ECTS
ECTS Course Catalogue
Course details
Course code: NTSS10255o16Semester: 2016/2017 summer
Name: Methematics II
Major: Food Technology and Nutrition
Study Type: first cycle
Course type: compulsory
Study Semester: 2
ECTS points: 5
Hours (Lectures / Tutorials / Other): 15 / 30 / 0
Lecturer: dr Zbigniew Jurzyk
Language of instruction: Polish
Learning outcomes: Knowledge: Student knows the definition of the indefinite integral and the basic methods of its calculation; knows the concept of the definite integral and understands its geometrical representation; knows the rules for the application of integral calculus to calculate the areas of plane figures, the length of arcs and volumes of solids of revolution; knows the definition of improper integrals and the rules of their calculation; knows the concept of multivariable functions, particularly a function of two variables; knows the definition of partial derivatives and the rules for their application; knows polar, cylindrical and spherical coordinates and the relationships between them; knows the concept of differential equation of the 1st and 2nd order; understands the notions of initial condition and boundary condition; knows how to apply differential equations in describing technical issues. Skills: Student knows how to use different methods for calculating indefinite integrals; can calculate definite integrals and apply them to calculate the areas of plane figures, the lengths of arcs and the volume of solids of revolution; can calculate improper integrals type 1 and 2; can calculate partial derivatives of a function of two variables; can determine the extremes of functions of two variables; can apply the differential function to estimate errors of calculation; knows the concept of differential equation, how to solve it and how to interpret the obtained results.
Competences: Social skills (Attitudes): Student is aware of possible applications of mathematical descriptions and models to various natural phenomena, can interpret the results and use them for different purposes in life.
Prerequisites: Mathematics at secondary school level as well as credit for the course Mathematics I.
Course content: Indefinite integral and its relationship with the function derivative. Various methods for calculating integrals. Definite integral and its use in calculation of selected limits of sequences. The use of integral calculus for assessing the areas of plane figures, the length of arcs and volumes of solids of revolution as well as the area of their walls. Improper integral type 1 and 2. The function of two variables. Extremes of a function. Differential function and its use to calculate the approximate value of an expression. Differential equations of 1st and 2nd order. Types of differential equations and the methods of solution.
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 short tests, 3 progress tests, final written exam.
Comment: