Mathematics (basic level) 0600-S1-CTZ-MATb

Lecture:

Indefinite integral:
- the concept of an antiderivative function
- elementary integrals
- fundamental properties of integrals
- integration by parts
- integration by substitution

Definite integral:
- the concept of a whole sum
- relationship with indefinite integral - Newton-Leibnitz theorem
- application for calculating surface areas
- improper integrals

Elements of linear algebra:
- Cartesian product
- the concept of linear space
- vectors and matrices and operations on them
- permutations and the sign of the permutation
- determinants and their basic properties
- scalar and vector products in R ^ 3
- inverse matrix
- matrix eigenvalues and vectors

Systems of linear equations:
- matrix representation of a system of linear equations
- Kronecker-Capelli theorem
- Cramer's rule

Multivariable Functions:
- partial derivatives
- local extremes of functions of several variables
- a study of local extremes of functions of two variables

----------------------
Tutorials:

Indefinite integral:
- integrals of elementary functions
- usage of basic properties of integrals
- integration by parts, including multiple
- integration by substitution

Definite integral:
- calculation of definite integrals using the Newton-Leibnitz theorem
- calculation of surface areas of flat areas
- calculation of surface areas and volumes of revolving solids
- calculation of improper integrals of various types

Elements of linear algebra:
- calculating the sum and product of matrices
- illustration of the concepts: transposed, unit, symmetric, orthogonal, and triangular matrix
- calculation of determinants of 2x2 and 3x3 matrices from the rules of Sarrus
- the Laplace expansion for computingh matrix determinants of higher degrees
- determining the order of the matrix
- calculation of scalar and vector products in R ^ 3, finding the length of a vector and finding orthogonality
- determination of the inverse matrix
- finding matrix eigenvalues and eigenvectors

Systems of linear equations:
- saving systems of linear equations in matrix form
- Kronecker-Capelli theorem
- finding solutions to systems of linear equations from Cramer's rule

Multivariable Functions:
- first and second-order partial derivatives
- local extremes of functions of multiple variables
- a study of local extremes of functions of two variables

Term 2022/23L:

None

Total student workload

(in Polish) - 60 godz. - zajęcia realizowane z udziałem nauczycieli (wykład + ćwiczenia) - 45 godz. - praca indywidualna - 15 godz. - przygotowania do procesu oceniania (zaliczenia) - 120 godz. - całkowity czas pracy studenta

Learning outcomes - knowledge

W1: The student knows the concepts of the antiderivative function and the indefinite integral, as well as the basic methods of calculating integrals; - K_W02 W2: The student knows what a definite integral is, how to calculate it, how to use it to calculate the area; - K_W02 W3: The student knows the basic concepts of linear algebra; knows what matrices and determinants are, how to solve the eigenproblem; - K_W02 W4: The student knows the matrix notation of systems of linear equations and knows how to use it to solve such a system; - K_W02 W5: The student knows the definition of functions of several variables and knows how to find the extremes of functions of two variables; - K_W02

Learning outcomes - skills

U1: The student calculates simple indefinite integrals using the integral by parts and by substitution methods; - K_U02 U2: The student calculates the definite integrals based on the Newton-Leibniz theorem; - K_U02 U3: The student performs matrix operations, calculates determinants, finds eigenvalues and eigenvectors; - K_U02 U4: The student solves systems of linear equations using matrix formalism; - K_U02 U5: The student calculates partial derivatives of functions of several variables, finds the extremes of functions of two variables; - K_U02

Learning outcomes - social competencies

K1: Creativity: The student thinks creatively to improve existing or create new solutions; - K_K02 K2: Conscientiousness and accuracy: The student is focused on the best possible performance of the task, takes care of details, and is systematic;- K_K03 K3: Perseverance and consistency: The student works systematically and has a positive attitude to the difficulties standing in the way to achieving the assumed goal, keeps deadlines and understands the need to work on all projects systematically; - K_K06 K4: Independence: The student entirely independently realizes the agreed goals, making sometimes difficult decisions; - K_K07

Expository teaching methods

- informative (conventional) lecture

Exploratory teaching methods

- practical

Prerequisites

High-school-level mathematics knowledge enriched with material from the first semester.

Course coordinators

Piotr Jankowski

Bibliography

Term 2022/23L:

None

Additional information

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

Description of 0600-S1-CTZ-MATb in USOSweb