Academy of Technical and
Art Applied Studies Belgrade

Mathematics 2 Course code: MAT2G | 6 ECTS credits

Basic information
Level of Studies: Undergraduate applied studies
Year of Study: 1
Semester: 2
Requirements:
Goal: The objective of the course is further improvement of students’ knowledge in selected mathematical fields relevant to modern engineers in civil engineering and architecture and in their diverse professional activity. Simultaneously, it is expected that prospective engineers adopt precision in thinking and methodical and systematic approach in solving problems of higher mathematics.
Outcome: Mastering the above mentioned knowledge in Mathematics 2 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. Differential calculus of a function of one real variable: Concept of a derivative and geometric interpretation of a derivative. Rules for derivative calculating. Differential of a function. Higher order derivatives of a function. Fermat's theorem. Rolle's theorem. Cauchy’s theorem. Lagrange's theorem. Bernoulli-Lopital theorem.
  2. Testing functions of one real variable.
  3. Determination of a tangent, normal and curvature circle of a function graph.
  4. Taylor and Macloren polynomial approximation.
  5. Functions of several variables. Limit and continuity of a function of several variables.
  6. Partial derivatives of functions of several variables of the first order. Partial derivatives of higher order. Total differentials of functions of several variables. Stationary points of functions of several variables: definition and their determination. Extreme values of functions of several variables: definition and procedure for their determination.
  7. Indefinite integral. Definition of an indefinite integral. Table of integrals. Methods for calculating an indefinite integral: replacement method, method of partial integration, integration of rational functions, integration of some irrational and transcendental functions.
  8. Definite integral. Definition of a definite integral. Properties of a definite integral. Connection between a definite and indefinite integral (Newton-Leibniz formula). Analytical methods of solving a definite integral. Applications of a definite integral: area of a plane figure, arc length of a curve in a plane, area of a surface of revolution and volume of solidsof revolution.
  9. Differential Equations. Concept of differential equations. Formation of differential equations. General and particular solution of a differential equation. First order differential equations. Second order linear differential equations with constant coefficients.
Practical instruction (Problem solving sessions/Lab work/Practical training):
  1. Calculation exercises from the fields discussed during lectures.
Textbooks and References
Number of active classes (weekly)
Lectures: 3
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
50
Final exam
Points
Written exam
0
Oral exam
40