VIRGINIA HIGHLANDS COMMUNITY COLLEGE

VIRGINIA HIGHLANDS COMMUNITY COLLEGE

SYLLABUS

COURSE NUMBER AND TITLE

MTH 272 - Applied Calculus II

COURSE DESCRIPTION

MTH 272 - APPLIED CALCULUS II (3 cr.)—Covers techniques of integration, multivariable calculus, and an introduction to differential equations. Prerequisite: MTH 271 or equivalent. 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. The student should be able to solve application problems using technology (graphing calculators and/or computer software).

SPECIFIC OBJECTIVES

The student should be able to solve differential equations, evaluate multivariable functions for given values, graph in three dimensions, find the distance between two points in three dimensions, find partial derivatives for a stated function, find relative extrema or saddle points for a given function, solve optimization problems, determine whether a given improper integral converages or diverges, evaluate indefinite integrals, evaluate multiple integrals.

UNITES TO BE COVERED

1. Improper Integrals

2. Differential Equations

3. Multivariable Calculus

4. Definite Integrals (revisited)

5. Indefinite Integrals (revisited)

6. Polar Coordinates

7. Relative extrema and saddle points

8. Multiple Integrals

GRADING CRITERIA

The grade for the course will be the average of two tests and twelve computer laboratory assignments (equal weight).

Letter grades for the course will be assigned as follows:

Average	Grade
90-100	A
80-89	B
67-79	C
50-66	D
Below 50	F

INSTRUCTIONAL MATERIALS

Text - Applied Calculus (3rd edition) by Claudia Taylor and Lawrence Gilligan; Brooks/Cole Publishing Co., Pacific Grove, California, 1993.

The Texas Instrument TI-86 graphing calculator will be used in class along with the mathematics software DERIVE. Students are encouraged to learn how to use these helpful tools. The calculator type may be changed in the Fall of 2004.

Students will be expected to do computer laboratory experiments to be graded as tests.

Specific homework assignments from the textbook are to be turned in. The exercise sets are carefully constructed. There are four types of exercises:

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 methods.
Example 1: Suppose that an investment is increasing at a rate of 6% per year, compounded continuously. If the initial investment was $2,000, what will the investment be worth in 10 years?
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: The number of bacteria in a certain culture increasing at a rate that is proportional to the number of bacteria present. Express this as a differential equation and find its general solution.
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.
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 many class periods during the 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 may explain concepts and procedures to other students. This reinforces the understanding of the problem for other 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.)