Analysis I E 1100-1Ind01
1. Elements of logic and set theory
- Equivalence relations
2. Real numbers
- Existence of suprema and infima
3. Sequences of real numbers
- Cauchy sequences
4. Metric spaces
- Balls, open sets
- Closed sets
- Sequences in metric spaces
5. Elements of general topology
- Continuous mappings
- Compactness
- Connectedness
6. Differential calculus
- Basic theorems
- Bernoulli-de l'Hospital rules
- Taylor's formula
- Maxima and minima
7. The Riemann integral
- Fundamental theorem of differential calculus
8. The functions log and exp
9. Series
- Series with positive terms
- Series with arbitrary terms
10. Sequences and series of functions
- Types of convergence, elementary theorems
- Power series
11. Elementary functions
12. Methods of integration
13. Stone-Weierstrass theorem
14. Additional topics
- Banach principle
- Convex functions
- Integrals with parameter
Mode
Prerequisites (description)
Course coordinators
Term 2024Z: | Term 2023Z: |
Learning outcomes
1. Mastering elementary mathematical analysis.
2. Gaining basic competence in reading and understanding mathematical texts.
3. Obtaining elementary techniques of analysis of real functions.
4. Obtaining experience and skill of identifying crucial mathematical properties of objects under study and application thereof.
Assessment criteria
Two mid-terms, final written exam, final oral exam. Grading citeria: mastering the subject, solving problems
Practical placement
None
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: