Theory: 60 %

Practice: 40 %

Recommended semester: 3

Study mode: full-time

Prerequisites: Mathematics II

Evaluation type: exam

Course category: compulsory

Language: english

Responsible instructor: Dr. Osztényi József

Responsible department: Department of Basic Sciences

Instructor(s): Dr. Osztényi József

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:

Course content - labs:

Acquired competences:
Knowledge:

Skills:

Attitude:

Autonomy and responsibilities:

Additional professional competences:

The students will become familiar with the basic concepts and tools of advanced mathematical analysis, they know and understand the scientific principles, relations and procedures that are necessary and required in engineering professions. They will be able to recognize a problem of higher mathematics, identify the adequate method to solve it and they can apply the method in a quick and precise manner. They are able to build an adequate mathematical model for a given technical problem, to generalize it for similar cases.

Requirements, evaluation, grading:
Mid-term study requirements:
Semester 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. Examination 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).
Exam requirements:

Study aids, laboratory background:

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.