ECTS
ECTS Course Catalogue
Course details
Course code: NTSS10239o15Semester: 2015/2016 winter
Name: Mathematics I
Major: Food Technology and Nutrition
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 5
Hours (Lectures / Tutorials / Other): 15 / 15 / 0
Lecturer: dr Zbigniew Jurzyk
Language of instruction: Polish
Learning outcomes: Knowledge: Student knows the concepts and the relationship between real and complex numbers; is familiar with the concepts of matrix and determinant; understands possible applications of elements of matrix calculus; is familiar with the concept of the system of equations and its solution methods; is familiar with the concept of a matrix’s rank and its relevance to the system solvability; knows the concepts of mathematical sequence and series as well as their properties; understands the concept of sequence convergence; can define the limit of a function at a point and understands the concept of continuous function; is familiar with the concept of a function derivative and the rules for its application; is familiar with the concept of the differential of a function and its possible applications; Skills: Student can solve equations in the domain of complex numbers; can represent a complex number in its trigonometric form and use the latter to calculate powers and roots of numbers; can determine the distribution of a rational function into the sum of partial fractions; can solve matrix equations; can calculate the determinant of any grade and can solve systems of linear equations. Student can use different methods of calculating the limits of sequences; can calculate the limits of functions and interpret the results as well as determine the continuity of functions; can calculate function derivatives; can apply differential calculus to study the convergence of a function; can apply differential functions to assess measurement errors.
Competences: Social skills (Attitudes): Student understands the importance of the mathematical methods and can use them in everyday life.
Prerequisites: Mathematics at secondary school level.
Course content: Numerical sets and the relationships between them. The concept of the set of complex numbers and their application to solving equations. Matrix calculus, the notions of a determinant and rank of a matrix. Applications in the theory of linear equations systems. Numerical sequences, the concept of the e number constant. Mathematical sequence limits. Elementary functions and their properties. The limit of function at a point and its application to determination of asymptotes and testing function continuity. Derivative of a function and its geometrical and physical interpretation. L'Hôpital’s rule. Extremes of a function. The study of monotonicity, convex/concave intervals and the inflection point. The application of differential calculus in technical issues.
Recommended literature: 1. M. Gewert, Z. Skoczylas, Analiza matematyczna 1. Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 2009; 2. M. Gewert, Z. Skoczylas, Analiza matematyczna 1, Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław 2009; 3. W. Krysicki, L. Włodarski. Analiza matematyczna w zadaniach cz.1, PWN Warszawa 2006.
Assessment methods: 10 short tests, 3 progress tests, final written exam.
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