TRI-COUNTY TECHNICAL COLLEGE

Pendleton, South Carolina

 Catalog Course Description:  This problem-based course extends the study of algebra, trigonometry, functions, vectors and basic calculus concepts.   Mathematical concepts are integrated with topics in material properties of matter in a problem-based learning environment.  Science, communications, and technology are integrated with mathematics throughout the course.  

Entry Level Skills: 

(1)      Apply logarithmic and exponential functions.

(2)      Graph trigonometric functions and apply complex numbers.

(3)      Apply fundamental trigonometric identities, inverses, equations, and introductory statistics.

(4)      Use polar/rectangular forms and conversions. 

Prerequisites:  MAT 182

Corequisites:  Enrollment in PHY 183 and EGR 183

Text(s):  Basic Technical Mathematics with Calculus by Allyn J. Washington (seventh  edition, 2000, Addison-Wesley Longman , Inc.).

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

                             Department Head                                 Division Chair

                            Dean of Instruction      

RATIONALE/GENERAL COURSE GOALS

The technical student needs to become familiar with the concepts of calculus as it is applied to technology problems.  This is especially true for the EET student as a tool in understanding electronics. 

The broad categories of these ideas and techniques are as follows: 

1.         Defining and calculating with the derivative.

2.         Applications of the derivative.

3.         Defining, calculating and applying the integral.

4.         The calculus of transcendental functions.

5.         An optional section on differential equations. 

SCHOOL-WIDE COMPETENCIES 

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

1.         read articles related to mathematics and write a summary of and a reaction to each article, using correct English and appropriate mathematical terminology;

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

3.         demonstrate basic concepts of differential and integral calculus and transcendental  functions;

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

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

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

7.         access computer-aided instructional programs as problem solving tools;

8.         demonstrate technical proficiency with a scientific calculator by performing skills appropriate to the course;

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

10.     set-up and calculate the solution to problems appropriate to the course;

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

UNIT REQUIREMENTS AND OBJECTIVES 

Project I:  The Derivative

The engineering technician works with physical phenomena that change.  The tool that mathematics uses to describe things that change is the rate of change.  The derivative is the instantaneous rate of change.  This first unit introduces the derivative after a brief review of functions, limits, and continuity.  Approximately 3½ weeks including testing, should be allowed for this unit. 

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

1.         translate a physical problem in function notation, identifying the dependent and independent variable, such as power is a function of current;

2.         identify and determine, using interval notation, the domain and range of a function;

3.         determine the limit of a function by using a calculator and applying the definition;

4.         determine points of discontinuity in equation form or on a graph;

5.         apply the four step process to differentiate a function;

6.         calculate a derivative at a given point;

7.          apply the constant and power rule in finding the derivative;

8.         apply the following rules in the differentiation of a function:

                        a) power

                b) product

             c) quotient

             d) chain

9.     differentiate a function implicitly;

10.     determine higher derivatives of a function. 

Textbook sections and suggested homework: 

This unit will cover the following sections:  3-1 (pp. 77-81), 3-2 (pp. 81-86), 3-4 (pp. 88-93), 3-6 (pp. 97-100), 23-1 (pp. 628-635), 23-2 (pp. 636-639) 23-3 (pp. 640-644), 23-4 (pp. 644-648), 23-5 (pp. 648-653), 23-6 (pp. 653-657), 23-7 (pp. 658-663 ), 23-8 (pp. 664-666), and 23-9 (pp. 666-670). 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 for you to master the material.

Project II:  Applications of the Derivative  

This unit will deal with the concepts and techniques of the derivative and its applications.  Some of these include tangents and normals, first and second derivative test, maximum and minimum, curvilinear motion, related rates, and differentials.  Approximately 3 weeks, including testing, should be allowed for this unit. 

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

1.         determine and apply the instantaneous rate of change, the derivative, to practical
problems such as current, velocity, voltage, acceleration, charge, area, volume, power and resistance;

2.         determine the equations of the tangent line and normal lines to a given curve;
apply the first derivative test to determine the extreme values of a given function and sketch its graph;

3.         determine the maximum or minimum value of resistance, power and current;

4.         use the second derivative test to determine concavity of a function and to sketch its graph;

5.         solve maximum and minimum problems such as minimizing power loss in a transmission line, the deflection of a beam, perimeter, area and volume problems, efficiency problems, etc.;

6.         determine velocity and acceleration vectors in curvilinear motion

7.         use implicit differentiation, solve related rate problems such as the change in current, rate of change of resistance, rate of change in distance, etc.;

Textbook sections and suggested homework: 

This unit will cover the following sections:  24-1 (pp. 674-678 ), 24-2 (pp. 678-681), 24-3 (pp. 681-685 ), 24-4 (pp. 686-689 ), 24-5 (pp. 690-695), 24-6 (pp. 696-699), 24-7 (pp. 700-706 ), 24-8 (pp. 706-710). 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 for you to master the material. 

Project III:  The Integral and the Antiderivative

While the derivative represents instantaneous change, the integral can be thought of as accumulated change.  It allows us to get information about the original function from its rate of change.  Graphically, the definite integral can be used to calculate the area under the curve.  We will see that integration and differentiation can be thought of as reverse processes.  Approximately 2½ weeks, including testing, should be allowed for this unit.  

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

1.         determine the antiderivative of a function;

2.         determine integrals using the basic formulas;

3.         calculate the area under a curve by using Riemann Sums;

4.         calculate definite integrals using the Fundamental Theorem of Integral Calculus;

5.         approximate the definite integral using the Trapezoid Rule and Simpson's Rule.  

Textbook sections and suggested homework: 

This unit will cover the following sections:  25-1 (pp. 715-717), 25-2 (pp. 718-722), 25-3 (pp. 723-727), 25-4 (pp. 728-730), 25-5 (pp. 731-734), and 25-6 (pp. 734-737). 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 for you to master the material. 

Project IV:  Applications of Integration  

Applications of integration will include, but not be limited to, velocity and displacement, voltage across a capacitor, area, volumes of rotation, centroids, moments of inertia, and work.  Approximately 2½ weeks, including testing should be allowed for this unit.

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

1.         use integration to find the velocity and displacement where appropriate;

2.         use integration to find the voltage across a capacitor;

3.         use integration to find the area under the curve;

4.         use integration to find the area between two curves;

5.         use integration to find volumes of rotation using shells or disks;

6.         use integration to find the centroid of an object;

7.         use integration to find the moment of inertia of an object;

8.         use integration to calculate the work done by a variable force. 

Textbook sections and suggested homework: 

This unit will cover the following sections: 26-1 (pp. 740-746 ), 26-2 ( pp. 746-751 ), 26-3 (pp.752-757 ), 26-4 (. 757-763 ), 26-5 (pp. 764-768 ), and 26-6 (pp. 769-774). 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 for you to master the material. 

Project V:  The Calculus of Transcendental Functions  

We need to discuss the calculus of the trigonometric, inverse trigonometric, logarithmic, and exponential functions.  A brief look at the derivative and integral of these transcendental functions will complete our calculus journey.  Approximately 2½ weeks, including testing, should be allowed for the unit. 

Upon completion of this unit the student should be able to differentiate and integrate transcendental functions by using appropriate tables.

Textbook sections and suggested homework: 

This unit will cover the following sections:  27-1 (pp. 778-783), 27-2 (pp. 784-787), 27-3 (pp. 787-790), 27-5 (pp. 796-799), 27-6 (pp. 800-803), 28-1 (pp. 811-814 ), 28-2 (pp. 814-817 ), 28-3 (pp. 817-823), 28-5 (pp. 824-828), and 28-6 (pp. 828-831). 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 for you to master the material. 

COURSE PROCEDURES 

Students in MAT 183 are part of an integrated curriculum that also includes EGR 183, ENG 183, and PHY 183.  All four courses must be taken together.  Grades will be kept separate for each course, but instructors will work closely together and students will be held responsible for material taught in all four courses, not only material taught in MAT 183.  Instructors will emphasize teaming skills and address different student multiple intelligences and learning styles.

Help outside class includes tutoring through full-time instructor office hours, Educational Services , Peer Tutoring  and the Learning Lab (OC 300). 

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 exact method of calculating your grade, which will include a comprehensive final exam, 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 

All forms of academic misconduct including, but not limited to, cheating on tests, plagiarism, collusion, and falsification of information will call for discipline.  Alleged violations will be handled according to College procedures.

A copy of the complete Procedure 3-2-1060.1, titled “The Student Code for the South Carolina Technical College System” can be reviewed in the Arts and Sciences Division Office.

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.