**Course title, code:** Mathematics II, GAGEBAN-ANALIZI2-1

**Name and type of the study programme:**

**Curriculum:**2021

**Number of classes per week (lectures+seminars+labs):**2+2+0

**Credits:**5

**Theory:**50 %

**Practice:**50 %

**Recommended semester:**2

**Study mode:**full-time

**Prerequisites:**

**Evaluation type:**exam

**Course category:**

**Language:**english

**Responsible instructor:**Dr. Ladics Tamás

**Responsible department:**Department of Basic Sciences

**Instructor(s):**Dr. Ladics Tamás

**Course objectives:**

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.

**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.

**Course content - 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 general and specific mathematical and scientific principles, rules, relationships and procedures necessary for the operation of the technical field.

__Skills:__

The students are able to identify a higher mathematical problem, the method to be used to solve it, and then, on the basis of the method chosen, to solve it quickly and accurately. In the case of practical problems, they are able to construct and select the mathematical model needed to solve the problem, and to generalise the problem in the case of similar problems.

__Attitude:__

Have the stamina and tolerance of monotony to carry out practical activities. Ability to work efficiently, qualitatively and continuously, to work independently and in cooperation with others, and to take responsibility for the work submitted.

__Autonomy and responsibilities:__

Ability to work efficiently, qualitatively and continuously, to work independently and in cooperation with others, and to take responsibility for the work submitted.

__Additional professional competences:__

**Requirements, evaluation, grading:**

**Mid-term study requirements:**

Two 45 minutes 30-30 points classroom writing paper. If the collected points are less then 50% of the total points, then we give the chance to write an additional classroom writing paper at the end of the semester. The condition of the exam is to get more than 50% of the total points of classroom writing papers.

**Exam requirements:**

The written exam is 40 points. The total points are sum of the 60 points (classroom writing paper) and 40 points (exam). Marks are calculated according to the valid TVSZ, on the basis of the obtained total score.

**Study aids, laboratory background:**

**Compulsory readings:**

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

**Recommended readings:**