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.
Mathematics I (GAJABAN-ANALIZI1-1)
Basic data
Name and type of the study programme
Vehicle Engineering, undergraduate program
Curriculum
2023
Classes / consultation hours
2 + 2 + 0 (L+S+Labs)
Credits
5 credits
Theory – Practice
Theory: 50%, Practice: 50%
Recommended semester
Semester 1
Study mode
full-time
Prerequisites
–
Evaluation type
Mid-term evaluation
Course category
Compulsory
Language
English
Instructors
Responsible instructor
Dr. Ladics Tamás
Responsible department
Department of Basic Sciences
Instructor(s)
Wang Shanshan, Dr. Ladics Tamás
Checked by
Kelemen János
Course objectives
Course content
Lectures
Three-dimensional 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.
Seminars
Solving exercises and practical problems related to the knowledge covered in the lecture, practising at skill level.
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 and grading
Mid-term study requirements
There will be four small test on practical lectures for 10 points each, a minimum of 3 points must be achieved; two large tests will be written on theoretical lectures for 30 points each, a minimum of 10 points must be achieved. There will be on occasion given at the end of the study period to retake tests and improve the final result. Attendance in lectures is compulsory, the minimum points must be achived in each test. The final grade will be given based on the achived points according to the TVSZ.
Generative AI usage
Use of GAI tools is not permitted for solving assignments. This means GAI tools cannot be used to complete formative or summative assessments, and using GAI constitutes academic misconduct. The use of AI tools for spelling and grammar checking does not fall under this prohibition.
Study aids, laboratory background
Materials shared on MsTeams.
Readings
Compulsory readings
George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano: Thomas' Calculus,Pearson, 2009.
Recommended readings
George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano: Thomas' Calculus,Pearson, 2009.