Course Details
Mathematics 1
Academic Year 2026/27
BAA101 course is part of 1 study plan
BPC-SIS / SI Winter Semester 1st year
The goal of the course is to deepen and strengthen the knowledge gained from high school math. Students will learn new techniques and mathematical methods, enhance their logical thinking, which will allow them to think and apply the knowledge they've gained in their specializations. Students should also learn to analyze a problem, choose the right approach, select the appropriate calculation method, and evaluate the result, which should lead to critical thinking. The course is divided into three topics: the first focuses on the basics of linear algebra; the second covers single-variable calculus; and the third is dedicated to the basics of integral calculus.
Credits
6 credits
Language of instruction
Czech
Semester
Course Guarantor
Institute
Forms and criteria of assessment
Entry Knowledge
High school math knowledge is required.
Aims
Professional Knowledge:
- Familiarity with matrix algebra and its application to solving systems of linear equations. Understanding of the fundamental concepts of differential and integral calculus of functions of one variable, including the geometric interpretation of selected concepts. Introduction to vector calculus and its applications.
Professional Skills:
- The student will acquire proficiency in differentiation and integration techniques and will learn how to analyze the behavior of functions.
- The student will be able to perform matrix operations, carry out elementary matrix transformations, compute determinants and inverse matrices, and solve systems of linear algebraic equations using both the Gaussian elimination method and inverse matrices.
General Competences:
- The student will be prepared to continue further studies that require knowledge and understanding of the topics covered in this course.
Basic Literature
STEIN, S. K: Calculus and analytic geometry. New York, 1989. (en)
LARSON, R.- HOSTETLER, R.P.- EDWARDS, B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. (en)
Recommended Reading
TRYHUK, V. - DLOUHÝ, O.: Modul GA01_M01 studijních opor předmětu GA01. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (cs)
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. (cs)
DLOUHÝ, O., TRYHUK, V.: Diferenciální počet I. CERM, 2009. (cs)
DANĚČEK, J., DLOUHÝ, O., PŘIBYL, O.: Matematika I. Modul 7 Neurčitý integrál. CERM, 2007. (cs)
SLOVAK, J., PANÁK, M., BULANT, M.: Matematika drsně a svižně. MU Brno, 2013. (cs)
BHUNIA, S. C., PAL, S.: Engineering Mathematics. Oxford University Press, 2015. (en)
Prerequisites
High school math knowledge is required.
Offered to foreign students
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
- Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix.
- Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
- Vector calculus (operations with vectors, dot, cross, and mixed products of vectors). Real linear space, linear combination and independent bases and dimension of a linear space.
- Solutions to systems of linear algebraic equations by Gauss elimination method, Frobenius theorem.
- Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
- Real function of one real variable and its basic properties, explicit and parametric definition of a function. Composite function and inverse to a function. Some elementary functions (inverse trigonometric functions).
- Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers. Rational functions and their decomposition into partial fractions.
- Limit of a function, continuous functions, basic theorems.
- Derivative of a function, its geometric and physical applications, rules of differentiation.
- Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial and Taylor's theorem.
- L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
- Anti-derivative, indefinite integral and its properties. Integration by parts and substitution methods in calculating integrals.
- Integration of selected functions (rational, trigonometric, irrational).
Exercise
13 weeks, 3 hours/week, compulsory
Syllabus
- High school repetition.
- Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix.
- Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
- Vector calculus (operations with vectors, dot, cross, and mixed products of vectors).
- Solutions to systems of linear algebraic equations by Gauss elimination method.
- Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
- Test 1. Some elementary functions (inverse trigonometric functions). Composite function and inverse to a function.
- Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers.
- Rational functions and their decomposition into partial fractions. Limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, rules of differentiation.
- Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial.
- Test 2. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
- Anti-derivative, indefinite integral and their properties. Integration by parts and substitution methods in calculating integrals.
- Integration of selected functions (rational, trigonometric, irrational).
Self-study
39 weeks, 1 hours/week
Individual preparation for an ending of the course
52 weeks, 1 hours/week