Mathematics in Architecture 2

Introducing students to the concepts from the curriculum, for their application in geometry and professional subjects.

Mastering the techniques of differential and integral calculus with an emphasis on the application in solving various geometric problems, applications in structural physics, technical mechanics and other professional subjects.

Basic concepts of functions of one variable; Different ways of representing functions: explicitly, implicitly, parametrically, in polar coordinates. Properties of elementary functions; Sequences of real numbers, Golden Section and Fibonacci sequence; Limes function; Continuous functions; Definition of the first derivative of the function and basic properties; Geometric interpretation of the first derivative of a function. Higher order derivatives; Application of derivation in determining tangents and norms to curves; Application of differential calculus in solving extreme problems in geometry; Application of differential calculus in testing functions and drawing graphs;
Primitive functions and indefinite integrals; Different integration methods. Definitive integral and its application for the calculation of the surfaces of straight figures, the volume of rotating bodies, the length of the arc of a curve, and for the calculation of the surface of a rotating surface; First order differential equations: equations with a separated variable, homogeneous differential equation, linear differential equation.

1. S. Kosić-Jeremić: Mathematics in architecture 2, University of Banja Luka, Faculty of Architecture, Civil Engineering and Geodesy, Banja Luka, 2022.

2. P. Miličić, M. Ušćumlić: Collection of Problems in higher mathematics 1, Scientific book, Belgrade 1999.

3. R. Kravarušić, M. Mijatović: Mathematics - Collection of Problems, Faculty of Economics, Banja Luka, 2002.

Colloquia, written and oral exam, class activity.

Lectures, exercises, consultations, independent work.