Learning Objectives for Calculus IIB
- Pre-requisite
- The student will know the mathematics needed to have a reasonable
expectation of success in the mathematics and statistics courses for which
Calculus 227 is a pre-requisite.
- Breadth
- The student will be able to solve problems involving integrals,
exponential functions, inverses of common functions, parametric curves and
polar coordinate systems, and techniques of integration.
- Communication
- The student will be able to write clear explanations of the techniques
of calculus including the proper use of standard mathematical notation.
- Technology
-
- The student will be able to use a CAS to graph parametric and polar
curves, calculate summations.
- The student will be able to use a CAS to graph functions (on a rectangular coordinate system), find derivatives, find definite and indefinite integrals, find the limit of a function.
- Connections/applicability
-
- The student will be able to model applications by using calculus.
- The student will be able to apply the content from Calculus I to solve
problems in Calculus II.
- Mathematical thinking
-
- The student will be able to recognize the problem type, select an
appropriate solution strategy and apply rules and procedures for solving the
problem.
- The student will begin to be able to apply theorems and major concepts of
calculus to solve real-world problems. The student will understand and
appreciate the applicability of calculus to nature, business, science, etc.
- Content
-
- To familiarize the students with the concept of exponential growth and
functions, and especially the differentiation and integration of exponential
functions.
- To increase the skill set of integration techniques that students know.
- To familiarize the students with the calculus of inverse functions (especially logs).
- To strengthen the notation and concept of summation (especially adding up
an infinite number of terms -- i.e. a limit).
- To introduce basic ideas of parametric equations, most especially polar
coordinates and functions of polar coordinates.
Website maintained by Andy Long.
Comments appreciated.