VIRGINIA HIGHLANDS COMMUNITY COLLEGE

SYLLABUS

COURSE NUMBER AND TITLE

MTH 271 - Applied Calculus I

COURSE DESCRIPTION

Presents limits, continuity, differentiation of algebraic and transcendental functions with applications, and an introduction to integration. Prerequisite: MTH 163 or MTH 166 or equivalent. (Credit will not be awarded for MTH 270 and 271). Lecture 3 hours per week.

BROAD GOALS OF THE COURSE

The student should gain a workable knowledge of the calculus techniques for the study of business, economics, management, and the social and life sciences.

SPECIFIC OBJECTIVES

In addition to the following specific objectives relating to calculus techniques, the student should be able to solve application problems using these techniques.

1. Simplify algebraic expressions

2. Factor

3. Solve equations (linear, quadratic, rational, radical, polynomial)

4. Solve inequalities (linear, quadratic, and rational)

5. Graph functions (linear, quadratic, polynomial, rational, radical)

6. Evaluate limits

7. Find discontinuities of given functions

8. Find vertical, horizontal, and oblique asymptotes for the graphs of rational functions

9. Find the derivative of a given function using the definition of derivative

10. Use differentiation rules (sum, difference, product, quotient, chain rule, and implicit differentiation) to differentiate a given function

11. Solve maximum and minimum problems applying differentiation

12. Solve related rate problems

13. Given a function of f(x) or y, find the differential of f or y (df or dy)

14. Determine where a given function is increasing or decreasing

15. Determine concavity of a given function

16. Find points of inflection for a given function

17. Locate local extreme values

18. Apply the First and Second Derivative Tests

19. Determine absolute extreme

20. Solve optimization problems

21. Sketch and determine the domain and range of exponential and logarithmic functions

22. Find derivatives of given exponential and logarithmic functions

23. Solve logarithmic problems with application to economics

24. Integrate indefinite integrals

25. Evaluate definite integrals

26. Find the area between two given curves

27. Find volumes using integration

28. Find the average value of a given function

29. Using integration techniques to find integrals of given functions

30. Use numerical integration techniques to approximate definite integrals

UNITS TO BE COVERED

Unit 1 - Chapter 1 and Chapter 2

Algebra Review, Functions, Limits, and the Derivative

Unit 2 - Chapter 3

Differentiation and Applications

Unit 3 - Chapter 4

Curve Sketching

Unit 4 - Chapter 5.3, 5.4, Chapter 6

Derivatives of Exponential and Logarithmic Functions Integration

Unit 5 - Chapter 7

Additional Topics in Integration

GRADING CRITERIA

There will be chapter tests and a final exam. The lowest of all tests except the last test will be dropped. No make-up tests will be given. The final grade will be the average of the chapter tests and the final exam (equal weight). Specific homework assignments for every chapter will be turned in with each test and will be used as extra credit for each test score. A test may be taken early (before the scheduled time) if discussed with the instructor in advance. A student with a 90% average may be exempt from the final exam.

Cheating is unacceptable and will be handled in accordance with the VHCC Honor System.

Letter grades for the course will be assigned as follows:

Average	Grade
90 and above	A
80-89	B
67-79	C
50-66	D
Below 50	F

INSTRUCTIONAL MATERIALS

Text - Applied Calculus (4th edition) by Claudia Taylor and Lawrence Gilligan; Brooks/Cole Publishing Co., Pacific Grove, California, 1993.

The Texas Instrument TI-85 graphing calculator will be used in class.This may be changed in the Fall of 2004. Students are encouraged to learn how to use this helpful tool.

Students will be expected to do specific homework assignments to be turned in with each unit test and will be used as extra credit for each unit test score.

The exercise sets are carefully constructed. There are four types of exercises:

General Education
Computational and Computer Skills	Set A exercises are designed with groups of problems keyed to specific examples of that section which serve as direct problem-solving models. Example 1 - Find the equation of the line tangent to the curve fex = x² - x - 6 at the point (3,0).
Critical Thinking and Computational and Computer Skills	Set B exercises include application problems and more challenging exercises. Calculus must be meaningful to students going directly into applied disciplines. From thinking through these applied problems, students leave the course with a strong sense of the usefulness of calculus as a tool for solving "real-world" problems. Example 2 - A company has determined that its profit, P (in dollars), is related to the number of units produced, x, by the equation P(x) = 300 x - 3x². Find the rate of change of the profit when 40 units are produced.
Communication (Reading and Writing) and Critical Thinking	Writing and Critical Thinking exercises are designed to encourage students to think about concepts and express their reasoning in writing. Example 3 - Explain the difference between the First and Second Derivative tests for finding local maximum and minimum values. Explain why or why not either test ever fails for any particular situation.
Computational and Computer Skills and Understanding Science and Technology	Using technology in Calculus exercises are designed for students using computer programs or graphics calculators. They extend the concepts using the power of technology.

INTERPERSONAL SKILLS AND HUMAN RELATIONS

Problem sessions in a lab setting will be held several times during each semester. Students are encouraged to work together and after completion of an assignment to check results with other students. After thinking through a problem a student will explain concepts and procedures to another student. This reinforces the understanding of the problem for both students. Working effectively in groups is a wonderful way to learn calculus!

Working one-on-one with a calculus tutor in Project Excel can be very helpful to many students. (Tutors can be scheduled in Room 315).