Academy of Technical and
Art Applied Studies Belgrade

Mathematics 1 Course code: MAT | 9 ECTS credits

Basic information
Level of Studies: Undergraduate applied studies
Year of Study: 1
Semester: 1
Requirements:
Goal: The course objective is to acquire the necessary knowledge in selected mathematical areas in order to train students to independently solve the kinds of mathematical problems that are required in geodetic profession at the level of the first cycle of higher education of applied studies. Simultaneously, the aim of the instruction is to help prospective engineers to adopt precision in thinking as well as methodical and systematic approach to solving problems of higher mathematics.
Outcome: Mastering the stipulated course material for Mathematics 1 is essential for a modern geodetic engineer and his/her diverse professional activity. Mastering the above mentioned knowledge in the course Mathematics 1 allows the student to follow lectures and exercises from a large number of professional and narrowly specialized courses at the academic program Geodesy-Geomatics easily and with understanding.
Contents of the course
Theoretical instruction:
  1. Statements and statement formulae. Quantors. Cartesian product. Relationships. Functions.
  2. Field of real numbers. Binomial formula. Field of complex numbers. Algebraic and trigonometric form of a complex number. De Moivre’s formula.
  3. Definition of a matrix. Matrix operations. Definition of determinants. Properties of determinants. Methods of calculating determinants. Inverse of a matrix. Matrix equations. Rank of a matrix. Elementary matrix transformations and matrix rank calculation.
  4. System of linear algebraic equations. Methods for their solution: Cramer's rule, matrix method, Gaussian elimination method. Kronecker-Capelli theorem.
  5. Vector algebra. Basic operations with vectors and scalars. Projection of vectors onto the axis. Linear dependence of vectors. Collinearity of vectors. Coplanarity of vectors. Decomposition of vectors. Scalar product of two vectors. Vector product of two vectors. Mixed product of three vectors. Terms of collinearity of two vectors. Terms of coplanarity of three vectors.
  6. Analytical geometry in space. Positioning of a point in space using Cartesian, spherical and cylindrical coordinates. Vector of position. Distance between two points. Various forms of the equation of plane. Distance of point from plane. Angle between two planes. Straight line in the space. Various forms of a straight line equation. The angle between two straight lines. Condition of parallelism of two straight lines. Condition of normality of two straight lines. Distance of a point from a straight line. Straight line and plane: angle between a straight line and plane; intersection point of a straight line and plane. Common normal of two straight lines. Distance between two straight lines in space.
  7. Number sequences. Accumulation point of sequence. Monotony and limitation of sequences. Limit of a sequence. Convergent and divergent sequences. General convergence criteria. More important sequences. Concept of number series. Convergent and divergent number sequences. Sequences with positive members.
  8. Introduction to real functions of one real variable (elementary functions, polynomials, rational, irrational, transcendental functions; properties of a function). Limit of a function. Operations with limit values. Continuity of a real function of one real variable.
Practical instruction (Problem solving sessions/Lab work/Practical training):
  1. Computational exercises from the fields that are discussed during lectures.
Textbooks and References
Number of active classes (weekly)
Lectures: 3
Practical classes: 3
Other types of classes: 0
Grading (maximum number of points: 100)
Pre-exam obligations
Points
activities during lectures
10
activities on practial excersises
0
seminary work
0
colloquium
50
Final exam
Points
Written exam
0
Oral exam
40