PELLISSIPPI STATE TECHNICAL COMMUNITY COLLEGE
MASTER SYLLABUS

BASIC CALCULUS AND MODELING 
MATH 1830

Class Hours: 4.0

 

Credit Hours: 4.0

 

Laboratory Hours: 0.0

 

Revised: Fall 2007

 

 

Catalog Course Description:

 

 

 

Topics include differentiation and integration of polynomial, rational, exponential, and logarithmic functions and methods of numerical integration.  Topics from business modeling, such as economic applications and case studies, will be explored with computer simulations, computer labs, or calculators.  A graphing calculator is required.

Entry Level Standards:

 

 

 

Students must be able to read at the college level.

Prerequisites:

 

 

 

High school algebra I, algebra II, precalculus and satisfactory placement scores; or MATH 1130 or MATH 1710 or MATH 1730 

Textbook(s) and Other Course Materials:

 

 

Textbook:
Lial, Margaret L., Thomas W. Hungerford, and John P. Holcomb,. Jr.  Mathematics with Applications, 9th edition, Pearson Education, Inc., 2007.
References:

Armstrong, Bill and Don Davis.  Brief Calculus:  The Study of Rates of Change, 2nd edition, Prentice-Hall, Inc., 2003.
Bittinger, Marvin L. and David J. Ellenbogen.  Calculus and Its Applications, Pearson Education, Inc., 9th edition, 2008. 
Warner, Stefan and Steven R. Costenoble.  Finite Mathematics + Applied Calculus, Brooks/Cole, 4th  edition, 2007.

Wilson, Frank C.  Finite Mathematics and Applied Calculus,  Houghton Miffllin Company, 2007.

Personal Equipment: 
A non-symbolic graphing calculator is required.  The TI-83, TI-83+, TI-84, or TI-84+ is recommended.

I. Week/Unit/Topic Basis:

 

 

 

 

Week 

Topic

 

1

Limits.  One-sided Limits and Limits Involving Infinity. 

 

2

Rates of Change.  Equations of Lines.  Tangent Lines and Derivatives.   

 

3

Tangent Lines and Derivatives.  Review.  Test 1. 

 

4

Techniques for Finding Derivatives.  Derivatives of Products and Quotients.

 

5

Factoring.  The Chain Rule. 

 

6

Derivatives of Exponential and Logarithmic Functions.  Continuity and Differentiability.   

 

7

Review.  Test 2.   Derivatives and Graphs.  

 

8

Derivatives and Graphs.  The Second Derivative. 

 

9

Optimization Applications.  Curve Sketching.

 

10

Curve Sketching.  Review.  Test 3. 

 

11

Antiderivatives.  Integration by Substitution.

 

12

Area and the Definite Integral.  The Fundamental Theorem of Calculus. 

 

13

The Fundamental Theorem of Calculus.  Applications of Integrals. 

 

14

Review.  Test 4.  Review for Comprehensive Final Exam.

 

15

Comprehensive Final Exam.

II. Course Objectives*:

 

 

 

A.

Use derivatives to analyze behavior of functions.  VI.1, 3, 5, 6

 

B.

Compute derivatives of algebraic, logarithmic, and exponential functions.  VI. 1, 3, 5

 

C.

Calculate integrals of algebraic, logarithmic, and exponential functions.  VI.1, 3, 5

 

D.

Use differentiation and/or integration to solve applications from business, economics, social and life science.  VI.1, 2, 3, 4, 5, 6

 

E.

Use calculus concepts to interpret, communicate, and report business application problems and their solutions in a clear and concise manner.  VI.1, 2, 3, 4, 5, 6

*Roman numerals after course objectives reference TBR's general education goals.

III. Instructional Processes*: 

 

 

Students will:

 

 

 

 

1.

Engage in collaborative activities to discuss and model business and economic applications by transforming data in tables into models and graphs and using the acquired information to determine maximum profit and revenue using strategies learned in calculus. Mathematics Outcome, Active Learning Strategy, Transitional Strategy

 

2.

Express ideas using the language and notation of mathematics.  Mathematics Outcome

 

3.

Use critical thinking skills to: interpret and apply rules such as the average of the Left and Right Sum Method to solve real-life problems such as finding the area of a pond. Technological Literacy Outcome, Active Learning Strategy, Transitional Strategy

 

4.

Use calculators to optimize functions and to approximate numerical derivatives and definite integrals.  Mathematics Outcome, Technological Literacy Outcome

 

5.

Use multiple approaches – graphical, symbolic, and verbal – to solve various problems involving differentiation and integration problems.  Mathematics Outcome, Technological Literacy Outcome

*Strategies and outcomes listed after instructional processes reference TBR's goals for strengthening general education knowledge and skills, connecting course work to experiences beyond the classroom, and encouraging students to take active and responsible roles in the educational process. 

IV. Expectations for Student Performance*: 

 

 

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

 

1.

Calculate the limit of an algebraic function.  B

 

2.

Recognize a continuous function.  A

 

3.

Calculate the derivative of an algebraic function by the delta process.  B

 

4.

Calculate the derivative of polynomials, products, quotients, powers, and implicit   functions using delta-derived rules.  B

 

5.

Use derivatives to solve application problems such as problems involving distance,   velocity, and acceleration; and maximum-minimum problems.  B, D, E

 

6.

Sketch curves using information obtained from the derivatives of a function.  B

 

7.

Find the derivatives of exponential and logarithmic functions.  B

 

8.

Integrate polynomial, power, logarithmic, and exponential functions and use this   knowledge to evaluate definite and indefinite integrals.  C, D

 

9.

Use derivatives to solve business/economic and life/physical sciences application   problems.  B, D, E

 

10.

Use integration to solve application problems that occur in business/economic and   life/physical sciences.  C, D, E

 

11.

Work with technology and applicable case studies/projects that involve real-world   data to enhance the conceptual understanding and usefulness of calculus and to provide training in an area that both business and industry are now demanding.  D, E

*Letters after performance expectations reference the course objectives listed above.

V. Evaluation:

 

 

 

A. Testing Procedures:  87.5% of grade

 

Students are evaluated primarily on the basis of tests, quizzes, homework, and the comprehensive final exam.  A minimum of 4 major tests is recommended. 

 

B. Laboratory Expectations:  12.5% of grade

 

Instructor discretion on case studies, lab and/or section projects

 

C. Field Work:

 

 None

 

D. Other Evaluation Methods:

 

 None

 

E. Grading Scale:

 

93     -     100      A 
88     -       92      B+ 
83     -       87      B 
78     -       82      C+ 
70     -       77      C 
60     -       69      D 
Below 60           F

VI. Policies:

 

 

 

A. Attendance Policy:

 

Pellissippi State Technical Community College expects students to attend all scheduled instructional activities. As a minimum, students in all courses must be present for at least 75 percent of their scheduled class and laboratory meetings in order to receive credit for the course. Individual departments/programs/disciplines, with the approval of the vice president of Academic and Student Affairs, may have requirements that are more stringent. 

 

B. Academic Dishonesty:

 

Individual instructors must distribute their policies on academic dishonesty and calculator use during the first week of classes.  In addition to other possible disciplinary sanctions that may be imposed as a result of academic misconduct, the instructor has the authority to assign either (1) an F or a zero for the assignment or (2) an F for the course.

 

C. Accommodations for disabilities:

 

If you need accommodations because of a disability, if you have emergency medical information to share, or if you need special arrangements in case the building must be evacuated, please inform the instructor immediately. Please see the instructor privately after class or in his/her office. Students must present a current accommodation plan from a staff member in Services for Students with Disabilities (SSWD) in order to receive accommodations in this course. Services for Students with Disabilities may be contacted by going to Goins 127 or 131 or by phone: 694-6751(Voice/TTY) or 539-7153.

 

D. Other Policies:

 

Make-up work:  Instructor discretion about make-up tests and/or assignments.

Cell phones:  Cell phones are to be either turned off or put on vibration mode while in class.  Instructor discretion as to penalty.