Subject 'Applied Mathematics'

Year:   2016/2017    2017/2018    2018/2019    2019/2020    2020/2021    

The course follows smoothly from the Mathematics syllabus and starts with revision of basic problems of plane and solid geometry, and linear algebra. It then introduces some more advanced differential and integral calculus of a function of one real variable, and finally it introduces basic geometrical applications of definite integral.
Short description of the course:
- Stereometry; matrices, their properties and arithmetic operations; determinants (up to order five) and their properties; Inverse matrices; systems of linear equations;
- vectors; straight lines on a plane; quadratic curves: ellipse, hyperbola and parabola;
- derivatives of elementary and composite functions of one real variable; extreme value problems;
- indefinite and definite integrals of a function of one real variable; techniques of integration: linear properties and table of integrals, integration by substitution and by parts;
- geometrical applications of definite integral: area under the graph of a function, volume of a solid of revolution and computing the arc length of a function.

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

By the end of this course, the student should
- be able to manipulate matrices and determinants, be familiar with their properties and understand their relation to systems of linear equations;
- be able to find inverse matrix and be able to solve matrix equations;
- be able to solve systems of linear equations using Cramer's rule and Gauss-Jordan method;
- be able to manipulate vectors in two and three dimensions, and to solve geometrical problems using vectors;
- be familiar with basic formulas in solid geometry and be able to find the total area and volume of the solids;
- be familiar with quadratic curves, be able to determine their equations and to draw their graphs;
- know the basic rules for differentiation and be able to apply derivatives in investigation of functions and to solve extreme value problems;
- 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.

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 homework 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 are appointed by the responsible lecturer.

Rakendusmatemaatika - M.Latõnina
Rakendusmatemaatika - R.Timmermann

2019: RR*  

2018: KK  RA  RR*  TD*  TK  TL  

2017: KK  KT  RA  RR*  RT  TD*  TK  TL  

2016: KT  RA  RR*  RT  TD*  TK  TL  

2015: KT  RA  RR*  RT  TD*  TL  

* Optional subject