**Course Syllabus **

**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 2.,* by James
Stewart, Sixth Edition, Brooks/Cole Publishing Company

**Learning Outcomes:** The student will be
able to:

- Compute areas under curves and between curves
- Compute volumes by disks, washers, shells, and cross-sections
- Compute arclength of a curve and surface area of a surface of revolution
- Solve applied problems involving force and work
- Exponentiate and differentiate exponential, logarithmic, inverse trigonometric, hyperbolic, and inverse hyperbolic functions
- Evaluate limits involving indeterminate forms using l´Hospital's Rule
- Evaluate antiderivatives using the techniques of u-substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, completing the square
- Evaluate improper integrals
- Compute area and arclength of curves in polar coordinates
- Determine whether a sequence converges or diverges
- 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
- Determine the radius of convergence and the interval of convergence of a power series
- Compute the Taylor series and Maclaurin series of a function

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

- A= 90-100%
- B= 80-90%
- C= 70-80%
- D= 60-70%
- F= below 60%