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
Prerequisites (description)
Course coordinators
Term 2025Z: | Term 2024Z: |
Main fields of studies for MISMaP
physics
Type of course
obligatory courses
Mode
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
More precisely:
To pass the exercises part, a student must obtain at least 25 points.
The maximum number of points that can be collected during the semester is 50 points (two midterm tests worth 20 points each and 10 points for activity during classes).
In special cases, when a student is short of the minimum by a small margin (ε), the instructor may offer a conditional pass for the exercises part.
Lecture:
To pass Analysis I R, students must take the written exam and obtain a positive result on the oral exam.
The following scenarios are possible:
1. Students who have passed the tutorials take both the **written** and **oral exams** in the **first examination period**.
Eligibility for the oral exam does **not depend** on the result of the written exam.
2. Students who were offered a conditional pass for the tutorials and obtained at least 10 points on the written exam in the first period are admitted to the oral exam in that same period.
If they did not earn 10 points, they follow scenario 4.
3. Students who did not pass the tutorials but obtained at least 10 points** on the written exam in the first period receive a pass for the exercises part and take the written exam again during the retake session.
If they score at least 6 points on the retake written exam, they are admitted to the oral exam.
4. Students who did not pass the tutorials and obtained fewer than 10 points on the written exam in the first period take the written exam again during the retake session.
If they score at least 6 points on the retake written exam, they are admitted to the oral exam.
The final grade is the sum of the oral exam points (max 20) and the written exam points (max 20):
| Total points | Grade |
| ------------ | ----- |
| 40 | 5! |
| 36–39 | 5 |
| 32–35 | 4.5 |
| 28–31 | 4 |
| 24–27 | 3.5 |
| 20–23 | 3 |
| < 20 | 2 |
The instructor may add **up to 3 extra points**, depending on the oral exam performance and the student’s overall situation.
**Remarks:**
* Students who did not attend the **midterm tests** and did not explain their absence **before the start of the exam session** are **not allowed** to take the written exam.
* Students following **scenario 1** who did not register for or did not appear at the **oral exam** and did not explain their absence beforehand must **retake the written exam** during the retake session. If they obtain at least 6 points, they are admitted to the oral exam.
* Other rules related to passing the course are contained in the **Faculty of Physics study regulations**.
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: