Course detail
Mathematics 1
FAST-BAA001Acad. year: 2024/2025
Real function of one real variable. Sequences, limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, basic theorems on derivatives, higher-order derivatives, differential of a function, Taylor expansion of a function, sketching the graph of a function.
Linear algebra (basics of the matrix calculus, rank of a matrix, Gauss elimination method, inverse to a matrix, determinants and their applications). Eigenvalues and eigenvectors of a matrix. Basics of vectors, vector spaces. Linear spaces. Analytic geometry (dot, cross and mixed product of vectors, affine and metric problems for linear bodies in 3D).
The basic problems in numerical mathematics (interpolation, solving nonlinear equation and systems of linear equations, numerical differentiation).
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Offered to foreign students
Entry knowledge
Rules for evaluation and completion of the course
Aims
They should know how to perform operations with matrices, elementary transactions, calculate determinants, solve systems of algebraic equations using Gauss elimination method.
Students will achieve the subject's main objectives. They will get the understanding of the basics of differential and integral calculus of functions of one variable and the geometric interpretations of some of the concepts. They will master differentiating and sketching the graph of a function.
They will be able to perform operations with matrices and elementary transactions, to calculate determinants and solve systems of algebraic equations (using Gauss elimination method, Cramer's rule, and the inverse of the system matrix). They will get acquainted with applications of the vector calculus to solving problems of 3D analytic geometry.
Study aids
Prerequisites and corequisites
Basic literature
DLOUHÝ, O., TRYHUK, V.: Diferenciální počet I. CERM, 2009. CZ 2009
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. CZ 2004
Recommended reading
LARSON, R.- HOSTETLER, R.P.- EDWARDS, B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. EN 2005
STEIN, S. K: Calculus and analytic geometry. New York, 1989. EN 1989
Elearning
Classification of course in study plans
- Programme BPC-SI Bachelor's
specialization VS , 1 year of study, winter semester, compulsory
- Programme BPC-MI Bachelor's 1 year of study, winter semester, compulsory
- Programme BKC-SI Bachelor's 1 year of study, winter semester, compulsory
- Programme BPA-SI Bachelor's 1 year of study, winter semester, compulsory
- Programme CZV1-AKR Lifelong learning
specialization PBC , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
Exercise
Teacher / Lecturer
Ing. Pavel Špaček, Dr.
Mgr. et Mgr. Jan Šafařík, Ph.D.
RNDr. Oto Přibyl
Mgr. Jana Bulantová, Ph.D.
doc. Ing. Vladislav Kozák, CSc.
RNDr. Mgr. Lucie Zrůstová, Ph.D.
doc. Mgr. Irena Hinterleitner, Ph.D.
doc. Mgr. Ing. Miroslav Trcala, Ph.D.
Ing. Petra Rozehnalová, Ph.D.
Mgr. Blanka Morávková, Ph.D.
Mgr. Eva Jansová, Ph.D.
Mgr. Hana Boháčková, Ph.D.
RNDr. Rudolf Schwarz, CSc.
Ing. Anna Derevianko, Ph.D.
Syllabus
1. Absolute value of a function. Quadratic equations in complex field. Conics. Graphs of selected elementary functions. Basic properties of functions. 2. Composite function and inverse to a function (inverse trigonometric functions, logarithmic functions). Numerical solutions of equations by bisection and regula falsi method. 3. Polynomial, sign of a polynomial. Lagrange and Newton interpolation polynomial. 4. Rational function, sign of a rational function, decomposition into partial fractions. 5. Limit of a function. Derivative of a function (basic calculation) and its geometric applications, basic formulas and rules for differentiating. 6. Derivative of an inverse function. Basic differentiation formulas and rules. Numerical differentiation. 7. Test I. Higher-order derivatives. Taylor theorem. L` Hospital's rule. Approximation of solutions of one equation in one variable by the Newton method. 8. Asymptotes of the graph of a function. Sketching the graph of a function. 9. Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix, solutions to systems of linear algebraic equations by Gauss elimination method. Numerical solutions of systems of linear equations. 10. Calculating determinants using Laplace expansion and rules for calculating with determinants. Calculating the inverse to a matrix using Jordan's method. Solutions of systems of linear equations by iteration. 11. Test II. Matrix equations. The discrete least square method. Eigenvalues and eigenvectors of a matrix. 12. Using dot and cross products in solving problems in 3D analytic geometry. 13. Mixed product. Seminar evaluation.
Elearning