TRI-COUNTY TECHNICAL COLLEGE

 COURSE SYLLABUS

 Course Prefix & Number:    __ MAT 130_________________ ____

Course Title:                          __ Elementary Calculus ____________

 Class  Hours                        Lab Hours                     Credits

Per week:  _3.0__                Per Week:  _0__           Awarded:  _3.0_

 Catalog  Description: This course includes the following topics:  differentiation and integration of polynomials, rational, logarithmic and exponential functions, and interpretation and applications of these processes.

 Entry Level Skills: College algebra facts and techniques

 Pre-requisites: College Algebra with Modeling, MAT 109 with a grade of C or better. 

Co-requisites: None

 Additional Information: Most colleges and universities do not award credit for both MAT 130 and MAT 140, so students should take care to enroll in the appropriate course

 Text(s)/Required Materials: Applied Calculus, special 3rd edition, by Hughes-Hallett, Gleason,

 Lock, Flath, et al., John Wiley & Sons, Inc., 2006.

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

 Course Competencies and Objectives/Major Course Topics:

 Unit 1:  Functions and Change

 Upon completion of this unit (Sections 1.1-1.9) the student should be able to:

 1.      Calculate the change of a function from a table of its values.

 2.      Calculate the average rate of change for a function.

 3.      Interpret the average rate of change in the context of an applied problem.

 4.      Relate a function to its graph and interpret the graph of an applied problem as a function.

 5.      Identify and construct linear functions.

 6.      Set up and solve problems applying functions to economics.

 7.      Set up and solve problems involving proportionality and power functions.

 8.      Recognize and describe functions which are concave up and concave down.

 9.      Identify and construct exponential and logarithmic functions.

 10.  Set up and solve problems involving compound interest and exponential growth and decay.

 11.  Apply shifts, stretches, and sums and compositions of functions to numerical, graphical, and analytical problems.

 12.  Describe the relationship between a polynomial and its graph, and solve problems involving polynomial functions.

 Unit 2:  Rate of Change:  The Derivative

 Upon completion of this unit (Sections 2.1-2.5) the student should be able to:

 1.      Relate information about the speed of an object to the graph of its position as a function of time.

 2.      Estimate numerically the instantaneous rate of change of a function defined analytically, graphically,  or numerically.

 3.      Solve problems involving the derivative of a function at a point and utilizing the  notation.

 4.      Sketch the graph of the derivative function of a function defined graphically.

 5.      Use the  notation and solve applied problems requiring an interpretation of the derivative.

 6.      Explain the interpretation of the second derivative, both analytically and in applied problems.

 7.      Solve economic problems involving cost and revenue.

 Unit 3:  Short-Cuts to Differentiation

 Upon completion of this unit (Sections 3.1-3.4) the student should be able to:

 1.      Calculate the derivatives of constants, powers of x, constant multiples of functions and polynomials.

 2.      Calculate derivatives of exponential and logarithmic functions.

 3.      Calculate derivatives of compositions of functions, using the Chain Rule.

 4.      Calculate derivatives of products and quotients of functions.

 Unit 4:  Using the Derivative

 Upon completion of this unit (Sections 4.1-4.4) the student should be able to:

 1.      Locate critical points of a function from its graph, a table of function values, and the formula for the function.

 2.      Determine whether a function has a local maximum or minimum at a given critical point.

 3.      Identify points of inflection of a function.

 4.      Find the global maximum and minimum of a continuous function defined on a closed interval.

 5.      Solve optimization problems involving profit and revenue.

 Unit 5:  The Integral

 Upon completion of this unit (Sections 5.1-5.5 and 7.1-7.3) the student should be able to:

 1.      Estimate the total distance covered by an object, given a table of its velocity at various times.

 2.      Estimate the total accumulated change of a quantity, given either a graph or a table of its rate of change.

 3.      Approximate a definite integral by calculating left-hand and right-hand sums.

 4.      Use a calculator or computer to calculate definite integrals numerically.

 5.      Find areas under curves using definite integrals.

 6.      Solve applied problems involving the definite integral; including problems where the marginal cost function is used to calculate the total cost.

 7.      Calculate the definite integral of a derivative, using the Fundamental Theorem of Calculus.

 8.      Calculate antiderivatives of polynomial functions.

 9.      Use antiderivatives to calculate definite integrals.

 Grade Calculation Method:   

 Grades for this course will be determined based upon the following criteria:

                  Five unit tests                                                   =         60 – 80 %

                  Homework/ Other assignments                  =            0 – 20 %

                  Comprehensive Final Exam                         =            15 – 20%

                                                TOTAL                                                      100%

  Prepared by_Gerald L. Marshall__   Date written or revised:_3/14/06__