ECTS
ECTS Course Catalogue
Course details
Course code: IGS10840o15Semester: 2015/2016 summer
Name: Math Analysis II
Major: Geodesy and Cartography
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 6
Hours (Lectures / Tutorials / Other): 30 / 28 / 0
Lecturer: dr hab. Ryszard Deszcz
Language of instruction: Polish / English
The course taught in English if the group has ≥6 students. The course taught in Polish with a possibility of support in English if the group has <6 students
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 several variables, and in particular, functions of two variables. Knows elements of differential geometry of curves and surfaces, and elements of vector analysis.
Skills: 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, compute curvature and torsion of a curve, determine tangent plane and normal line at a regular point of a surface, compute the first fundamental form of a surface.
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:
Prerequisites: Linear Algebra, Mathematical Analysis I
Course content: Functions of several variables, differential geometry of curves and surfaces, double integrals, triple integrals, line integrals, Green’s formula, surface integrals, Stokes’ theorem, elements of vector analysis: gradient, divergence and curl.
Recommended literature:
Assessment methods: Heinbockel, J.H., Introduction to Calculus, Vol. I, Vol. II, 2012. (Paper or electronic copies for noncommercial use may be made freely without explicit permission of the author. All other rights are reserved). 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).
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