ECTS
ECTS Course Catalogue
Course details
Course code: ICSS10127o15Semester: 2015/2016 summer
Name: Mathematical Analysis
Major: Safety Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 6
Hours (Lectures / Tutorials / Other): 30 / 30 / 0
Lecturer: dr hab. Ryszard Deszcz
Language of instruction: Polish
Learning outcomes: Knowledge: Understands the civilization’s significance of mathematics and its applications. Knows basic theorems from selected sections of mathematics. Knows elements of differential and integral calculus of functions of one variable and elements of differential and integral calculus of functions of several variables. Knows elements of vector analysis. Skills: Use differential calculus of a function of one variable to the investigation of a function of one variable, use integral calculus of a function of one variable to compute of given geometrical quantities, solve differential equations of some types, determine extrema of a function of two variables, use integral calculus of a function of two or three variables to compute of given geometrical quantities, compute gradient and directional derivative of a function, and divergence and curl of a vector field. Social competences (attitudes): knows limitations of his/her own knowledge and understands the need for further education, understands and appreciates the importance of intellectual honesty in his/her own activities and those of other people; behaves ethically.
Competences: Finishing the course enables the student to examine natural phenomena and processes and provides a background for the further study of Statistics and Physics.
Prerequisites: Linear algebra
Course content: Limit of a sequence, limits, continuity and derivatives of a function of one variable, Lagrange’s theorem, de L’Hospital’s rule, Taylor’s formula, investigation of the shape of a function of one variable, number series, tests for convergence of series, functional 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. Functions of several variables, double integrals, triple integrals, line integrals, Green’s theorem, directional derivative, gradient, divergence, curl.
Recommended literature: Trench W.F., Introduction to real analysis, Free Edition 1.06, January 2011. ISBN 0-13-045786-8. (this book was published previously by Pearson Education).
Assessment methods: Obligatory completion of tutorials, a written exam. Minimum required for passing: 50%.
Comment: