Courses list

Wersja polska

Course code: RSSN10228o12
Semester: 2012/2013 summer
Name: Mathematics 2
Major: Environmental Protection
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 2
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 II. The indefinite integrals, basic formulas of integral calculus. Integration by parts and by substitution. Definite integrals, Leibniz-Newton formula. Geometrical applications of define integrals. Improper integrals. Functions of two variables, limits and continuity. Extremum of a function of two variables. Matrices, arithmetric operations on matrices. Determinants, basic properties of determinants. Inverse matrix, rank of a matrix. Systems of linear equations.Theorems of Cramer and Kronecker-Capelli. Elements of analytic geometry. Equations of a plane and a straight line. Surfaces of the second order.

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 II Obligatory completion of the course. Obligatory written or oral exam Minimum required knowledge for passing: 60%.

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