Analysis I 390-FS1-1AM1
1. Basic information about mathematical proofs, mathematical logic and set theory.
2. Sequences and numerical series. Geometric series. Convergence criteria: d'Alembert, Cauchy. Harmonic series divergence. Euler number e.
3 Functions of one variable. Limit of a function, continuity, differentiability. Properties of the derivative. Chain rule.
4. Local and global extremes. Convexity, asymptotes. investigation of functions of one real variable.
5. Inverse function theorem. Derivative of inverse function. Lagrange's mean value theorem. Taylor's theorem. L'Hospital's rule.
6. Power series. Overview of elementary functions. The exponential function. Logarithm. Trigonometric, hyperbolic and cyclometric functions.
7. Sequences and functional series, uniform convergence.
8. Definite integral (Riemann integral). Approximate methods of calculating integrals. Newton-Leibnitz theorem. Improper integrals.
9. Basic information on the generalization of the notion of the integral (Stieltjes integral, Lebesque integral), sets of zero measure. Integral criterion of series convergence.
10. Basic information about Fouriere series
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Term 2024:
1. Basic information about mathematical proofs, mathematical logic and set theory. |
Term 2025:
1. Basic information about mathematical proofs, mathematical logic and set theory. |
Type of course
Prerequisites (description)
Course coordinators
Term 2024: | Term 2025: |
Mode
Learning outcomes
Knowledge, the graduate knows and understands:
1. higher mathematics techniques to the extent necessary for the quantitative description, understanding and modeling of physical problems of medium complexity (KP6_WG2)
2. and is able to explain descriptions of regularities, phenomena and physical processes using the languages of mathematics, in particular is able to independently recreate basic theorems and laws (KP6_WG3)
Skills, the graduate is able to:
3. analyze problems in the field of physical sciences and astronomy and find their solutions based on the known theorems and methods (KP6_UW);
Social competences, the graduate is ready to:
4. critical assessment of knowledge and received content (KP6_KK1)
Assessment criteria
During classes, students solve computational problems and are given homework. The emphasis is on acquiring several skills, described as the main learning outcomes. The effects are checked by written tests (two during the semester). Activity in classes and creativity in the approach to solved problems are also assessed. After completing the education in the Mathematical Analysis, there is an exam to verify the acquired knowledge.
Bibliography
W. Rudin: Principles of mathematical analysis
W.Krysicki, L.Włodarski: Analiza matematyczna w zadaniach,
M.Gewert, Z.Skoczylas, Analiza matematyczna I
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Term 2024:
W. Rudin: Principles of mathematical analysis |
Term 2025:
W. Rudin: Principles of mathematical analysis |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: