Course title, code: Mathematics I, GAGEBANANALIZI11
The aim of the course is to make the students learn the basic concepts and tools of advanced mathematical analysis that are necessary and required in engineering studies and later on in their profession.
Threedimensional vectors. Solving systems of linear equations. Matrices, multiplication of matrices, inverse matrix, rank. Linear transformations, eigenvector, eigenvalue. Complex numbers. Elementary operations of complex numbers. Power and nth root in trigonometric form. Real sequences and their properties. Convergence, special limits. Real functions of a single variable. Elementary functions and their properties. Limits of real functions, continuity. Differential calculus of one variable functions. Rules and procedures of differentiation. Applications of differential calculus: sketching graphs, local and global extrema, shape of curves.
Course content  seminars:
Solving exercises and practical problems related to the knowledge covered in the lecture, practising at skill level.
Knowledge:
Knowledge of the general and specific mathematical and scientific principles, rules, relations and procedures necessary for the operation of the technical field. The students are able to identify a higher mathematical problem, the method to be used to solve it, and then, on the basis of the method chosen, to solve it quickly and accurately.
Ability to work efficiently, qualitatively and continuously, to work independently and in cooperation with others, and to take responsibility for the work submitted.
In the case of practical problems, they are able to construct and select the mathematical model needed to solve the problem, and to generalise the problem in the case of similar problems.
Have the stamina and tolerance of monotony to carry out practical activities.
Midterm study requirements:
During the semester two tests will be written. At the end of the semester the students can write one test to improve their final evaluation. For a satisfactory grade a performance of at least 50% is required.
Exam requirements:

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano: Thomas' Calculus, Pearson, 2009.