Subject 'Mathematical Analysis'

Year:   2010/2011    2011/2012    2012/2013    2013/2014    2014/2015    

The concept of a function. The limit of a sequence and its properties. The limit of a function of one variable and its properties. Continous functions, their properties. The derivative of a function of one variable, its interpretations, properties and conditions of existence. L'Hospital's Rule. Differential. Higher-order derivatives. Composite functions and their derivatives. Implicit differentiation. Logarithmic derivative. Parametric functions and their derivatives. Increasing and decreasing functions. Extrema of functions. Concavity. The pont of inflection. Asymptotes. Applications of limits and derivatives for treating of functions. Functions of two variables, their limits and continuity. Partial derivatives.

The aim is to deepen students' knowledge and practical applications of differential calculus of functions of one (real) variable and functions of several variables; to give the concept of a function of two variables and partial derivatives.

The student is able to find the limit and the derivative of a function and use these skills while studying the course of aforesaid function.

Lectures and solving tasks in practical classes; independent work with theoretical materials and preparing for practical classes; solving tasks and preparing for tests and exam.

1. Kangro, G. Matemaatiline analüüs I. (1982)
2. Liiva, T. Kõrgem matemaatika. Analüütiline geomeetria. Lineaaralgebra. (2004)
3. Liiva, T. Kõrgem matemaatika II. Diferentsiaalarvutus. (2007)
4. Loone, L., Soomer, V. Matemaatilise analüüsi algkursus. (2007)
5. Lõhmus, A., Petersen, I., Roos, H. Kõrgema matemaatika ülesannete kogu. (1982)
6. Piskunov, N. Diferentsiaal- ja integraalarvutus I. (1981)
7. Puusemp, P. Kõrgema matemaatika ülesannete kogu. (1988)
8. Reimers, E. Matemaatilise analüüsi praktikum. I, II. (1988)
9. Tammeraid, I. Matemaatiline analüüs I. (2002)

Exam, test, group assignments, presentation, project work

2015: FOR*  

2014: AT  ET  FOR*  HE  ME  RG  RT  TE  TL  TT  

2013: AT  ET  HE  ME  RG  RT  TE  TL  TT  

2012: AT  EI  ET  GI  LI  MI  RT  TEI  TI  

2011: AT  EI  GI  LI  MI  RT  TEI  TI  

2010: AT  EI  GI  LI  MI  RT  TEI  TI  

2009: AT  EI  GI  LI  MI  RT  TEI  TI  

* Optional subject