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.

Details of description:

1.Performing basic calculations of differential and integral calculus
2. Differentiation of complex functions, inverse functions and implicit functions.
2. Local and global extremes of functions of two variables.
Calculation of Jacobian.
3. Double and triple integrals and their applications.
4. Calculation of gradient, rotation, divergence.
5. Calculation of line integrals (work, field circulation along a curve) and surface integrals (flux field). Checking 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 differential equations in physics.
9.Getting to know the basic tools provided by the selected package for symbolic calculations.

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)

The main goal of the course is to introduce students to the foundations of the multivariable calculus and basic methods for solving ordinary differential equations. These methods play a crucial role in physics. The course provides an essential background for the majority of physics subjects taught throughout the entire degree program.

Course coordinators

Term 2024:

Jan Żochowski

Term 2023:

Zbigniew Hasiewicz

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).

The SI use is allowed for the translations, the bibliography preparing and computer modeling. The SI is forbidden during the colloquiums and the examination periods.

Assessment criteria

Students should be present on lectures and lessons of calculations. They are stimulated for asking the questions and initiating the discussion.

Written colloquium and examination undergo after the end of the practical and lecture of differential and integral calculus II, respectively. They verify acquirement of knowledge.

Students get the series of questions, exercises and problems for individual and unassisted solving. Content of the series of questions is correlated with the lecture and practical.

Assessment of student learning is based on the grade, which includes:

1. Ability to solve the problems from definite parts of differential and integral calculus II.

2. Creative approach to solved problems.

Permanent grading by lecturer is included.

Final grade is expressed by the number established in the study regulation, which includes evaluation of the knowledge, abilities and competencies of the student. 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).

Assessment levels:

very good 5, from 100% to 91%,
plus good 4,5, from 90% to 81%,
good 4, from 80% to 71%,
plus passable 3,5, from 70% to 61%,
passable 3, from 60% to 51%,
negative 2, from 50% to 0%.

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