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, 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. Students will also learn about parametric equations, Polar coordinates and their applications to calculus. The use of a graphing calculator will be an integral part of this course. A computer algebra system, such as MATLAB, will be introduced in this course.

Credits

4

Prerequisite

MATH 181 or equivalent with a grade of C or higher

Hours Weekly

4 hours weekly

Course Objectives

1. Apply basic integral rules to solve geometry and physics application problems.
2. Differentiate and integrate hyperbolic functions.
3. Recognize and apply the appropriate method of integration to solve a problem.
4. Approximate definite integrals numerically.
   
5. Evaluate improper integrals.
6. Determine the direction field of a differential equation.
7. Solve separable differential equations.
   
8. Determine the convergence or divergence of a sequence; and if it converges, find its limit.
9. Apply the appropriate test to determine whether an infinite series converges or diverges.
10. Calculate either the exact or an approximate value of a convergent infinite series.
11. Approximate a function with a Taylor polynomial.
12. Apply the properties of power functions to determine the radius of convergence.
13. Apply calculus to understand parametrically defined curves.
14. Apply calculus to understand the graphs of equations in polar coordinates.
15. Use a computer algebra system as a means of discovery, to reinforce concepts, and as an efficient problem solving tool.

Course Objectives

1. Apply basic integral rules to solve geometry and physics application problems.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
2. Differentiate and integrate hyperbolic functions.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
3. Recognize and apply the appropriate method of integration to solve a problem.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
4. Approximate definite integrals numerically.
   

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
5. Evaluate improper integrals.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
6. Determine the direction field of a differential equation.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
7. Solve separable differential equations.
   

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
8. Determine the convergence or divergence of a sequence; and if it converges, find its limit.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
9. Apply the appropriate test to determine whether an infinite series converges or diverges.

   This objective is a course Goal Only

   Learning Activity Artifact

   • Other (please fill out box below)
   • Exam

   Procedure for Assessing Student Learning

   • Other (please fill out box below)
   • Scoring key
10. Calculate either the exact or an approximate value of a convergent infinite series.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Exam

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Scoring key
11. Approximate a function with a Taylor polynomial.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Exam

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Scoring key
12. Apply the properties of power functions to determine the radius of convergence.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Exam

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Scoring key
13. Apply calculus to understand parametrically defined curves.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Exam

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Scoring key
14. Apply calculus to understand the graphs of equations in polar coordinates.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Exam

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Scoring key
15. Use a computer algebra system as a means of discovery, to reinforce concepts, and as an efficient problem solving tool.

    This objective is a course Goal Only

    Learning Activity Artifact

    • Other (please fill out box below)
    • Project

    Procedure for Assessing Student Learning

    • Other (please fill out box below)
    • Rubric