Courses list

Wersja polska

Course code: RSSN10227o12
Semester: 2012/2013 winter
Name: Mathematics 1
Major: Environmental Protection
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 4
Hours (Lectures / Tutorials / Other): 9 / 18 / 0
Lecturer: dr hab. Elżbieta Musiał prof. nadzw. UP we Wrocławiu, dr Joanna Kamińska
Language of instruction: Polish


Learning outcomes: During the course the students gain theoretical knowledge of differential calculus of functions of one variable and get the theoretical background required to continue the course in the next semester.

Competences: Having completed the course, students understand phenomena and processes concerning protection of the environment. Completion of that course prepares for furher mathematical education in the field.

Prerequisites: Mathematics at the secondary school level.

Course content: Mathematics I. Real numbers, functions of one variable, domain, monotonicity. Logarithmic and exponential function. Logarithmic and exponential equations and inequalities. Periodic functions, inverse functions, inverse trigonometric functions. Limits of sequences, basic methods of computation of limits of sequences, the number e. Limits of functions of one variable, basic methods of computation of limits of functions. Asymptotes of functions, continuity of function. Incrementary ratio, derivative of a function, computation of derivatives of functions. Continuity and derivation. Geometric interpretation of the derivative of the first order. Indeterminate forms, deL’Hospital’s rule. Extremum of a function. The points of inflection of the graph of a function, convexity and concavity of the graph of a function. Investigation of the shape of a function of one variable. Differential and its aplications.

Recommended literature: 1. Krysicki W., Włodarski L., Analiza matematyczna w zadaniach, cz. I i cz. II, PWN Warszawa, 2005. 2. Gewert M., Skoczylas Z., Analiza matematyczna 1, Definicje, twierdzenia, wzory, Oficyna wydawnicza GiS, Wrocław 2007. 3. Gewert M., Skoczylas Z., Analiza matematyczna 1, Przykłady i zadania, Oficyna wydawnicza GiS, Wrocław 2007. 4. Gewert M., Skoczylas Z., Algebra liniowa 1, Definicje, twierdzenia, wzory, Oficyna wydawnicza GiS, Wrocław 2007. 5. Gewert M., Skoczylas Z., Algebra liniowa 1, Przykłady i zadania, Oficyna wydawnicza GiS, Wrocław 2007. 6. Leja F., Rachunek różniczkowy i całkowy, PWN, Warszawa 1976. 7. Fichtenholz G.M., Rachunek różniczkowy i całkowy, tom I, II i III, PWN, Warszawa 2004.

Assessment methods: Mathematics I Obligatory completion of the course. Minimum required knowledge for passing: 60%.

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