 grade points for each credit hour attempted.  (When the student retakes the course, the “F” is negated and the higher grade is used in GPA calculations.)

WF      Withdrawn – Failing      “WF” is used in GPA calculations, earns no credit hours, and carries 0 grade points for each credit hour attempted.  (When the student retakes the course, the “WF” is negated; and the higher grade is used in GPA calculations.)  “WF” may be given from the first day after the tenth week through the last day of class before the final examination period if the student is failing.  (The time period for awarding “WF” grades will be prorated for ten-week summer session terms and for other terms of varying lengths.)

W        Withdrawn                   “W” is not used in GPA calculations, earns no credit hours, and generates no grade points.

ATTENDANCE POLICY

Tri-County Technical College believes that class attendance is crucial to student success.  Therefore, any student who accumulates more absences during the semester than the class meets in a two-week period is subject to being dropped from the class.  The number of allowable absences during the summer term or other terms of varying length will be 10% of the total number of class meetings.

A student who arrives late may, at the discretion of the instructor, be marked absent for that class.  A student who continually arrives late to class is subject to being dropped from the class.  In extenuating circumstances, a student may request readmittance to class by meeting with the instructor and explaining the circumstances of the absences.  If the instructor agrees to readmit the student, the student will be informed of the requirements which must be met to successfully complete the course.

ARTS AND SCIENCES DIVISION POLICY ON ACADEMIC DISHONESTY

1.      Academic dishonesty as used here includes using another’s work without giving credit to the source and cheating.

2.      Charges of academic dishonesty must be substantiated by evidence.

3.      The instructor has the option of dealing with a first offense in one of two ways:

a.   giving an “F” or a “0” for that particular assignment.

b.   demanding that the student redo the assignment.

4.      With second offenses, the instructor may assign a grade of “F” for the course.

5.      The student may appeal the decision to the Faculty-Student Behavior Committee.

STUDENTS WITH DISABILITIES

If you have a documented disability and require special assistance or accommodations, please contact the Coordinator of Counseling in the Counseling Center.

FIRE EMERGENCY PROCEDURE

Fire extinguishers, fire alarm pull boxes, and evacuation maps are located in strategic areas throughout the buildings.

In the event of a fire, the person discovering the fire must do the following:

1.      Activate the pull box.

2.      Obtain an outside line by dialing 9.  If you cannot obtain an outside line, contact the switchboard operator at extension “0" and ask for an outside line.

3.      Dial 911 and report the location of the fire.

4.      Dial 1800 (Security) and let ring at least ten times.

Inform security that fire alarm box has been activated and 911 called.  Controllable fires should be dealt with by the appropriate application of fire extinguishers and other fire control equipment.

At the instance of an alarm, all faculty and staff are responsible for seeing that the following items are accomplished:

1.      All students clear the classroom and building in a rapid and orderly manner and proceed to a site at least fifty feet from the building.

2.      The instructor will close the door when the last student has cleared the classroom.

General Information

1.      All individuals in a building should be evacuated in a rapid and orderly manner.  “All individuals” includes handicapped individuals who should be assisted in whatever manner is required to place them in a safe location.

2.      If a fire occurs in one of the extension locations of the College, faculty and students are to follow the guidelines established by the extension.  Extension locations include such places as B.J. Skelton Career Center, Easley High School, or the Anderson Mall.

3.      Injuries as a result of a fire should be dealt with according to Procedures 4-8-1010.2, Employee Illness and Injury and 4-8-1010.3, Student Illness and Injury.

The administrator responsible will provide guidelines suitable for dissemination and posting and will distribute them to all faculty and staff at the beginning of each term.  The procedure for fire emergencies must be included in each syllabus.