Download Calculus with Analytic Geometry II: MAT231 Course Outline, Central Arizona College and more Lab Reports Analytical Geometry and Calculus in PDF only on Docsity!
COURSE OUTLINE
Central Arizona College 8470 N. Overfield Road Coolidge, AZ 85228 Phone: (520) 494-5206 Fax: (520) 494-
Prefix/Number: MAT
Course Title: Calculus with Analytic Geometry II
Course Description :
Techniques of integration, improper integrals, applications of calculus, elements of analytic geometry sequences and series.
Semester Hours : 4 Times for Credit: 1
Lecture/Lab Ratio : 4 Lectures
Pre-requisites: MAT221; RDG100A or RDG100B
Co-requisites: None
Cross Listed: None
Grading Options: A/F
Approved Modalities: F2F, Hybrid, IITV
Central Arizona College MAT231 – Calculus with Analytic Geometry II Page 2 of 3
Learning Outcome Statements:
Upon completion of this course the student will be able to:
- Extend the operations of differentiation and integration to functions and their inverses.
- Apply L'Hopital's Rule.
- Use algebraic and numerical techniques for evaluating integrals.
- Apply integration in applied problems.
- Identify convergence or divergence of an improper integral.
- Analyze curves in the plane defined using parametric and polar equations.
- Identify convergence or divergence of sequences and series having numerical terms.
- Formulate a Taylor Series generated by a given function at a given value.
- Extend the operations of differentiation and integration to functions defined by a power series.
- Calculate the volume of a solid of revolution.
- Locate the center of a mass.
Standards:
The student will meet the learning outcomes at the following level, degree or measurement:
- Apply the appropriate rule of differentiation to find the derivative of various functions including inverse trigonometric and hyperbolic functions, functions defined parametrically and in polar coordinates.
- Identify and utilize the proper techniques of integration to solve problems related to distance, velocity, acceleration, arc length, volume, area, force and work.
- Generate the indefinite integral of a function by applying the appropriate techniques of integration. The techniques are to include integration by parts, trigonometric substitution, partial fractions, rationalizing the denominator, using integration tables and numerical techniques (trapezoidal, midpoint and Simpson's Rules)
- Given a function whose limit results in an indeterminate form, evaluate the limit using L'Hopital's rule.
- Given a function defined in rectangular coordinates, express the function as a system of parametric equations.
- Given a function defined in rectangular coordinates, convert the function to polar coordinates by applying the appropriate conversion relationships.
- Given a function expressed in polar coordinates or parametrically, graph the function.
- Apply the appropriate rule or theorem to determine if an improper integral converges or diverges.
