Springfield Technical Community College

ACADEMIC AFFAIRS

Course Number:	MATH 222	Department:	Mathematics	
Course Title:	Applied Mathematics 2	Semester:	Spring	Year:	1997	

Objectives/Competencies

Course Objective	Competencies	
1.	Understand fundamental concepts of polynomial equations.

2.	Understand rational exponents.

3.	Solve linear inequalities in one and two variables.

4.	Recognize graphs that represent functions.

5.	Be able to compute the difference quotient.

6.	Find the derivative of a function using the definition.

7.	Recognize discontinuity in the graphs of some rational functions.

8.	Understand and use derivative notation.

9.	 Understand and use fundamental rules of differentiation.

10.	Work-applied problems that involve derivatives.

11.	Apply the calculus to analyze graphs of functions.

12.	Apply derivatives to applied problems.

13.	Integrate basic functions.

14.	Work definite integral problems.

15.	Interpret integration as finding the area under a curve.
 	1. 	Identify variable, coefficient, exponent, and the degree of a polynomial.

1. 	Given x to a unit fraction, l/n, write this as the nth room of x.
2. 	Given x to the a/b power, write this as the bth root of x to the a power.
3. 	Verify that the nth root of x is a if and only if a to the nth power is x.

1. 	Given an inequality in two variables, graph the boundary line and shade in the half-plane that contains the solution set.
2. 	Define test point.
3. 	Use test point to determine the half-plane containing the solution set.

1. 	Use the vertical line test to determine whether or not a relation is a function.
2. 	Test a set or ordered pairs to determine whether or not they are a function.

1. 	Compute f(a) for a function, where a is a real number.
2. 	Compute f(a + h) for a function.
3. 	Compute f(a + h) - f(a).
4. 	Compute (f(a + h) - f(a))/h and simplify.

1. 	Compute the limit of simple functions.
2. 	Compute derivatives using the limit as h approaches zero of first, second, and third degree polynomials in x.

1. 	Given a rational function, determine whether or not there are points of discontinuity.
2. 	Factor a rational expression and reduce whenever possible.
3. 	Evaluate rational expressions that are indeterminate in form.
4. 	Reduce rational expressions by eliminating common factors.

1. 	Understand that y’, f’(x), df(x)/dx, and Dxf(x) refer to finding a derivative.

1. 	Find the derivatives of the following:
a. 	x to the nth power
b. 	the product of two functions
c. 	the quotient of two functions
d. 	the chain rule
e. 	e to the f(x) power
f. 	the natural logarithm of f(x)

1. 	Solve problems involving marginal analysis:
a. 	marginal cost
b. 	marginal revenue
c. 	marginal profit

1. 	Use the first derivative to determine where the function is increasing, decreasing or at a maximum or minimum and whether it is relative or absolute.
2. 	Use the second derivative to determine concavity, the points of inflection, and the points o discontinuity.
3. 	Sketch the curve and identify the extrema, the points of inflection, the roots, the intervals where the function is increasing or decreasing, the intervals where the function is concave up or concave down., and the points of discontinuity.

1. 	Use derivatives to solve problems involving marginal cost, revenue, and profit.
2. 	Find changes in cost for any level of production when the cost function is known.
3. 	Solve problems involving exponential growth and decay.

1. 	Integrate the following types of functions:
a. 	polynomial functions
b. 	power functions
c. 	natural logarithms
d. 	exponential functions
2. 	Find the constant of integration when one functional value of the original function is known.

1. 	Integrate all functions studied in indefinite integration as the integral goes from a to b.
2. 	Recognize that the integral of f(x) dx from a to a is zero.

1.	Find the integral of f(x) dx as x goes from a to b as an area problem where the integral is the area function bounded by f(x), the axis between a and b.