Academy of Technical and
Art Applied Studies Belgrade

Mathematics 1 Course code: MAT1 | 6 ECTS credits

Basic information
Level of Studies: Undergraduate applied studies
Year of Study: 1
Semester: 1
Requirements:
Goal: The objective of the course is acquiring the necessary knowledge of selected areas of mathematics which are relevant to modern engineers of construction and architecture and their diverse professional activity. At the same time, it is expected that prospective engineers adopt precision in thinking as well as methodical and systematic approach to solving problems of higher mathematics.
Outcome: Mastering the above mentioned knowledge within the course Mathematics 1 allows students to follow lectures and exercises from the majority of applied and narrowly specialized courses in the academic program of the civil engineering department easily and with understanding.
Contents of the course
Theoretical instruction:
  1. Statements and propositional 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 determinant. Properties of determinants. Methods of calculating determinants. Definition of a matrix. Matrix operations.Inverse of a matrix. Matrix equation. Rank of a matrix. Elementary matrix transformations and matrix rank calculation.
  4. System of linear algebraic equations. Methods for their solution: Gaussian elimination method. Cramer's rule, matrix method, Kronecker-Capelli theorem, homogeneous system.
  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. Algebraic curves of the second order. Reducinga curve of the second order in canonical form.
Practical instruction (Problem solving sessions/Lab work/Practical training):
Textbooks and References
Number of active classes (weekly)
Lectures: 2
Practical classes: 2
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
60
Final exam
Points
Written exam
0
Oral exam
30