MATA174 Introduction to mathematical analysis 4 (5 cr)

Improper integrals. Number series. Sequences and series of functions and their convergence. Power series. Taylor polynomials and Taylor series.

• knows the definition(s) of improper integral and knows how to study their convergence
• knows the definition for the convergence of a number series and is able to recognize the most common series 
• is able to use the most common convergence tests
• knows the definitions for point wise and uniform convergence for function sequences and series, and is able to use them
• knows which properties are stable under uniform convergence
• knows how to apply Weierstrass' test to study uniform convergence 
• is familiar with the definitions of power series and its radius convergence, and knows how to study the convergence of a power series
• knows what are Taylor polynomials and how they can be used to study limits
• is able to recognize the most common power series representations

Introduction to mathematical analysis 1-3

Lecture notes (in Finnish)

The contents of the study-module correspond to Fitzpatrick: Advanced Calculus, chap. 8-9. or Brannan: A first course in Mathematical Analysis, chap. 3 and 8.