TRI-COUNTY TECHNICAL COLLEGE

COURSE SYLLABUS

Catalog Course Description: This course includes the following topics:  partial derivatives; extrema problems; multiple integration; continuous probability distributions; difference equations; management and economic applications.

Entry Level Skills:   (1)  Be able to apply the fundamental concepts of limits and continuity to polynomial, rational, algebraic, and exponential and logarithmic functions.  (2) Be able to find and evaluate the derivative of polynomial, rational, algebraic, and exponential and logarithmic functions.  (3)  Use the concepts of the differential calculus in the solution of problems in economics, agriculture, business, and the social sciences.  (4)  Apply the concepts of definite integration to set up and solve numerically problems involving total accumulated change of a quantity, area under a curve, and Riemann sums.

Prerequisites:  MAT 130, Elementary Calculus

Text:  Applied Calculus, customized 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:                                                                     

Instructional Goals:  The goals of this course are to provide students with:

1.         an introduction to the basic concepts of integral calculus of one variable;

2.         an introduction to the basic concepts of the calculus of two variables;

3.         an understanding of the basic methods and techniques of multivariable calculus;

4.         an introduction to differential equations;

5.         continued development of skills and understanding in mathematical modeling;

6.         experience with basic applications of the calculus especially to business and economics, the life sciences, managerial sciences, and the social sciences;

7.         continued fostering of the critical thinking abilities and analytical skills.

Unit 1:  Differentiation and Integration Concepts and Techniques

Upon completion of this unit (Sections 2.2-3, 3.3-4, 5.1-5) the student should be able to:

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

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

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

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

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

Unit 2:  Integration Techniques and Applications

Upon completion of this unit Sections 6.1-4, 7.1-4) the student should be able to:

1.         calculate antiderivatives of polynomial, exponential, reciprocal functions, and their sums, differences, and constant multiples.

2.         use antiderivatives to calculate definite integrals.

3.         apply the integral to solve problems involving average values, consumer and producer surplus, and present and future value.

4.         calculate improper integrals, if they converge.

Unit 3:  Functions of Several Variables

Upon completion of this unit (Sections 9.1-5) the student should be able to:

1.         Determine the domain of a multivariable function and compute individual function values.

2.         Sketch and interpret contour diagrams of functions of two variables.

3.         Calculate first and second order partial derivatives of a given function.

4.         Use partial derivatives to estimate values of a function.

5.         Estimate partial derivatives given a contour diagram.

6.         Solve optimization problems for functions of several variables.

Unit 4:  Multiple Integration and Probability

 (You received copies of sections 16.1, 16.2, 16.3, 16.6 of Calculus—Single and Multivariable, 4th Ed., by Hughes-Hallett, Gleason, Lock, McCallum, et al., John Wiley & Sons, Inc., 2005 as a part of the special edition of the textbook for this course.) 

Upon completion of this unit (Sections 16.1-3, 8.1-3, 16.6) the student should be able to:

1.         calculate reasonable over- and underestimates of the integral of functions of two variables given in table form.

2.         calculate double and triple integrals by iterated integration.

3.         apply multiple integration to finding areas, volumes, and mass.

4.         interpret statements and graphs of probability density functions, and cumulative distribution functions.

5.         solve problems involving probability density and cumulative distribution functions, including a joint density function of two variables.

6.         use integration to calculate the median and mean of a continuous probability distribution.

Unit 5:  Differential Equations

Upon completion of this unit (Sections 10.1-7) the student should be able to:

1.         recognize a differential equation and check a function to determine if it is a solution of a given differential equation.

2.         construct a slope field for a given differential equation, and sketch several possible solutions from a given slope field.

3.         apply differential equations to exponential growth and decay problems involving population growth, continuously compounded interest, and elimination of drugs.

4.         solve problems involving differential equations of the form , and problems leading to a logistic model.

5.         interpret and solve problems involving the interaction of two populations, such as the predator-prey problem.

6.         use a differential equation to model the spread of a disease.

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__