MATA173 Introduction to mathematical analysis 3 (5 cr)

The derivative and Riemann-integral for functions of one real variable: their definitions and basic results. The fundamental theorem of Calculus.

• knows the definition and geometric interpretation of derivative, and the basic rules of differentiation
• can formulate the Mean Value Theorem and knows its most important consequences
• is familiar with the definition of Riemann-integral and integrability
• knows Riemann's criterion for integrability
• knows the basic properties of integral and the basic results about integrability
• is able to estimate the value of an integral using inequalities
• understands how the Fundamental Theorem of Calculus connects derivative and integral to each other
• knows the theoretical justifications of integration by parts, change of variables in integral, and L'Hopital's rule.

Introduction to mathematical analysis 1 and 2

Lecture notes (in Finnish)

The contents of the study-module correspond to

D. Brannan: A first course in mathematical analysis, chap. 6-7,

or

P. Fitzpatrick: Advanced Calculus, chap. 4 and 6