OPF:INMBAKVM Quantitative Methods - Informace o předmětu

INMBAKVM Quantitative Methods

Rozsah

2/2/0. 7 kr. Ukončení: zk.

Vyučující

Mgr. Radmila Krkošková, Ph.D. (přednášející)
Mgr. Radmila Krkošková, Ph.D. (cvičící)

Garance

doc. RNDr. David Bartl, Ph.D.
Katedra informatiky a matematiky – Obchodně podnikatelská fakulta v Karviné
Kontaktní osoba: Mgr. Radmila Krkošková, Ph.D.

Rozvrh

Čt 13:05–14:40 A318

• Rozvrh seminárních/paralelních skupin:

INMBAKVM/01: Čt 14:45–16:20 A318, R. Krkošková

Omezení zápisu do předmětu

Předmět je určen pouze studentům mateřských oborů.

Předmět si smí zapsat nejvýše 30 stud.
Momentální stav registrace a zápisu: zapsáno: 3/30, pouze zareg.: 2/30

Mateřské obory/plány

• Economics and Management (program OPF, B_EME)

Cíle předmětu

The course aims to familiarize students with the fundamental concepts and terminology of algebra and mathematical analysis, enabling them to apply the established notions, theoretical results and computational methods in subsequent courses, particularly those that are economically oriented.

Výstupy z učení

After completing the course, the student will be able to:
- define the linear space of a matrix;
- apply the rules for operations with matrices;
- compute the determinant of a matrix;
- explain the meaning and use of determinants;
- use Cramer’s rule to solve systems of linear equations;
- define arithmetic and geometric sequences;
- distinguish an arithmetic sequence from a geometric sequence;
- explain the concept of a convergent sequence and a divergent sequence;
- define real-valued functions of a single real variable and their properties;
- describe, sketch and graphically represent elementary functions;
- explain the concept of the derivative of a function;
- analyse the behaviour of a function using differential calculus;
- explain the concept of the indefinite integral and the definite integral;
- apply the definite integral in practical problems.

Osnova

• 1. Introduction and a Brief History of Mathematics
  Mathematics in ancient Greece, mathematics in Europe. Emergence of centres of knowledge in the 17th century, mathematical analysis in the 18th century, development of mathematics in the 19th and the 20th century. Calculator, computer, and mathematics. Sets, set notation, propositions and logical operations, set relations and operations. Mapping. Number sets.
• 2. Vector Spaces, Matrices and Matrix Algebra
  Arithmetic vector space. Linear combination of vectors, linear dependence and independence of vectors. Basis of a vector space, elementary properties and characterizations of a basis, the dimension of a vector space. Matrices. Addition of matrices and multiplication of a matrix by a constant, vector space of matrices. Square matrices. Transformation of a matrix into (upper) triangular form. The rank of a matrix. Identity matrix, singular and non-singular and matrices. Multiplication of matrices and its properties. Inverse matrix. Solution of matrix equations.
• 3. Systems of Linear Algebraic Equations, Determinants
  The matrix of the coefficients of the system of linear equations, the augmented matrix. Frobenius theorem and its corollary. Gauss elimination method. Gauss-Jordan elimination method. Homogeneous systems of linear equations and its solution set (linear subspace). Determinant of a matrix, definition, elementary properties, geometrical meaning, Laplace expansion of a determinant and Leibniz formula, computation of the determinant (elimination method, other methods). Determinant of a singular and non-singular matrix. Cramer’s rule. Adjugate (classical adjoint) matrix and finding the inverse matrix.
• 4. Sequences and the Limits of Sequences, Series and Infinite Sums
  Arithmetic and geometric sequence (progression). Finite and infinite sequence. Bounded and unbounded sequence. Monotone sequence. Convergent and divergent sequence. The limit of a sequence and its properties. Bolzano-Weierstrass Theorem. Infinite series and its sum. Convergent and divergent series, geometric series. Necessary condition for the convergence, the tail (remainder) of a series. Series with positive terms, alternating (oscillating) series, convergence criterions. Alternating series, Leibniz criterion.
• 5. The Limit and Continuity of a Function
  A real function of a real variable. Least upper bound (supremum), greatest lower bound (infimum), bounded function, monotone function, convex and concave function. Injective and inverse function. Elementary functions, their domains, properties and graphs. Continuous functions and their properties. The limit of a function at a point and the properties of the limit.
• 6. Differential Calculus, Sketching the Graph of a Function, L'Hospital’s Rule
  The derivative of a function, geometrical meaning, continuity of a function having a bounded derivative. Derivative of arithmetic operations, chain rule, derivative of the inverse function. Differential, derivatives of higher orders. Sketching the graph of a function. Taylor’s series and Taylor’s polynomial. L'Hospital’s rule.
• 7. Indefinite Integral (Antiderivative) and Definite Integral
  Primitive function (antiderivative), integration by parts, integration by substitution. Riemann definite integral. Newton integral. Newton-Leibniz formula. Geometrical meaning (area of a planar region). Improper integral, convergence and divergence of the improper integral.

Literatura

povinná literatura
• STEWART, James; Daniel K. CLEGG a Saleem WATSON. Calculus. 9th Edition. Cengage, 2020. ISBN 978-0-357-11346-2. info
• HUGHES-HALLETT, Deborah; Andrew M. GLEASON a William G. MCCALLUM. Calculus: Single and Multivariable. 8th Edition. Wiley, 2021. ISBN 978-1-119-69655-1. info
• HUGHES-HALLETT, Deborah; Andrew M. GLEASON; Patti Frazer LOCK a Daniel E. FLATH. Applied Calculus. 7th Edition. Wiley, 2021. ISBN 978-1-119-79906-1. info

doporučená literatura
• CHIANG, A. C., WAINWRIGHT, K. Fundamental Methods of Mathematical Economics, 4th edition. New York:McGraw-Hill, 2005. ISBN 978-0070109100. info
• BRADLEY, Teresa. Essential Mathematics for Economics and Business. 4th Edition. Wiley, 2013. ISBN 978-1-118-35829-0. info
• WISNIEWSKI, Mik. Introductory Mathematical Methods in Economics. Second Edition. McGraw-Hill, 1996. ISBN 0-07-709109-4. info
• STEWART, James; Lothar REDLIN a Saleem WATSON. Precalculus: Mathematics for Calculus. 8th Edition. Cengage, 2023. ISBN 979-8-214-03181-1. info
• STEWART, James; Daniel K. CLEGG a Saleem WATSON. Calculus: Early Transcendentals. 9th Edition. Cengage, 2020. ISBN 978-0-357-11351-6. info
• STEWART, James. Calculus: Concepts and Contexts. 4th Edition. Cengage, 2018. ISBN 978-1-337-68766-9. info
• MECKES, Elizabeth S. a Mark W. MECKES. Linear Algebra. Cambridge University Press, 2018. ISBN 978-1-107-17790-1. info
• TRENCH, William F. Introduction to Real Analysis. 2013. URL info
• STEWART, James a Daniel CLEGG. Brief Applied Calculus. 1st Edition. Cengage, 2011. ISBN 978-0-534-42382-7. info
• LANG, Serge. Short Calculus: The Original Edition of “A First Course in Calculus”. Springer, 2002. ISBN 978-0-387-95327-4. info
• COURANT, Richard. Differential and Integral Calculus, Volume 1. 2nd Edition. Wiley, 1988. ISBN 978-0-471-60842-4. info
• COURANT, Richard. Differential and Integral Calculus, Volume 2. 2nd Edition. Wiley, 1988. ISBN 978-0-471-60840-0. info
• LANG, Serge. Introduction to Linear Algebra. Second Edition. Springer, 1986. ISBN 978-1-4612-7002-7. info

neurčeno
• GARCIA, Stephan Ramon a Roger A. HORN. Matrix Mathematics: A Second Course in Linear Algebra. 2nd Edition. Cambridge University Press, 2023. ISBN 978-1-108-83710-1. info
• LANG, Serge. Basic Mathematics. Springer, 1988. ISBN 978-0-387-96787-5. info
• LANG, Serge. Calculus of Several Variables. Third Edition. Springer, 1987. ISBN 978-1-4612-7001-0. info

Výukové metody

text-based work, seminar assignment, cooperative and collaborative learning, teaching through practical examples applied to theoretical concepts

Metody hodnocení

Requirements for the student: attendance at seminars min. 70 %, mid-term test, final test.
Assessment: mid-term test (30 % of assessment), final test (70 % of assessment).
Assessment methods: mid-term written test, final written test.

Vyučovací jazyk

Angličtina

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