The aim of studying and bibliography

The main aim of study: The aim of the course is to familiarize students with the following concepts of mathematical analysis: the notion of the curve, surface, multiple integral, line integral, surface integral. Students should understand these concepts and gain practical ability to solve related tasks.

The general information about the module: The module is implemented in the fourth semester in the form of lectures (30 hours) and exercises (30 hours).

Bibliography required to complete the module

Bibliography used during lectures

1	A. Birkholc	Analiza matematyczna. Funkcje wielu zmiennych	Wydawnictwo Naukowe PWN, Warszawa.	2013
2	W. Rudin	Podstawy analizy matematycznej	Wydawnictwo Naukowe PWN, Warszawa.	2012

Bibliography used during classes/laboratories/others

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	Oficyna Wydawnicza GiS.	dow.
2	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach. Cz. II	PWN, Warszawa.	dow.

Bibliography to self-study

1	M. Gewert, Z. Skoczylas	Analiza matematyczna II. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS.	dow.
2	M. Gewert, Z. Skoczylas	Analiza matematyczna II. Kolokwia i egzaminy	Oficyna Wydawnicza GiS.	dow.

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 on differential and integral calculus of functions of one variable and linear algebra.

Basic requirements in category skills: Ability to calculate derivative, integral, limits, to investigate monotonicity.

Basic requirements in category social competences: Student is prepared to undertake objective and justified actions in order to solve the posed exercise.

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 the double integrals and the triple integrals	lecture, exercises	written test, exam	K_W01++ K_W02+ K_W03++ K_W04++ K_W07++ K_U13+++ K_U14+++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
02	can apply multiple integrals to calculate surface areas and volumes of solids	lecture, exercises	kolokwium, egzamin	K_W01+ K_W04++ K_W07++ K_U13+++ K_U14+++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
03	can calculate curve integrals of a scalar and a vector field	lectures, exercises	written test, exam	K_W01+ K_W03++ K_W05++ K_W07++ K_U13+ K_U14++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
04	can calculate simple surface integrals	lecture, exercises	written test, exam	K_W01+ K_W04+ K_U13+ K_U14++	P6S_UW P6S_WG P6S_WK

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
4	TK01	Multiple integrals. Jordan measure. Measurability of a set in Jordan sense. The concept of double integral. Changing of double integral onto iterative integrals. Triple integral. Changing of triple integral onto iterative integrals. geometrical and mechanical applications of multiple integrals.	W01 - W12, C01 - C12	MEK01 MEK02
4	TK02	Curves and surfaces in three dimensional space. The concept of an arc a curve. The concept of a piece of surface. The orientation of the piece of surface.	W13 - W16, C13 - C16	MEK03 MEK04
4	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.	W17 - W24, C17 - C24	MEK03
4	TK04	Surface integral. The concept of the surface integral of a vector field. Properties of surface integrals. Applications of surface integral in the field theory. Gauss-Ostrogradski theorem and stokes theorem.	W25 - W30, C25 - C30	MEK01 MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 4)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 4)	The preparation for a Class: 10.00 hours/sem. The preparation for a test: 30.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 4)		The participation in Advice: 5.00 hours/sem.
Exam (sem. 4)	The preparation for an Exam: 30.00 hours/sem.	The written exam: 3.00 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	A credit for the lecture is based on the written exam. There is a possibility of exemption from the exam based on a good grade of a class.
Class	Student is obliged to pass each module outcome defined for the course.The grade from the classes is the arythmetic mean of grades of module outcomes (rounded to the obligatory scale). Student's activity during tutorials can raise the grade.
The final grade	The final grade is the weighted mean of grades of the classes (with weight 2) and the exam ( with weight 1), rounded to the obligatory scale (provided that student have passed both the classes and the exam). In case of being exepted from the exam the final grade is the grade of the classes.

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 : no

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