Courses list

Wersja polska

Course code: IGS10049o10
Semester: 2010/2011 winter
Name: Mathematics I
Major: Geodesy and Cartography
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 6
Hours (Lectures / Tutorials / Other): 30 / 30 / 0
Lecturer: dr hab. Ryszard Deszcz
Language of instruction: Polish


Learning outcomes: The student comprehends mathematical interpretations of natural occurrences and phenomena and knows how to use mathematical methods in Earth sciences, especially in geodesy and cartography.

Competences: Finishing the course enables the student to examine natural phenomena and processes and provides a background for the further study of Mathematics II, Mathematics III, Statistics, Physics, Adjustment, Geodesy.

Prerequisites: Mathematics on the secondary school level (comprehensive secondary school of a general profile).

Course content: Limit of a sequence, limits, continuity and derivatives of a function of one variable, Lagrange theorem, L’Hospital’s rule, Taylor formula, Maclaurin formula, investigation of the shape of a function of one variable, number series, tests for convergence of series, power series, indefinite integrals, definite integrals, Leibniz-Newton formula, improper integrals, first-order ordinary differential equations, second-order ordinary differential equations, Cauchy problem, applications.

Recommended literature: Krysicki W., Włodarski L., Analiza matematyczna w zadaniach, cz. I i cz. II, PWN Warszawa, 2005.
Gewert M., Skoczylas Z., Analiza matematyczna 1, Definicje, twierdzenia, wzory, Oficyna wydawnicza GiS, Wrocław 2007.
Gewert M., Skoczylas Z., Analiza matematyczna 1, Przykłady i zadania, Oficyna wydawnicza GiS, Wrocław 2007.
Gewert M., Skoczylas Z., Analiza matematyczna 2, Definicje, twierdzenia, wzory, Oficyna wydawnicza GiS, Wrocław 2006.
Gewert M., Skoczylas Z., Analiza matematyczna 2, Przykłady i zadania, Oficyna wydawnicza GiS, Wrocław 2006.
Leja F., Rachunek różniczkowy i całkowy, PWN, Warszawa 1976.
Fichtenholz G.M., Rachunek różniczkowy i całkowy, tom I, II i III, PWN, Warszawa 2004.
Niczyporowicz E., Krzywe płaskie: wybrane zagadnienia z geometrii analitycznej i różniczkowej, PWN, Warszawa 1991.

Assessment methods: Obligatory completion of tutorials, a written exam and (optionally) an oral exam

Comment: The scope and subject of the material have been agreed on with the lecturers: Mathematics II, Mathematics III, Statistics, Physics, Adjustment, Geodesy.