Courses list

Wersja polska

Course code: IISS10427o14
Semester: 2014/2015 summer
Name: Mathematical Analysis
Major: Environmental Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 8
Hours (Lectures / Tutorials / Other): 30 / 45 / 0
Lecturer: dr hab. Ryszard Deszcz
Language of instruction: Polish


Learning outcomes: Knowledge He knows the basic theorems of the known branches of mathematics, knows the basics of differential and integral calculus of functions of one and the basis of differential calculus and integral calculus of functions of several variables, with particular emphasis on the function of two variables; familiar elements of classical differential geometry of curves and surfaces and elements of vector analysis. Knowledge Uses calculus for investigating the functions of one variable, use calculus of functions of one variable to calculate some geometrical quantities, solve the differential equations of selected types, either the extremes of function of two variables, used integral calculus of functions of two and three variables to calculate some geometrical quantities, calculate the curvature and torsion of the curve, determines a plane tangent and normal at the point of a regular surface, the metric tensor determines the coordinates of the surface.

Competences: He knows his own limitations of knowledge and understands the need for further education, understands and appreciates the importance of intellectual honesty in the activities of their own and other people, act ethically.

Prerequisites: Algebra.

Course content: Within the boundary, continuity and derivatives of functions of one variable, the Lagrange theorem, the rule de L'Hospital, Taylor and Maclaurin formulas, the study of a function of one variable, series of numbers, the criteria of convergence, power series, indefinite integrals, definite integrals, Leibniz formula -Newton, improper integrals, ordinary differential equations of first order, ordinary differential equations of the second order, the Cauchy problem and applications. Functions of two or more variables, elements of classical differential geometry of curves and surfaces, double integrals, triple integrals, line integrals, Green's theorem, surface integrals, Stokes' theorem, theorem Gauss-Ostrogradski, elements of vector analysis: gradient, divergence, rotation.

Recommended literature:

Assessment methods: Assessment of exercise on the basis of the results of ongoing tests and assessments. Written exam. The final score consist of score from classes (50%) and lecture (50%).

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