MATA171 Introduction to mathematical analysis 1 (5 cr)
Description
Real numbers and inequalities, basic concepts of functions, elementary functions, continuity of a real function, the limit of a function and its basic properties, asymptotic behavior of functions.
In this study-module, the students practices reading and writing mathematical texts, as well as using mathematics in speech. Additionally, the student practices basic skills in logical reasoning and exercises their application.
Learning outcomes
After the course, the student
- can apply inequalities to estimate the size of a given expression.
- knows how to solve inequalities with absolute values and use triangle inequalities.
- knows the basic concepts of functions and elementary functions.
- knows the epsilon-delta definitions of continuity and limit for real functions and can apply these definitions.
- understands the connection and difference between limit and continuity.
- is capable of applying basic properties of limits for calculating them.
- is capable of determining the asymptotic behavior of a function.
- is capable of reading proofs and following their logical structure.
- is capable of solving simple proof exercises and presenting them coherently.
Description of prerequisites
Good command of the long mathematics curriculum of high school.
MATP100 Introduction to mathematics or MATA132 How to prove it? are recommended.
Study materials
Lecture notes (in Finnish)
The contents of the study-module correspond to:
Protter & Morrey: A first course in real analysis, chap. 1 and 2.1-2.4
or
M. Spivak: Calculus, chap. I-II