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.

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