Matrixes and determinants, solving of linear equations system, fundamental definitions of 3D-analytical geometry. Differential and integral calculations for one-variable functions. Matrix calculations. Inverse matrix. System of linear equations — formula of Cramer, Kronecker-Capelli.
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Matrixes and determinants, solving of linear equations system, fundamental definitions of 3D-analytical geometry. Differential and integral calculations for one-variable functions. Matrix calculations. Inverse matrix.
System of linear equations — formula of Cramer, Kronecker-Capelli. Method of the Gauss elimination and triangulization. Vector calculations, scalar, vector and mixed product. Plane and line equations. Surface and curve of second order. Differential calculations. Limit and continuity of a function. Definition of the derivative. Integral calculations of one-variable function and its applications in geometry. Jurlewicz, Z. Gewret, Z. Krysicki, L. Kajetanowicz, J. Chalfen, T.
Chalfen, J. Student be able to use methods of matrix calculations to solving a system of linear equations. He can apply matrix calculations to solving a problem in analytical geometry in 3-D space. He can apply a differential calculations to analysis of variability of function. He be able to use an integral methods to geometric calculations.
Student appreciates a necessity of exact problems formulation. He understands an important sense of technical sciences in environmental and spatial management. He understands a necessity of self-education. Skip to main menu Skip to submenu Skip to content. Print syllabus.
Choosen plan division: this week course term. Course descriptions are protected by copyright. You are not logged in log in. Mathematical knowledge from secondary school. Compulsory: T. Assessment methods and assessment criteria:. Choosen plan division: this week course term see course schedule. Lecture, 30 hours more information Tutorials, 30 hours more information.
Objectives of the course: Introduction to linear algebra. Basic algebraic structures groups, fields, linear spaces and properties of algebraic operations. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems:. Cartesian products. Relations orderings, partitions and equivalence relations.
Algebra Liniowa 2 - Przykłady I Zadania, Jurlewicz, Skoczylas, Gis 2003
Lecture 1 - Preliminaries Presentation of various algebraic objects with particular emphasis on differences and relationships between them. Definitions of number sets: natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, vectors and matrices. Relationships between the objects: the representation of a set of vectors as a matrix, the representation of a complex number as a vector. Lecture 2 - Properties of number sets Divisibility of integers, the congruence modulo, Chinese Remainder Theorem, different number systems.
Some basic information about the module
The name of the module: Calculus and linear algebra. The name of the faculty organization unit: The faculty Electrical and Computer Engineering. The name of the module department : Department of Mathematics. The contact details of the coordinator: the building L, room E, phone , kpupka prz. The main aim of study: To acquaint students with the basics of differential and integral calculus of functions of one variable and with the elements of linear algebra. Basic requirements in category knowledge: Basic mathematical knowledge of secondary school.