Uniwersytet w Białymstoku - Centralny System UwierzytelnianiaNie jesteś zalogowany | zaloguj się
katalog przedmiotów - pomoc

Analysis I

Informacje ogólne

Kod przedmiotu: 390-ERS-1AM1 Kod Erasmus / ISCED: 13.201 / (0533) Fizyka
Nazwa przedmiotu: Analysis I
Jednostka: Wydział Fizyki
Grupy:
Punkty ECTS i inne: 8.00
zobacz reguły punktacji
Język prowadzenia: angielski
Rodzaj przedmiotu:

fakultatywne

Założenia (opisowo):

(tylko po angielsku) Lecture on differential and integral calculus of functions of one variable. The exercises focus on developing accounting skills.

Tryb prowadzenia przedmiotu:

w sali

Skrócony opis: (tylko po angielsku)

Brief overview of the mathematical foundations (aimed at showing the extent of the subject and interesting threads rather than completeness), with a slightly broader discussion of numerical series.

Classical discussion of the differential calculus of functions of one variable, with an emphasis on investingation of functions and Taylor series. Detailed discussion of indefinite and definite integrals of functions of one variable.

Pełny opis: (tylko po angielsku)

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

Literatura: (tylko po angielsku)

W. Rudin: Principles of mathematical analysis

W.Krysicki, L.Włodarski: Analiza matematyczna w zadaniach,

M.Gewert, Z.Skoczylas, Analiza matematyczna I

Efekty uczenia się: (tylko po angielsku)

Student:

1. Learns the basic mathematical apparatus of mathematical analysis and other branches of higher mathematics, necessary for the further study of physics.

2. Gains computational skills and the ability to use mathematical tools to formulate and solve problems in physics and related disciplines.

3. Can carry out basic mathematical reasoning.

4. Uses mathematical language to describe physical reality.

5. Possesses computational skills in the field of differential and integral calculus of functions of one variable.

6. Is familiar with the issues of higher mathematics which are important for the further study of physics.

7. Can apply the methods of higher mathematics to the problems of mathematical and natural sciences.

Metody i kryteria oceniania: (tylko po angielsku)

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 a written and oral exam to verify the acquired knowledge.

Praktyki zawodowe:

Nie ma

Zajęcia w cyklu "Rok akademicki 2019/20" (zakończony)

Okres: 2019-10-01 - 2020-06-30
Wybrany podział planu:


powiększ
zobacz plan zajęć
Typ zajęć: Konwersatorium, 60 godzin więcej informacji
Wykład, 45 godzin więcej informacji
Koordynatorzy: Jan Cieśliński
Prowadzący grup: Jan Cieśliński, Artur Kobus
Lista studentów: (nie masz dostępu)
Zaliczenie: Przedmiot - Egzamin
Konwersatorium - Zaliczenie na ocenę
Opisy przedmiotów w USOS i USOSweb są chronione prawem autorskim.
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.