Theory: 50 %

Practice: 50 %

Recommended semester: 2

Study mode: full-time

Prerequisites: Calculus 1

Evaluation type: exam

Course category: compulsory

Language: english

Responsible instructor: Dr. Ladics Tamás

Responsible department: Department of Basic Sciences

Instructor(s): Dr. Pusztai Béla Gábor

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:

1. Integral calculus of functions with one variable, methods of determining the indefinite integral. Antiderivatives, indefinite integral. Integrals of elementary functions, integral types with certain composite fuctions. 2. Integration with substitution, integration by parts. 3. Riemann-Integral, Newton-Leibniz formula, applications: calculating area, surface, volume. 4. Functions with multiple variables, domain, graph, limit, continuity; 5. Calculus of multivariable functions: partial derivatives of first and second order. Critical points of functions. 6. Finding extreme values; 7. Double integral, calculating the double integral on a normal domain. 8. Calculating double integrals on non-normal domains. 9. Ordinary differential equations (ODE). Separable ODEs, 10. ODEs that can be transformed to separable ODEs, first order linear ODEs, 11. Second order ODEs wit some veriables missing. 12. Second order linear ODEs of constant coefficients. 13. Applications of differential equations.

Course content - seminars:

1. Integral calculus of functions with one variable, methods of determining the indefinite integral. Antiderivatives, indefinite integral. Integrals of elementary functions, integral types with certain composite fuctions. 2. Integration with substitution, integration by parts. 3. Riemann-Integral, Newton-Leibniz formula, applications: calculating area, surface, volume. 4. Functions with multiple variables, domain, graph, limit, continuity; 5. Calculus of multivariable functions: partial derivatives of first and second order. Critical points of functions. 6. Finding extreme values; 7. Double integral, calculating the double integral on a normal domain. 8. Calculating double integrals on non-normal domains. 9. Ordinary differential equations (ODE). Separable ODEs, 10. ODEs that can be transformed to separable ODEs, first order linear ODEs, 11. Second order ODEs wit some veriables missing. 12. Second order linear ODEs of constant coefficients. 13. 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, grading:
Mid-term study requirements:
During the semester three tests will be written, for 20-20 points. To improve the final result the students can rewrite one of the tests at the end of the semester. In this case the old test result will be replaced 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:

Compulsory readings:

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano: Thomas' Calculus,Pearson, 2009.

Recommended readings: