ECTS
ECTS Course Catalogue
Course details
Course code: IISS10409o12Semester: 2012/2013 winter
Name: Algebra
Major: Environmental Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 7
Hours (Lectures / Tutorials / Other): 30 / 30 / 0
Lecturer: dr hab. Wiesław Szulczewski, prof. nadzw.
Language of instruction: Polish
Learning outcomes: Uses the notion of linear space, vector, matrix, knows how to calculate determinants and knows their property; solve systems of linear equations with constant coefficients, calculates the eigenvalues and eigenvectors of the matrix.
Competences: He knows his own limitations of knowledge and understands the need for further education.
Prerequisites:
Course content: Basic mathematical logic. Action in the set of complex numbers. Polynomials of a complex variable. Fundamental theorem of algebra. Rational functions and distribution to simple fractions. Algebra of matrices and determinants. Matrix equation. The Government of the matrix. Systems of linear equations. Eigenvalues and eigenvectors of the matrix, the matrix characteristic polynomial. Analytical Geometry in the plane. Linear transformations. Vector space. Analytic geometry in space. Selected class of curves and surfaces of the second degree.
Recommended literature: First Mostowski, A., Stark, M., 1975, Elements of higher algebra, PWN, Warsaw. Second Mostowski, A., Stark, M., 1976, Linear Algebra, McGraw-Hill, London. 3rd Jurlewicz T., Z. Skoczylas, 1999 (and later editions), Linear Algebra first Definitions, theorems, models, GIS Publishing House, Wroclaw. 4th Jurlewicz T., Z. Skoczylas, 1999 (and later editions), Linear Algebra first Examples and exercises, GIS Publishing House, Wroclaw. 5th F. Hopper, 1976, Analytical Geometry, McGraw-Hill, London. 6th S. Smolik, 2004, the tasks of the application of mathematics to the Agricultural Academy, Warsaw Agricultural University, Warsaw.
Assessment methods: Assessment of exercise on the basis of the results of ongoing tests and assessments. Written and oral exam.
Comment: Lecture 1: Fundamentals of mathematical logic. Lecture 2: Actions in the set of complex numbers. The geometric interpretation of complex numbers, trigonometric form of a complex number. De Moivre formula, square roots of complex numbers. Lecture 3: complex variable polynomial. Lecture 4: The fundamental theorem of algebra. And the distribution of rational functions into partial fractions .. Lecture 5: Algebra of matrices and determinants. Operations on matrices, determinants property, claim Laplace, Cauchy's theorem. Lecture 6: The matrix inverse, matrix equations, types of square matrices, rank of a matrix. Lecture 7: Systems of linear equations. Tw. Cramer. Lecture 8: Systems of linear equations. Tw. Kronecker-Capelli. Lecture 9: Gaussian elimination method. Homogeneous systems of linear equations. Lecture 10: Eigenvalues and eigenvectors of the matrix, the matrix characteristic polynomial. Lecture 11: Analytical Geometry in the plane. Linear transformations. Lecture 12: Space Vector. Lecture 13: Analytical Geometry in space. Cash vector - scalar, vector and mixed. Lecture 14: Equations of the plane and straight into space. Lecture 15: Selected class of curves and surfaces of the second degree.