Calculus

A tantárgy neve magyarul / Name of the subject in Hungarian: Kalkulus

Last updated: 2024. június 17.

Budapest University of Technology and Economics
Faculty of Electrical Engineering and Informatics

Calculus BProf, BSc
Course ID Semester Assessment Credit Tantárgyfélév
TE90AX55 1 2/3/0/v 6  
3. Course coordinator and department Dr. Nagy Noémi,
4. Instructors dr. Nagy Noémi (assistant professor)

dr. Pataki Gergely

dr. Farkas Lóránt Ernő

Bodrogné dr. Réffy Júlia

dr. Nagy Ilona

dr. Tasnádi Tamás

 Department Of Analysis And Operations Research, Analysis Group, Faculty of Natural Sciences

5. Required knowledge 
High school studies.
6. Pre-requisites
Kötelező:
Training.Code=("5N-A9")

A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

Ajánlott:
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7. Objectives, learning outcomes and obtained knowledge The objective is to provide the students with the required theoretical background in calculus for further engineering.
8. Synopsis
  1. Basics of linear algebra. Determinant of a matrix. Solving a system of linear equations.
  2. Real sequences. Special limits, number e. Operations on convergent sequences. Monotonic and bounded sequences.
  3. Elementary functions and their inverses.
  4. Complex numbers.
  5. Limit of real functions of a single variable, some important limits. Continuity. 
  6. Differentiability of real functions of a single variable. Differentiation rules, derivatives of elementary functions. Curve sketching for a function, local and absolute extrema, monotonicity and convexity. L′Hospital rule, Taylor theorem.
  7. Integral of functions of a single variable. Properties of the Riemann integral, Newton-Leibniz theorem, antiderivatives, integration by parts, integration by substitution. Integration in special classes of functions. Improper integrals. Applications of the integral.
13. References, textbooks and resources

Thomas' Calculus, Giordano Frank R. – Joel Hass – Thomas George Brinton – Maurice D. Weir, TYPOTeX


14. Required learning hours and assignment
Kontakt óra70
Félévközi készülés órákra38
Felkészülés zárthelyire24
Házi feladat elkészítése0
Kijelölt írásos tananyag elsajátítása0
Vizsgafelkészülés48
Összesen180
15. Syllabus prepared by dr. Tasnádi Tamás, Department Of Analysis And Operations Research, Analysis Group, Faculty of Natural Sciences