Calculus II

Objectives:

The objective of the course is to give an introduction to the central ideas and results from real analysis

Content:

An introduction to real analysis with an emphasis on the Riemann integral, basic properties of curves and surfaces, convergence of sequences and series, and also vectors and functions of several variables.

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

• knows the basic properties of continuous functions, including the notion of uniform continuity.
• knows the theory of the Riemann integral for bounded functions.
• knows the basic concepts in the theory of sequences and series.
• knows the basic theory of plane curves.
• knows the theory of functions of several variables, including the notions of continuity and differentiability.
• knows the theory of extreme values for functions of several variables.

Skills

The student

• can determine if a bounded function is integrable.
• can use a variety of tests to check convergence of sequences and series.
• can compute the length of a curve and the area bounded by a closed course.
• can compute the partial derivates of functions of several variables and use this to solve various problems, including extreme value problems.

General Competence

The student

• has gained a basic understanding of central ideas and results from calculus that enables the student to apply these methods in an independent fashion in relevant situations