The aim of the subject is to familiarise students with the basic concepts and methods of higher mathematics (analysis) and the related terms, relations and theorems necessary for the study of engineering.
Calculus II (GAINBAN-ANALIZI2-1)
Basic data
Name and type of the study programme
Computer Science Engineering, undergraduate program
Curriculum
2022
Classes / consultation hours
2 + 2 + 0 (L+S+Labs)
Credits
5 credits
Theory – Practice
Theory: 50%, Practice: 50%
Recommended semester
Semester 2
Study mode
full-time
Prerequisites
Calculus I
Evaluation type
Colloquium
Course category
Compulsory
Language
English
Instructors
Responsible instructor
Dr. Ladics Tamás
Responsible department
Department of Basic Sciences
Instructor(s)
Dr. Ladics Tamás
Checked by
Kovács Márk
Course objectives
Course content
Lectures
Review of differentiation and applications. Integral of functions of a single variable. Methods of integration, the fundamental theorem of calculus (Newton-Leibniz formula), applications, improper integrals. Series. Power series, Taylor and Fourier series. Functions of two variables: partial derivative, extreme value problems. Double integrals and their applications. Differential equations (DE). Separable DEs, first order linear DEs, second order linear DEs of constant coefficients. Applications of differential equations.
Seminars
Integral calculus of functions with one variable, methods of determining the indefinite integral. Riemann-Integral, Newton-Leibniz formula, applications: calculating area, surface, volume. Calculus of multivariable functions: partial derivatives, extreme value problems; double integral and its applications. Ordinary differential equations (ODE). Separable ODEs, first order linear ODEs, second order linear ODEs of constant coefficients. Applications of differential equations.
Acquired competences
Knowledge
- Knowledge of the principles and methods of natural sciences (mathematics, physics, other natural sciences) relevant to the field of IT.
Skills
–
Attitude
- He/she makes an effort to work efficiently and to high standards.
Autonomy and responsibilities
–
Additional professional competences
- Efficient use of digital technology, knowledge of digital solutions to fulfill educational objectives
Requirements, evaluation and grading
Mid-term study requirements
The course ends with an exam. A signature is needed to sign up for the exam. The requirements to get the signature are: being present on the classes; having at least 30 points altogether from the midterm tests; reaching at least 5 points in each "large TESTS". There will be 3 large TESTS for 15-15 points each, from the three large parts of the material. There will be 5 small tests for 4-4 points each. In the last week the tests can be repeated if necessary. Tests can be repated by parts of the whole material for 27-19-19 points, according to the first, second and third part, small tests merged into the large ones.
Exam requirements
In the exam period the students write an exam for 40 points. The points gained in the midterm tests (max 65) will be added to the points achieved in the exam and the final mark will be given according to that sum, according to the valid TVSZ (regulation of study and examination).
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.