Contents

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. A graphing calculator is required. The use of a computer algebra system will be an integral part of the course.

Credits

4

Prerequisite

MATH 181 or equivalent with a grade of C or higher

Hours Weekly

4 hours weekly

Course Objectives

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