Course Unit Code | 310-2210/01 |
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Number of ECTS Credits Allocated | 7 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | First Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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Name of Lecturer(s) | Personal ID | Name |
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| KRC76 | Mgr. Jiří Krček |
Summary |
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Linear Algebra: An algebraic vector, basic terms. A matrix, the rank of a
matrix, elementary treatments of a matrix. Systems of linear equations. A determinant, determinant properties. Foundations of the matrix calculus.
The Real-Valued Function of a Real Variable: Definition, the domain of definition, the range of values, the graph of a function. Properties of functions. Inverse, composite functions. Basic elementary functions.
The sequence of real numbers and the limit of the sequence. The limit of a function at a point. The continuity of a function.
The Derivation of a Function: Derivation definition and the geometric significance of the derivation. The derivation of basic elementary functions.
Derivation Applications: A tangent and a normal. Monotony. Local and absolute
extreme values of a function. Convexity, concavity, inflection points. Asymptotes. The behaviour of a function.
The Indefinite Integral: An indefinite integral and a primitive function. Basic formulas. Integration by parts. The method of substitution.
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Learning Outcomes of the Course Unit |
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The goal of the cource is to introduce grounding of linear algebra, differential and integral calculus.
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Course Contents |
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1 Linear algebra: Vectors, matrice (basic properties).
2 Determinants (basic properties, calculation, evaluation).
3 Matrix inversion.
4 Systems of linear equations, Cramer’s rule, Gaussian elimination.
5 Functions of one real variable (definitions and basic properties).
6 Elementary functions.
7 Limit of the function, continuity of the functions , basic rules.
8 Differential calculus functions of one real variable. The derivative of function (basic rules for differentiation).
9 Derivatives of selected functions.
10 Differential of the function, parametric differentiation, highes-order derivative.
11 Applications of the derivatives.
12 Monotonic functions and extremes of function, convexity and concavity of a function.
13 Integral calculus: antiderivative and indefinite integral for functions of one variable.
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Recommended or Required Reading |
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Required Reading: |
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James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 |
Vrbenská, H., Němčíková, J.: Základy matematiky pro bakaláře I. Skriptum VŠB-TUO, Ostrava 1999. ISBN 80-7078-351-6
Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II. Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
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Recommended Reading: |
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[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6 |
Burda, P.-Kreml, P.: Diferenciální počet funkcí jedné proměnné. Skriptum VŠB, Ostrava 2004. ISBN 80-248-0634-7
Burda,P.: Algebra a analytická geometrie. Skripta VŠB-TU, Ostrava 1997. ISBN 80-7078-479-2
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Planned learning activities and teaching methods |
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Lectures, Individual consultations, Tutorials, Other activities |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 20 | 5 |
Examination | Examination | 80 (80) | 30 |
písemka | Written test | 60 | 25 |
teorie | Oral examination | 20 | 5 |