MODULE DESCRIPTION Module code Module name Algebra liniowa Module name in English Linear Algebra Valid from academic year 013/014 MODULE PLACEMENT IN THE SYLLABUS Subject Level of education Studies profile Form and method of conducting Specialisation Unit conducting the module Module co-ordinator Automatic Control and Robotics 1 st degree (1st degree / nd degree) General (general / practical) Full-time (full-time / part-time) The Department of Mathematics Beata Maciejewska, PhD Approved by: MODULE OVERVIEW Type of subject/group of subjects Module status Language of conducting Module placement in the syllabus - semester Subject realisation in the academic year Initial requirements Examination Number of ECTS credit points 4 Method of conducting Basic (basic / major / specialist subject / conjoint / other HES) Compulsory (compulsory / non-compulsory) Polish 1 st semester Winter semester (winter / summer) Mathematical knowledge and skills concerning secondary education syllabus (module codes / module names) Yes (yes / no) Per semester 0 0 Lecture Classes Laboratory Project Other TEACHING RESULTS AND THE METHODS OF ASSESSING TEACHING RESULTS
Module target The module covers basic issues as regards linear algebra and analytical geometry: complex number domain, matrices, determinants, systems of linear equations, and analytical geometry in space. The aim of the module is to deliver indispensable mathematical apparatus to students (in order to solve equations in a complex domain, matrix equations, systems of linear equations, and the issues of analytical geometry). Calculus of vectors (together with the application of geometry in mechanics) comprises a substantial part of the course. Effect symbol Teaching results Teaching methods (/l/p/other) subject effects effects of a field of study A student is familiar with complex numbers. A student is acquainted with the fundamentals of a matrix and vector calculus. A student knows the selected solutions concerning the systems of linear equations. A student has knowledge on basic concepts of analytical geometry. A student knows basic types of quadrics. A student is capable of solving polynomial equations in the set of complex numbers. A student is able to make operations on matrixes; a student can also calculate determinants. A student can solve the systems of linear equations. Moreover, a student can select an appropriate method as regards solving a system of equations. A student is capable of solving simple equations concerning analytical geometry. In addition, a student is able to apply a calculus of vectors in practice. A student is able to draw diagrams of basic quadrics. A student understands the necessity of continuous education and raising his/her competences as regards mathematical methods applied in solving typical engineering problems. Additionally, a student is able to improve and perfect the acquired knowledge and skills as regards the methods of solving linear equations (together with their systems), a matrix as well as vector calculus. A student is aware of the responsibility for his/her own work; moreover, a student is able to comply with the principles of teamwork. c K_K01 K_K04 T1A_K01 T1A_K03 T1A_K04 Teaching contents: Teaching contents as regards lectures Lecture number Teaching contents teaching results for a module 1 The set of complex numbers. Geometrical interpretation of a complex
3 4 number. Operations on the set of complex numbers. Complex number module and argument. An algebraic, trigonometric, and exponential form of a complex number. De Moivre s and Euler s formulas. The root of a complex number. Geometrical interpretation as regards the value of a complex number root. Solving polynomial equations in a complex domain. Matrices and their types. Matrix algebra. A determinant. The properties of determinants (together with calculating them). Laplace expansion. Inverse matrix. Matrix equations. The systems of linear equations. Matrix form of systems of equations. 5 Cramer s formulas. Gauss s elimination method. 6 Vectors. Operations on vectors. Scalar, vector, and mixed product. 7 The elements of analytical geometry on a plane. 8 The elements of analytical geometry in space: a straight line and a plane. 9 Mutual position of points, straight lines, and planes in space. 10 Quadrics. A canonical form and diagrams of basic second-order surfaces. Teaching contents as regards Class number 1 Teaching contents Geometrical interpretation of a complex number. Operations on the sets of complex numbers. Presenting a complex number in a trigonometric form. Raising a complex number to a power. Determining a complex number root. Solving polynomial equations in a complex domain. Reference to teaching results for a module 3 Operations on matrices. Calculating determinants. 4 Inverting a matrix. Solving matrix equations. Solving systems of linear equations with the use of Cramer s formulas and 5 Gauss s elimination method. 6 Operations on vectors. Scalar, vector, and mixed product. 7 Determining equations of a plane and straight line. 8 Examining mutual position of points, straight lines, and planes in space. 9 Quadrics. A canonical form as well as the diagrams of basic second-order
surfaces. 10 A test. The methods of assessing teaching results Effect symbol Methods of assessing teaching results (assessment method, including skills reference to a particular project, laboratory assignments, etc.) Observing a student s involvement during the, discussions during the Observing a student s involvement during the, discussions during the STUDENT S INPUT Type of student s activity ECTS credit points Student s workload 1 Participation in lectures 0 Participation in 0 3 Participation in laboratories 4 Participation in tutorials (-3 times per semester) 8 5 Participation in project 6 Project tutorials 7 Participation in an examination 8 Participation in a final test on laboratory 9 Number of hours requiring a lecturer s assistance 50 (sum) 10 Number of ECTS credit points which are allocated for assisted work (1 ECTS credit point=5-30 hours) 11 Unassisted study of lecture subjects 10 1 Unassisted preparation for 0 13 Unassisted preparation for tests 10 14 Unassisted preparation for laboratory 15 Preparing reports 16 Preparing for a final test on laboratory 17 Preparing a project or documentation 18 Preparing for an examination 10 19 Preparing questionnaires
0 Number of hours of a student s unassisted work 50 (sum) 1 Number of ECTS credit points which a student receives for unassisted work (1 ECTS credit point=5-30 hours) Total number of hours of a student s work 50+50=100 3 ECTS credit points per module 1 ECTS credit point=5-30 hours 4 4 Work input connected with practical Total number of hours connected with practical 80 5 Number of ECTS credit points which a student receives for practical (1 ECTS credit point=5-30 hours) 3.