Course Syllabus – Fall 2005

Course Number: MATH 2644

Course Title: Calculus II

Hours Credit: 4 hours

Prerequisites: MATH 1634

Instructor: Varies (multiple sections)

Instructor Office Hours: Varies (at least 10hrs/week)

Course Description: A continuation of MATH 1634. The definite integral and applications, calculus of transcendental functions, standard techniques of integration, sequences and series.

Topics: Applications of the definite integral, derivatives and integrals of exponential, logarithmic, and inverse trigonometric functions, indeterminate forms and l´Hospital's Rule, hyperbolic and inverse hyperbolic functions, techniques of integration, polar coordinates and plane curves, and infinite series.

Text: Single Variable Calculus, Early Transcendentals Vol 1., by James Stewart, Fifth Edition, Brooks/Cole Publishing Company, 1999

Learning Outcomes: The student will be able to:

  1. Compute areas under curves and between curves
  2. Compute volumes by disks, washers, shells, and cross-sections
  3. Compute arclength of a curve and surface area of a surface of revolution
  4. Solve applied problems involving force and work
  5. Exponentiate and differentiate exponential, logarithmic, inverse trigonometric, hyperbolic, and inverse hyperbolic functions
  6. Evaluate limits involving indeterminate forms using l´Hospital's Rule
  7. Evaluate antiderivatives using the techniques of u-substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, completing the square
  8. Evaluate improper integrals
  9. Compute area and arclength of curves in polar coordinates
  10. Determine whether a sequence converges or diverges
  11. Determine whether a series converges conditionally, converges absolutely, or diverges using geometric series, p-series, the comparison test, the limit comparison test, the integral test, the ratio test, the root test, and the alternating series test
  12. Determine the radius of convergence and the interval of convergence of a power series
  13. Compute the Taylor series and Maclaurin series of a function

Grading Methods: Tests, Quizzes, Final Exam, Homework; Percentages decided by instructor.

Grading Scale: