MATA172 Introduction to mathematical analysis 2 (5 cr)
Description
Continuity and limit for functions of one real variable. Basic properties of continuous functions. Uniform continuity.
In this study-module, students practice reading and writing mathematics. They learn the basics of logic and practice proving mathematical statements.
Learning outcomes
The student
- knows the epsilon-delta definition for continuity, and is able to apply the definition in simple situations
- knows the characterization of continuity in terms of limits of sequences
- is familiar with the most important consequences of continuity
- knows the definition of limit of a function
- understands the connection between continuity and limit, and knows how they differ
- is able to formulate and prove mathematical claims
- has improved her/his ability to read and write mathematics
Description of prerequisites
Introduction to mathematical analysis 1
Study materials
Lecture notes (in Finnish)
The contents of the study-module correspond to
D. Brannan: A first course in
mathematical analysis, chap. 4-5,
or
P. Fitzpatrick: Advanced Calculus, chap. 3.
Completion methods
Method 1
Method 2
Teaching (5 cr)
Lectures 42 h and exercises. The weekly exercises are handed in and graded. To attend the final exam, the students must receive enough bonus-points from the exercises (the exact amount is mentioned in the teaching schedule).
Lecture notes (in Finnish)
Teaching
10/23–12/15/2023 Lectures
12/14–12/14/2023 Exam
1/10–1/10/2024 Exam
Exam (5 cr)
Final exam.
The contents of the study-module correspond to
D. Brannan: A first course in mathematical analysis, chap. 4-5,
or
P. Fitzpatrick: Advanced Calculus, chap. 3.