1. Course Description:

Prerequisite: MAC 2311 or satisfactory score on the mathematics placement test. This course is designed to follow MAC 2311. Topics include inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, areas, volumes, centroids, work, fluid pressure, length of arc, trigonometric integrals, integration techniques, polar coordinates, indeterminate forms, improper integrals, infinite series, plane curves, parametric equations, conic sections, and computer work. (Credit is not also given for MAC 2234 or MAC 2254.) Five hours weekly.

2. Major Learning Outcomes:

1. The student will be able to apply knowledge of the inverse trigonometric functions and of the hyperbolic and inverse hyperbolic functions to evaluate integrals.
2. The student will be able to apply knowledge of applications of the definite integral.
3. The student will be able to apply knowledge of certain techniques of integration.
4. The student will be able to apply knowledge of polar coordinates, plane curves, parametric equations and conic sections.
5. The student will be able to apply knowledge of indeterminate forms, improper integrals and Taylor’s formula.
6. The student will be able to apply knowledge of infinite series.

3. Course Objectives Stated in Performance Terms:

1. The student will be able to apply knowledge of the inverse trigonometric and of the hyperbolic and inverse hyperbolic functions to evaluate integrals.

1. The student will be able to find derivatives of inverse trigonometric functions and integrals which yield inverse trigonometric functions.
2. The student will be able to state definitions of hyperbolic sine, cosine and tangent functions.
3. The student will be able to find the derivatives of hyperbolic functions.

2. The student will be able to apply knowledge of applications of the definite integral.

1. The student will be able to solve area problems using the definite integral.
2. The student will be able to solve volume problems using the definite integral.
3. The student will be able to solve work problems using the definite integral.
4. The student will be able to find the length of arc of a plane function with definite integrals.
5. The student will be able to solve fluid pressure problems with definite integrals.
6. The student will be able to find the center of mass with definite integrals.

3. The student will be able to apply knowledge of certain techniques of integration.

1. The student will be able to use the methods of parts, trigonometric substitution and partial fractions to do integration problems.
2. The student will be able to integrate rational functions of the sine and cosine functions.
3. The student will be able to find integrals by using integral tables.

4. The student will be able to apply knowledge of polar coordinates, plane curves, parametric equations and conic sections.

1. The student will be able to define basic terms related to polar coordinates and be able to plot points in a polar coordinate system.
2. The student will be able to convert from rectangular to polar coordinates and vice versa.
3. The student will be able to graph the limacon, cardioid, rose, spiral, line and circle.
4. The student will be able to find area and arc length in polar coordinates.
5. The student will be able to obtain parametric equations of a given plane curve and to eliminate the parameter.
6. The student will be able to find the slope and concavity of a curve given parametrically.
7. The student will be able to find the length of arc of a curve given parametrically.
8. The student will be able to graph parabolas, ellipses, and hyperbolas and extract useful information from those graphs.
9. The student will be able to sketch the graph of a conic section in polar coordinates when one focus is at the pole.

5. The student will be able to apply knowledge of indeterminate forms, improper integrals and Taylor’s formula.

1. The student will be able to use L’Hopital’s Rule to evaluate limits which go to one of the following indeterminate forms of limits:

   

2. The student will be able to integrate improper integrals with infinite limits of integration.
3. The student will be able to integrate improper integrals of sectionally continuous functions involving infinite discontinuities.
4. The student will be able to state and use Taylor’s formula.

6. The student will be able to apply knowledge of infinite series.

1. The student will be able to define a sequence determine if it is increasing or decreasing, find lower and upper bounds if they exist and determine convergence or divergence.
2. The student will be able to define an infinite series, the sum of a series, and the nth partial sum of a series.
3. The student will be able to determine the convergence or divergence of the following infinite series:

1. Constant term
2. Geometric
3. Harmonic
4. Positive term
5. Alternating

4. The student will be able to do the following with a power series:

1. Find convergence interval using the ratio and root tests
2. Differentiate it
3. Integrate it

5. The student will be able to define the Taylor and Maclaurin series for a given analytic function.
6. The student will be able to use the Binomial Theorem as it applies to infinite series.

4. Criteria Performance Standard:

To earn a grade of C or better the student will achieve at the 70 percent level or higher on classroom measures.

Revised 8/84
DBT 11/20/90
Effective Session 19911
3 YR C&I Review 8/94
C&I 3/17/98; DBT 4/20/98
Effective Session 19981
C&I 4/28/98; DBT 5/29/98
Effective Sess 19981