ECTS
ECTS Course Catalogue
Course details
Course code: IBN10127o13Semester: 2013/2014 winter
Name: Selected topics in algebra
Major: Civil Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 5
Hours (Lectures / Tutorials / Other): 9 / 18 / 0
Lecturer: dr Roman Dąbrowski
Language of instruction: Polish
Learning outcomes: Knowledge Student knows the concept of real and complex numbers and has knowledge of the relationship between these sets; he knows the terms matrix and determinant, knows problems that can be solved using matrices; is familiar with systems of linear equations and their methods of solving; knows the term rank of a matrix and understands its importance to the question of solvability system, knows the terms vector, line and plane in three dimensional space; knows basic formulas for area and volume of selected areas and solids. Skills Student can solve equations in the complex domain, is able to present complex numbers in the trigonometric form and use it to calculate powers and roots of numbers; is able to solve the matrix equation and to calculate the determinant of a matrix of any degree by at least two methods; can solve the system of linear equations using Cramer's formulas, calculate the area of any parallelogram and the volume of any parallelepiped in space, is able to designate the equation lines and planes satisfying certain conditions, is able to use the geometric method for solving some problems.
Competences: He understands the importance of algebraic methods to describe geometric problems and notes the relationship between the different parts of mathematics and their links to technical sciences.
Prerequisites: Mathematics at secondary school.
Course content: The sets of real, rational and irrational numbers. Operations in the set of complex numbers. Geometrical interpretation of complex number. Trigonometric form and Moivre formula. Polynomials of complex variable. Matrix algebra. Determinant of matrix. Inverse matrix. Systems of linear equations. The theorems of Cramer and Kronecker-Capelli. Vectors in R3. Operations over set of vectors. Inner, outer and mixed product of vectors. Applications to calculate of area and volume. Plane and line equation in three dimensional space.
Recommended literature: T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1, Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 1999 T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1, Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław 1999 W. Krysicki, L. Włodarski. Analiza matematyczna w zadaniach cz.1, PWN Warszawa 1997 Mostowski A., Stark M, Algebra liniowa, PWN, Warszawa, 1976.
Assessment methods: obligatory passing grades of classes and exam after semester- at least 60% .
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