Courses list

Wersja polska

Course code: IBS10034o16
Semester: 2016/2017 winter
Name: Mathematical analysis 1
Major: Civil Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 7
Hours (Lectures / Tutorials / Other): 30 / 28 / 0
Lecturer: dr Zbigniew Jurzyk
Language of instruction: Polish


Learning outcomes: Knowledge Student: • knows concepts of number sequence and series and their properties • understands convergence of sequences and series • knows definition of limit of a function • understands what continuity of a function means • knows derivative of function and its applications • knows applications of differential of a function • knows definitions of indefinite and definite integrals of a function and basic methods for its calculations Skills Student: • can calculate limits of sequences using different methods • can examine convergence of numeric series using classical convergence criteria • can calculate limits of functions and interpret results of calculations, including determining continuity of the function • can calculate derivatives of functions • can apply differential calculus method for determining properties of functions • can use differential of a function for estimate measurement errors • can use basic methods for calculating integrals

Competences: Understands the importance of presented mathematical methods and can use them every dayPassing the course permits learn physic and other technical courses.

Prerequisites: Mathematics at secondary school level.

Course content: • Sequences. • The e number. • Number series. • The d'Alembert, Cauchy and comparative convergence criteria. • Elementary functions and their properties. • The limit of a function at a point. • Application of limits for determining asymptotes and testing continuity. • The derivative of a function, its geometrical and physical interpretation. • The d'Hospital principle. • Extremes of functions. • Examining the monotonicity, convexity and inflection points of a function. • Application of differential calculus in technical issues. • Antiderivative and its relation to derivative. • Miscellaneous methods for calculating integrals.

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 quizzes , 3 tests , written exam .

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