Courses list

Wersja polska

Course code: IBS10246o16
Semester: 2016/2017 summer
Name: Mathematical Analysis II
Major: Civil Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 6
Hours (Lectures / Tutorials / Other): 30 / 28 / 0
Lecturer: dr Zbigniew Jurzyk
Language of instruction: Polish


Learning outcomes: Knowledge: The student: • knows the concept of definite integral • understands its geometrical interpretation • know the rules for using integrals to calculate arc lengths, areas of plane figures and volumes of solids • knows definition and principles for calculating improper integrals • knows concept of multivariate function, and in particular a function of two variables • knows definition of partial derivatives and the rules for their use • knows polar, cylindrical and spherical coordinate systems and the relationships between them • knows definitions of double integral and fields of its application • knows definition of ordinary differential equation of order 1 or 2 • knows how to apply differential equations in technical issues Skills: • is able to calculate definite integrals • can apply integrals for calculating the arc lengths, areas of figures and volumes of solids of revolution • can calculate improper integrals of 1st and 2nd type • can determine partial derivatives of function of two variables • can determine extremes of function of two variables • can use differential of a function to estimate calculation errors • can describe figures in Cartesian and polar coordinates • knows what is double integral over normal region • can calculate double iterated integrals • knows applications of double integrals • can calculate volumes of solids and areas of the fields • knows the concept of differential equation, can solve it and interpret the results

Competences: • is aware of applying differential equations methods to problems in technical and natural sciences • can interpret obtained results and apply them adequately

Prerequisites: • mathematics at secondary school level • mathematical analysis 1

Course content: • Definite integral. Application of definite integral in calculation of some limits. • Applying the integral calculus for calculating area of figures, length of arcs, volumes and areas of solids of revolution. • Improper integrals if 1st and 2nd type. • Function of 2 variables. • Extremes of functions. • Derivative and its applications. • Differential and its application in approximate calculations. • Double integral. • Calculating volumes of solids and areas of fields. • Description of regions in different coordinate systems. • Differential equations of 1st and 2nd order. • Types of differential equations. • Methods for solving differential equations.

Recommended literature: 1. M. Gewert, Z. Skoczylas, Analiza matematyczna 2, Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 2009 2. M. Gewert, Z. Skoczylas, Analiza matematyczna 2, Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław 2009 3. W. Krysicki, L. Włodarski. Analiza matematyczna w zadaniach cz.1, 2 PWN Warszawa 2006

Assessment methods: 10 quizzes , 3 tests , written exam .

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