Subject 'Mathematics II'

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

The course consists of three parts: linear algebra, analytic geometry and elements of mathematical analysis.
The topics from linear algebra are
- matrices, their properties and arithmetic operations;
- determinants (up to order five), their properties, Inverse matrices, matrix equations;
- solving of systems of linear equations using matrix solution, Cramer's rule and Gauss-Jordan elimination method.
The topics from analytic geometry are
- vector algebra: vectors, linear operations with vectors, scalar product, vector product and mixed product;
- straight lines and planes, their mutual positions;
- quadratic curves: ellipse, hyperbola and parabola.
The topics from mathematical analysis are
- functions of one real variable, their representations (explicit and implicit forms, geometric and parametric representation) and classes (even and odd functions, periodic and invertible functions);
- elementary, composite and inverse functions;
- limit of function (one-sided and two-sided limits, limits at infinity and infinite limits) and continuity.

The aim of the course is to provide students with a general overview of the basic themes and issues in linear algebra, analytic geometry and mathematical analysis. The most important themes of mathematical analysis like differential and integration calculus will be introduced in Mathematics III. 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 acquainted with various equations of straight line and plane, and be able to compose them from different initial data;
- be familiar with quadratic curves, be able to determine their equations and to draw their graphs;
- be familiar with various representations, classes and types of functions of one real variable, be able to determine their domain and range, and be able to find inverse function;
- be able to calculate one-sided, two-sided and infinite limits.

The course consists of 80 contact hours: lectures, practical lessons, group study.
Independent work is about 76 academical hours: working through the lecture materials, solving practical exercises, e-learning, preparing for the tests.

1. Kaarli, K. Algebra praktikum. Lineaarvõrrandisüsteemid. Tartu, 1986.
2. Kolde, R. Koonuselõiked. Tallinn, Valgus, 1991.
3. Liiva, T. Kõrgem matemaatika. Analüütiline geomeetria. Lineaaralgebra. TTK, Tallinn, 2004.
4. Liiva, T. Kõrgem matemaatika II. Diferentsiaalarvutus. TTK, Tallinn, 2007.
5. Loone, L., Soomer, V. Matemaatilise analüüsi algkursus. TÜ Kirjastus, Tartu, 2007, 2009.
6. Käerdi, H. Lineaaralgebra elemendid. 2. tr., Sisekaitseakadeemia, Tallinn, 2005.
7. Lõhmus, A., Petersen, I., Roos, H. Kõrgema matemaatika ülesannete kogu. Valgus, Tallinn, 1982.
8. Paal, E. Lineaaralgebra. TTÜ Kirjastus, Tallinn, 2004.
9. Piskunov, N. Diferentsiaal- ja integraalarvutus I. Valgus, Tallinn, 1981.
10. Puusemp, P. Lineaaralgebra ja analüütiline geomeetria. Avita, Tallinn, 2009.
11. Puusemp, P. Lineaaralgebra. Avita, Tallinn, 2000.
12. Puusemp, P. Kõrgema matemaatika ülesannete kogu I. Polütehniline Instituut, Tallinn, 1988.
13. Reimers, E. Matemaatilise analüüsi praktikum I, Valgus, Tallinn, 1988.
14. Tammeraid, I. Matemaatiline analüüs I. TTÜ kirjastus, Tallinn, 2003.
15. Tiidt, U. Kõrgem matemaatika. Analüütilise geomeetria ja lineaaralgebra elemendid. EPMÜ MI, Tartu, 1999.
16. Tuulmets, L. Analüütilise geomeetria praktikum I, II, III. TRÜ, Tartu, 1978, 1985, 1980.
17. Zaitsev, L. Kõrgem matemaatika. Õpik tehnikumidele. 3. tr., Valgus, Tallinn, 1973.
18. Väljas, M. Analüütiline geomeetria. TTÜ kirjastus, Tallinn, 2012.
19. E-learning course materials at Moodle environment (http://ekool.tktk.ee).

During the course a student has to pass three tests and to present two 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.

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