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Analysis I E

General data

Course ID: 1100-1Ind01 Erasmus code / ISCED: 11.101 / (0541) Mathematics
Course title: Analysis I E Name in Polish: Analiza I R
Organizational unit: Faculty of Physics
Course groups: Physics, individual path; 1st year courses
ECTS credit allocation (and other scores): 9.00
view allocation of credits
Language: Polish
Prerequisites (description):

None

Mode:

Classroom

Short description:

First part, extended level

Full description:

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

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 methods and assessment criteria:

Two mid-terms, final written exam, final oral exam. Grading citeria: mastering the subject, solving problems

Practical placement:

None

Classes in period "Winter semester 2021/22" (past)

Time span: 2021-10-01 - 2022-02-20
Choosen plan division:


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see course schedule
Type of class: Class, 60 hours more information
Lecture, 60 hours more information
Coordinators: Katarzyna Grabowska
Group instructors: Katarzyna Grabowska, Marcin Kościelecki, Marcin Napiórkowski, Bartosz Zawora
Students list: (inaccessible to you)
Examination: Course - Examination
Lecture - Examination

Classes in period "Winter semester 2022/23" (future)

Time span: 2022-10-01 - 2023-01-29
Choosen plan division:


magnify
see course schedule
Type of class: Class, 60 hours more information
Lecture, 60 hours more information
Coordinators: Paweł Kasprzak
Group instructors: Paweł Kasprzak, Marcin Kościelecki
Students list: (inaccessible to you)
Examination: Course - Examination
Lecture - Examination
Course descriptions are protected by copyright.
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