MATH-182 Calculus II

This course is the second in a three-part calculus sequence. Applications include area bounded by curves, volume by rotating and slicing, arc length, work, and centers of mass. Integration techniques taught include integration by parts, partial fractions, trigonometric substitution, numerical integration, and improper integrals. Students will be introduced to hyperbolic functions, elementary differential equations, direction fields, parametric equations, polar coordinates and their applications. The study of sequences and infinite series will include tests for convergence of the various types of series, leading to power series and Taylor series. The use of a computer algebra system will be an integral part of the course.

Credits

4

Prerequisite

MATH-181 or equivalent; a grade of C or higher is recommended

Hours Weekly

4 hours weekly

Course Objectives

1. 1. Apply basic integral rules to application problems.
2. 2. Memorize and apply the derivatives of the hyperbolic and inverse trigonometric functions and
   hyperbolic functions.
3. 3. Apply the rules for the integrals of hyperbolic functions and integrals arising from inverse
   trigonometric functions.
4. 4. Recognize and apply the appropriate method of integration to solve a problem.
   
5. 5. Evaluate improper integrals.
6. 6. Apply L'Hopital's Rule to find limits of appropriate indeterminate forms.
7. 7. Use other methods to find limits of indeterminate forms where L'Hopital's Rule is inappropriate.
   
8. 8. Determine the convergence or divergence of a sequence; and if it converges, find its limit.
9. 9. Determine whether an infinite series converges or diverges.
10. 10. Apply the properties and principles of infinite series to calculate either the exact or an
    approximate value of an infinite series.
11. 11. Graph equations in polar and parametric form
12. 12. Use the computer algebra system, DERIVE, as a means of discovery, to reinforce concepts, and
    as an efficient problem solving tool.

Course Objectives

1. 1. Apply basic integral rules to application problems.
2. 2. Memorize and apply the derivatives of the hyperbolic and inverse trigonometric functions and
   hyperbolic functions.
3. 3. Apply the rules for the integrals of hyperbolic functions and integrals arising from inverse
   trigonometric functions.
4. 4. Recognize and apply the appropriate method of integration to solve a problem.
   
5. 5. Evaluate improper integrals.
6. 6. Apply L'Hopital's Rule to find limits of appropriate indeterminate forms.
7. 7. Use other methods to find limits of indeterminate forms where L'Hopital's Rule is inappropriate.
   
8. 8. Determine the convergence or divergence of a sequence; and if it converges, find its limit.
9. 9. Determine whether an infinite series converges or diverges.
10. 10. Apply the properties and principles of infinite series to calculate either the exact or an
    approximate value of an infinite series.
11. 11. Graph equations in polar and parametric form
12. 12. Use the computer algebra system, DERIVE, as a means of discovery, to reinforce concepts, and
    as an efficient problem solving tool.