Theory: 60 %

Practice: 40 %

Recommended semester: 3

Study mode: full-time

Prerequisites:

Evaluation type: exam

Course category:

Language: english

Responsible instructor: Dr. Osztényi József

Responsible department: Department of Basic Sciences

Instructor(s): Dr. Ladics Tamás

Course objectives:
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.

Course content - lectures:

Differential geometry: curves and surfaces. Line and surface integrals of vector-valued functions. Divergence and curl of a vector field. Green’s and Stokes’s Theorem. Complex functions: limits, continuity and differentiation. Elementary and regular complex funtions. Integration of complex function. Cauchy's integral formula. Random experiment, frequencies. Elementary probability models. Probability spaces. Conditional probability and independence. Random variables. Distribution function and density function. Expected value, variance and moments. Statistical sample, empirical distribution function. Estimating the expectation and the variance. Point estimations: maximum-likelihood method. Confidence intervals. Hypothesis testing: compare means: u-test, one sample t-test, two samples t-test. Estimating the covariance and correlation. Linear regression.

Course content - seminars:

The curriculum of the practice is the same as the curriculum of the lecture.

Course content - labs:

The lab curriculum is the same as the lecture curriculum.

Acquired competences:
Knowledge:

Knowledge of the general and specific mathematical and scientific principles, rules, relationships and procedures necessary for the operation of the technical field.

Skills:

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. 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.

Attitude:

Have the stamina and tolerance of monotony to carry out practical activities. Ability to work efficiently, qualitatively and continuously, to work independently and in cooperation with others, and to take responsibility for the work submitted.

Autonomy and responsibilities:

Ability to work efficiently, qualitatively and continuously, to work independently and in cooperation with others, and to take responsibility for the work submitted.

Additional professional competences:

Requirements, evaluation, grading:
Mid-term study requirements:
During the semester three tests will be written, for 20-20 points. At the end of the semester the students can write one test to increase their points by replacing the results by the new one.
Exam requirements:

In the exam period the students write an exam for 40 points. They will be evaluated based on their total points (at most 100 possible) according to the valid TVSZ (regulation of study and examination).

Study aids, laboratory background:

Lessons upload to MS TEAMs.

Compulsory readings:

-

Recommended readings:

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano: Thomas' Calculus,Pearson, 2018. Joseph Bak , Donald J. Newman: Complex Analysis, Springer-Verlag New York Inc., 2010. Marco Taboga: Lectures on Probability Theory and Mathematical Statistics, ‎ CreateSpace Independent Publishing Platform, 2017.