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functions of any angle. Trigonometric circle. Trigonometric identities and reduction formulas. Trigonometric equations and inequalities.
3. Sequences of real numbers. Arithmetic and geometrie sequences. Finite and infinite limit of a sequence. The number e. Calculation of simple limits. Finite and infinite limit of a function at a point. Heine definition	3
4. One-sided limits. Limits at infinity. Methods of calculation of limits. Indeterminate expressions. Asymptotes. Continuity of a function at a point and on an interval. Discontinuity points and their classification.	3
5. Derivative of a function at a point. Calculation of derivatives of basie elementary functions. Differentiation formulas. One-sided and infinite derivatives. Higher order derivatives. Geometrie interpretation of a derivative. Tangent linę.	3
6. Ratę of change. Differentials and their applications. Approximate solution of equations. L’Hospital rule. Power and exponential functions and their derivatives. Exponential equations and inequalities.	3
7. Injective functions. Inverse function and its derivative. Logarithmic and inverse trigonometric functions and their derivatives. Logarithmic equations and inequalities.	3
8. Intervals of monotonicity of a function. Local extremes. Necessary and sufficient conditions for existence of local extremes. Examination of a function. Maximum and minimum values of a function on a set. Applications to geometry, physics and technics.	3
9. Indefinite integrals, definition and basie properties. Integration by parts. Integration by substitution. Integration of rational functions.	3

• Classes

Contents of particular hours	Number of hours
1. Exercises illustrating the materiał presented during the lectures.	18

• Basic literaturę

1.    G. Decewicz, W. Żakowski, Matematyka. Cz. 1, WNT, Warszawa 1991._

2.    M. Gewert, Z. Skoczylas, Analiza matematyczna 1. Definicje, twierdzenia, wzory. Oficyna

Wydawnicza GiS, Wrocław 2002._

3.    M. Gewert, Z. Skoczylas, Analiza matematyczna 1. Przykłady i zadania. Oficyna

Wydawnicza GiS, Wrocław 2002._

4.    W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach. Cz. I, PWN, Warszawa

1993._

• Additional literaturę

1.    M. Fichtenholz, Rachunek różniczkowy i całkowy. T. I,II, PWN, Warszawa 1995._

2.    M. Gewert, Z. Skoczylas, Oprać. Analiza matematyczna 1. Kolokwia i egzaminy. GiS,

Wrocław 2002._

3.    R. Leitner, Zarys matematyki wyższej dla studiów technicznych. Cz. 1, 2 WTN, Warszawa

1994._

4.    F. Leja, Rachunek różniczkowy i całkowy ze wstępem do równań różniczkowych. PWN,

Warszawa 1977._

5.    H. i J. Musielakowie, Analiza matematyczna, T. I, cz. 1 i 2, Wydawnictwo Naukowe UAM,