SYLLABUS
COURSE TITLE
FACULTY/INSTITUTE
LINEAR ALGEBRA AND GEOMETRY
FACULTY OF MATHEMATICS AND NATURAL
SCIENCES
COURSE CODE
DEGREE PROGRAMME
FIELD OF STUDY
DEGREE LEVEL
ENGINEERING PHYSICS
PRIMARY
COURSE FORMAT
YEAR AND SEMESTER
NAME OF THE TEACHER
FORMA
MODE
STUDIÓW/STUDY
1ST YEAR, 1ST SEMESTER
DR MIROSŁAW ŁABUZ
COURSE OBJECTIVES
- TO FAMILIARIZE STUDENTS WITH FUNDAMENTALS OF ALGEBRA, NOTATION AND ITS
CALCULATION APPLICATIONS
- TO MAKE STUDENTS AWARE OF THE FIELD OF COMPLEX NUMBERS, MATRICES AND
LINEAR SPACES
- TO TRAIN SKILLS OF APPLICATION OF CORRECT FORMULAS AND RELATIONS FOR
CALCULATIONS
- TO TRAIN SOLVING PROBLEMS AND EXERCISES CONCERNING VECTORS, MATRICES,
COMPLEX NUMBERS, AND LINEAR SPACES
PREREQUISITES
KNOWLEDGE OF MATHEMATICAL SYMBOLS, AND BASIC
MATHEMATICAL OPERATIONS, VECTORS, AND FIELDS
KNOWLEDGE:
LEARNING OUTCOMES
- HAS THE KNOWLEDGE WITHIN THE FIELD OF ELEMENTARY
MATHEMATICS, LINEAR ALGEBRA AND GEOMETRY, AND
ELEMENTS
OF
DISCRETE
MATHEMATICS,
INCL.
MATHEMATICAL METHODS OF PHYSICS AND NUMERICAL
METHODS, NECESSARY FOR THE DESCRIPTION AND
MODELING OF PHYSICAL PHENOMENA, AND SIMPLE
TECHNICAL OBJECTS, ESPECIALLY USING A DIGITAL
TECHNIQUE
SKILLS:
- IS ABLE TO APPLY NUMERICAL METHODS FOR SOLVING
SELECTED PHYSICAL AND TECHNICAL PROBLEMS; IS ABLE TO
USE ALSO ANALYTICAL, SIMULATION, AND EXPERIMENTAL
METHODS TO FORMULATE AND SOLVE GIVEN PROBLEMS
FINAL COURSE OUTPUT - SOCIAL COMPETENCES
- UNDERSTANDS THE NECESSITY OF A CONTINUOUS STUDY
(STUDIES OF THE SECOND AND THE THIRD DEGREE,
POSTGRADUATE
STUDIES,
COURSES),
INCREASING
PROFESSIONAL, PERSONAL AND SOCIAL COMPETENCES
COURSE ORGANISATION –LEARNING FORMAT AND NUMBER OF HOURS
LECTURE
EXERCISES
TOTAL
: 45 H
: 30 H
: 75 H
COURSE DESCRIPTION
LECTURE
- INTRODUCTION OF BASICS OF ALGEBRA, PERMUTATIONS, ACTIONS, GROUPS AND FIELDS,
- INDEX NOTATION AND ITS CALCULATION APPLICATIONS,
- EXTENSION OF THE FIELD OF REAL NUMBERS R, BY THE IMAGINARY UNITY I INTO THE THE
- FIELD OF COMPLEX NUMBERS C,
- OPERATIONS IN LINEAR SPACES,
- VECTOR AND MATRIX CALCULATIONS, INCLUDING SOLVING OF SETS OF EQUATIONS WITH
THE - USE OF CRAMER METHOD,
- AFFINE SPACES, ELEMENTS OF ANALYTICAL GEOMETRY,
- LINEAR SPACE, ORTHONORMAL BASIS
EXERCISES
- MULTIPLICATION AND DIVISION OF POLYNOMIALS, NEWTON BINOMIAL
- KRONECKER DELTA, MATHEMATICAL INDUCTION
- VECTORS, SCALAR AND VECTOR MULTIPLICATION
- COMPLEX NUMBERS – REAL AND IMAGINARY PART, MODULE, PHASE, COMPLEX
CONJUGATION, TRIGONOMETRIC AND GEOMETRIC FORM, GRAPHIC FORM OF COMPLEX
NUMBERS
- MATRICES: ADDITION, MULTIPLICATION, INVERSE MATRIX, SOLVING SETS OF EQUATIONS
- LINEAR SPACE, ORTHONORMAL BASIS, VECTOR NORMALIZATION
METHODS OF INSTRUCTION
REQUIREMENTS AND ASSESSMENTS
LECTURE, SOLVING CALCULATION PROBLEMS DURING
EXERCISES
- STUDENTS ARE RESPONSIBLE FOR THEIR OWN
LEARNING,
- STUDENTS ARE REQUIRED TO BE FAMILIAR WITH THE
PROPER PROBLEMS BEFORE EACH CLASS
- ASSESSMENT AFTER EACH CLASS, INCL. TESTS AND
VERBAL ANSWERING
GRADING SYSTEM
TOTAL STUDENT WORKLOAD
NEEDED TO ACHIEVE EXPECTED
LEARNING OUTCOMES EXPRESSED
IN TIME AND ECTS CREDIT POINTS
LANGUAGE OF INSTRUCTION
INTERNSHIP
MATERIALS
EXAM (50%)
TESTS, ACTIVITY (50%)
LECTURE: 45 H
EXERCISES: 30 H
CLASSES PREPARATION: 30 H
INDIVIDUAL TUTORIALS: 15 H
EXAM PREPARATION: 30 H
TOTAL: 150 H
ECTS: 5
ENGLISH
PRIMARY OR REQUIRED BOOKS/READINGS:
- R. A. SHARIPOV, COURSE OF LINEAR ALGEBRA AND
MULTIDIMENSIONAL GEOMETRY
- I. R. SHAFAREVICH, A. REMIZOV, LINEAR ALGEBRA AND
GEOMETRY
- M. L. BOAS, MATHEMATICAL METHODS IN THE PHYSICAL
SCIENCES
SUPPLEMENTAL OR OPTIONAL BOOKS/READINGS:
ACADEMIC BOOKS FOR ALGEBRA