Subject 'Mathematics III'

Year:   2015/2016    2016/2017    2017/2018    2018/2019    2019/2020    

The course follows smoothly from the Mathematics II syllabus ending with revision of functions of one real variable and limits. This course starts with revision of basic differential calculus of functions of one and two variables. It then introduces some more advanced integral calculus, and finally it introduces differential equations with applications.

Short description of the course: derivative of a function of one real variable, differential of a function, derivatives of higher order; geometrical and physical meanings of derivative, application of derivative in investigation of functions; function of two real variables, partial derivatives; indefinite integral, definite integral and its applications; differential equations and its applications in engineering and natural sciences.

The aim of the course is to provide students with a general overview of the basic themes and issues in differential and integration calculus including differential equations. The material in this course is absolutely fundamental to nearly all areas of natural sciences and engineering. In this course, students develop logical and mathematical thinking ability as well.

By the end of this course, the student should
- know the basic rules for differentiation and be able to find derivatives of elementary and composite functions;
- be able to apply derivatives in investigation of functions and be able to solve extreme value problems;
- be familiar with geometrical and physical interpretations of derivative of a function;
- be familiar with functions of two real variables and be able to find partial derivatives;
- be familiar with the basic techniques of integration and be able to find area under the graph of a function, volume of a solid of revolution and the arc length of a function using integrals;
- be able to solve simple first and second order ordinary differential equations and be able to solve word problems using differential equations..

Lectures, practical lessons, group study, e-learning.

During the course a student has to pass tests and to present homeworks. The tasks of the tests and homeworks are composed on the basis of the standard problems solved at the practical lessons and according to the topics from the course program. The number of tests and homework assignments during the course can be changed by the responsible lecturer.

2019: FOR*  

2018: AT  ET  FOR*  HE  ME  RG  TE  

2017: AT  ET  FOR*  HE  ME  RG  TE  TT  

2016: AT  ET  FOR*  HE  ME  RG  TE  TT  

2015: AT  ET  HE  ME  RG  TE  TT  

* Optional subject