The aim of studying and bibliography

The main aim of study: The aim of the course is to familiarize students with such topics of mathematical analysis, such as: partial derivatives, extrema of functions of two variables, double and triple integrals, curve integrals, surface integrals, their applications and use of CAS Maxima software.

The general information about the module: The module consists of 30 hours of lectures, 30 hours of classes and 15 hours of laboratories. It ends with an exam.

Bibliography required to complete the module

Bibliography used during lectures

1	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	2008.
2	W. Żakowski, W. Kołodziej	Matematyka cz.2. Analiza matematyczna	WNT, Warszawa.	2013.
3	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Definicje, twierdzenia, wzory	GiS, Wrocław.	2016.
4	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach cz.2	PWN, Warszwa.	2011.
5	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	GiS, Wrocław.	2016.
6	P.N. de Souza, R.J. Fateman, J. Moses, C. Yapp	The Maxima Book	http://maxima.sourceforge.net.
7	G. Berman	Zbiór zadań z analizy matematycznej	Pracownia Komputerowa Jacka Skalmierskiego, Gliwice.	2000.

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: Knowledge of the basics of the differential and integral calculus of one variable function.

Basic requirements in category skills: Ability to calculate limits and derivatives of functions and basic indefinite and definite integrals.

Basic requirements in category social competences: Preparation for taking substantively justified mathematical actions to solve the posed problem.

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	Can calculate partial derivatives and extrema of functions of two variables.	lecture, solving classes, laboratory	test, written exam	K_W01+ K_U01+	P6S_UW P6S_WG
02	Can calculate the double integrals and the triple integrals.	lecture, solving classes, laboratory	test, written exam	K_W01+ K_U01+	P6S_UW P6S_WG
03	Can calculate curve integrals	lecture, solving classes, laboratory	test, written exam	K_W01+ K_U01+	P6S_UW P6S_WG
04	Can calculate surface integral.	lecture, solving classes, laboratory	test, written exam	K_W01+ K_U01+ K_K01+	P6S_KK P6S_UW P6S_WG
05	Can calculate derivatives of multiple variables and multiple integrals in the CAS Maxima and perform graphs of functions in 2D and 3D.	laboratory	project at the computer	K_W02+ K_K02+	P6S_KK P6S_KO P6S_WG

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
2	TK01	Differential calculus of functions of several variables. Partial derivatives. Extrema of functions of two variables.	W1-W12, C1-C12, L1-L5	MEK01 MEK05
2	TK02	Double and triple integrals. Iterated integrals. Applications of multiple integrals.	W13-W20, C13-C20, L6-L10	MEK02 MEK05
2	TK03	Curve integrals. Curve integral of a scalar field, its properties and applications. Curve integral of a vector field and methods of its evaluating. Green theorem and its applications.	W21-W26, C21-C26, L11-L13	MEK03 MEK05
2	TK04	Surface integral. The concept of the surface integral of a vector field. Properties of surface integrals.	W27-W30, C27-C30, L14-L15	MEK04 MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 3.00 hours/sem. Studying the recommended bibliography: 2.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 5.00 hours/sem. The preparation for a test: 8.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 3.00 hours/sem.
Laboratory (sem. 2)	The preparation for a Laboratory: 5.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Making the report: 5.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 1.00 hours/sem.
Exam (sem. 2)	The preparation for an Exam: 10.00 hours/sem.	The written exam: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	Written exam. The obvious exercises and the extra exercises. The obvious exercises must be solved. Only the obvious exercises - 3.0.
Class	Written tests. The obvious exercises and the extra exercises. The obvious exercises must be solved.
Laboratory	Project at the computer (obligatory).
The final grade	After the credit of all types of classes the final grade is the average of grade of classes (x 0,4), grade of laboratory (x 0,2) and grade of exam (x 0,4).

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : yes

Available materials : undersigned the leaf of format what the highest A4, double-recorded, with any content

The contents of the module are associated with the research profile: no