The aim of studying and bibliography

The main aim of study: Providing the fundamental knowledge from the differential and integral calculus. The student will understand mathematical language and basis calculus to formulate and solve physical problems. The student will acquaint with some basic mathematical knowledge from differential and integral calculus and adopt the abilities of use mathematical tools in physics.

The general information about the module: The course includes properties of set theory, sequences, fundamental properties of the functions of one and several variables, differential calculus of one and several variables, indefinite and definite integral and applications of differential and integral calculus in physics.

Teaching materials: Materiały w wersji elektronicznej umieszczone na stronie domowej

Bibliography required to complete the module

Bibliography used during lectures

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 1, definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław .	2006
2	J. Stankiewicz, K. Wilczek	Rachunek różniczkowy i całkowy funkcji jednej zmiennej, Teoria, przykłady, zadania	Oficyna wydawnicza Politechniki Rzeszowskiej, Rzeszów.	2000
3	J. Stankiewicz, K. Wilczek	Rachunek różniczkowy i całkowy funkcji wielu zmiennych, Teoria, przykłady, zadania	Oficyna wydawnicza Politechniki Rzeszowskiej, Rzeszów.	2000
4	M. Gewert, Z. Skoczylas	Analiza matematyczna 2, definicje, twierdzenia, wzory	Oficyna wydawnicza GiS, Wrocław.	2006

Bibliography used during classes/laboratories/others

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 1, przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2006
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2, przykłady i zadania	Oficyna wydawnicza GiS, Wrocław.	2006

Basic requirements in category knowledge/skills/social competences

Formal requirements: Secondary school level, secondary-school certificate

Basic requirements in category knowledge: Basic knowledge of mathematics on secondary school level

Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the secondary school

Basic requirements in category social competences: The 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 OEK
01	knows elements of logic and sets theory. Understand the notion of sqeuence, and the limit of the sequence. Understand the notion of improper limit, indeterminate forms. Knows the Euler constant as a limit of the sequence.	lecture, classes	written exam, colloquium	K_W004+	T1A_W01++ W02++ W04+ W05+
02	Knows functions of one real variable and elementary functions. Understand the limit of function, divergent functions, continuous functions and its properties.	lecture, classes	written exam, colloquium	K_W004+ K_K006+	T1A_W01++ W02++ W04+ W05+ K01++
03	student knows the notion of derivative, determine the derivatives of simple derivatives. Know how to use derivatives to determine the properties of function of one real variable.	lecture, classes	written exam, colloquium	K_W014+ K_U013+ K_K006+	T1A_W01+++ W02+++ W04+ U01+ InzA_U02+++ U05+ K01+
04	student knows the notion of the indefinite and definite integral. Calculate simple integrals. Apply methods of integration in practice.	lecture, classes	written exam, colloquium	K_W014+ K_U013+	T1A_W01+++ W02+++ W04+ U01+ InzA_U02+++ U05+
05	knows the notion of functions of several variables, vector functions and its basic properties. Knows the basic applications in physics.	lecture, classes	written exam, colloquium	K_W003+ K_W014+ K_U013+	T1A_W01+++ W02+++ W04+ W05+ U01+ InzA_U02++ U05+

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
1	TK01	The basic problems in logic and set theory. Sequences, limit of sequences.	W01- W08, C01- C08	MEK01
1	TK02	Functions of one variable. Composite functions, onetoone functions, inverse functions. Elementary functions. A limit of a function. Asymptotes. Limit, continuity.	W09 - W25, C09- C25	MEK02
1	TK03	Functions of one variable. Composite functions, onetoone functions, inverse functions. A limit of a function. Asymptotes. Limit, continuity, The derivative of a function and its interpretations. The Mean Value Theorem. Graph sketching and problems of extrema. . Various geometric and physical applications. LHospital rule. Concavity of functions. Taylors formula.	W26 - W36, C26- C36	MEK03
1	TK04	Antiderivatives. The indefinite and definite integral. Techniques of integration. Applications to physics.	W37 - W50, C37- C50	MEK04
1	TK05	Functions of several variables. Partial derivatives. Directional derivatives, the gradient. Extrema. The derivative of a vector function.	W51 - W60, C51- C60	MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)	The preparation for a test: 10.00 hours/sem.	contact hours: 60.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 10.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 60.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 4.00 hours/sem.	The participation in Advice: 4.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 20.00 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	Examination paper will consist of 5 structured questions (answers only). Grading score 3.0 for 50% - 60%, 3.5 for 61% - 70%, 4.0 for 71% - 80%, 4.5 for 81% - 90%, 5.0 for 91% - 100%
Class	3 tests. Grading score for each test 3.0 for 50% - 60%, 3.5 for 61% - 70%, 4.0 for 71% - 80%, 4.5 for 81% - 90%, 5.0 for 91% - 100% . Final grade is medium from the evaluation of all tests.
The final grade	medium from the evaluation of classes and exam

Sample problems

Required during the exam/when receiving the credit
Funkcje_jednej_zmiennej_1.pdf

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