Calculus II 390-FG1-1RRC2

ECTS points: 6

Student's workload balance: lecture (15 hours), practical (45 hours),
laboratory (15 houts), consultations (15 hours), domestic work and preparations for tests and exams (60 hours).

Quantified indicators:

Student's workload related to classes requiring direct lecturer's participation - 4.8 ECTS. Student's workload related to practical classes - 0.6 ECTS.

Term 2024:

Description:

1.Performing basic calculations of differential and integral calculus
2. Differentiation of composite functions, inverse functions and implicit functions.
2. Local and global extremes of functions of two variables and many variables.
Calculation of Jacobian.
3. Double and triple integrals and their applications.
4. Calculation of gradient, rotation, divergence, Laplasjan and other differential operators.
5. Calculation of line integrals (work, field circulation along a curve) and surface integrals (flux field). Applications of the Stokes theorem.
6. Solving ordinary differential equations of the first order: equations with separated variables, substitution method.
7. Solving scalar linear equations with constant coefficients. The method of varying constants for heterogeneous equations.
8. Applications of the differential equations in physics.
9. Symbolic calculations by computer.

ECTS points: 6

Student's workload balance: lecture (15 hours), practical (45 hours), laboratory (15 houts), consultations (15 hours), domestic work and preparations for tests and exams (60 hours).

Quantified indicators:

Student's workload related to classes requiring direct lecturer's participation - 4.8 ECTS. Student's workload related to practical classes - 0.6 ECTS.

Prerequisites (description)

(in Polish) Celem przedmiotu jest zapoznanie studentów z podstawami analizy matematycznej funkcji wielu zmiennych oraz podstawowymi metodami rozwiązywania równań różniczkowych zwyczajnych. Metody te pełnią kluczową rolę w fizyce. Przedmiot stanowi konieczną podstawę w nauczaniu większości przedmiotów z zakresu fizyki w toku całych studiów.

Course coordinators

Jan Żochowski

Type of course

Term 2024:

(in Polish) ogólne kierunkowe
obligatory courses

General:

obligatory courses
(in Polish) ogólne kierunkowe

Requirements

Calculus I

Prerequisites

Intoductory Mathematics

Mode

(in Polish) w sali

Number of hours of remote classes

Zero.

Learning outcomes

1. Student knows the techniques of advanced mathematics, necessary for the quantitve description and modeling of medium complexness physical problems (KP6_WG2).
2. Student, by applying mathematics ,is able to explain the regularities of physical phenomena and processes. He also can reconstruct fundamental theorems and laws (KP6_WG3).
3. Student has the abilities of applying the advanced mathematics for physical fundamental phenomena analysis. Student is able to reconstruct main theorems and equations of fundamenrtal laws of nature and to perform their proofs. (KP6_UK2).

Assessment criteria

The grade is issued on the basis of the results of two tests (arithmetic mean of percentage results) and activity (maximum 10% added to the test result):
0% - 50% - ocena niedostateczna
51% - 60% - ocena dostateczna
61% - 70% - ocena dostateczna plus
71% - 80% - ocena dobra
81% - 90% - ocena dobra plus
91% - 100% - ocena bardzo dobra

Bibliography

1. W.Krysicki, L.Włodarski: Analiza matematyczna w zadaniach, PWN, Warszawa 1998.
2. R.Rudnicki: Wykłady z analizy matematycznej, PWN, Warszawa 2001.
3. M.Gewert, Z.Skoczylas, Analiza matematyczna II, GiS, Wrocław 2004.
4. M.Gewert, Z.Skoczylas, Równania różniczkowe zwyczajne, GiS, Wrocław 2003.
5. M.Gewert, Z.Skoczylas, Elementy analizy wektorowej, GiS, Wrocław 2000.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 390-FG1-1RRC2 in USOSweb