BA_Ma_1 Mathematics 1

University of Finance and Administration
Winter 2025
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Taught in person.
Guaranteed by
Ing. Šárka Čížková, Ph.D.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Dita Egertová
Prerequisites
There are no prerequisites for this course.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Clarification of the terms of linear algebra and their mutual relationships (vector spaces, matrix operations, solutions to the system of linear equations). Presenting the sequence and its limit; function; continuous function and the limit of a function; and elementary functions to the students. Understanding the mathematical operation of a derivative and its main properties; learning to calculate the derivatives of functions; learning the basic theorems in differential calculus.
Learning outcomes
At the end of the course students will be able to: -solve a linear system by matrices -evaluate limits of functions and limits of sequences -evaluate a derivative of a function -evaluate a limit of function by l'Hospital's rule
Syllabus
  • 1. Vectors and vector spaces
  • 2. Matrices. Matrix rank
  • 3. Matrix operations. Inverse matrices
  • 4. Determinants. Matrix equations
  • 5. Systems of linear equations
  • 6. Sequences. Limits of sequences
  • 7. Basic functions and their properties
  • 8. Function properties. Inverse functions
  • 9. Continuity and limits of functions
  • 10. Derivatives and their properties
  • 11. Derivatives of composite functions
  • 12. Applications of derivatives – L’Hospital’s Rule, tangent equations to graphs
Literature
    required literature
  • Mathematics for Economics Plný text k dispozici By: Hoy, Michael; Rees, Ray; Stengos, Thanasis; Livernois, John; McKenna, Chris. Edition: 3rd ed. Cambridge, Mass : MIT Press. 2011. eBook.
  • Neustupa J.: Mathematics I. Vydavatelství ČVUT, Praha 2004, 2. vydání
    recommended literature
  • Mathematics for economic universities, Jindřich Klůfa, Nikola Kaspříková, Vydavatel: EKOPRESS ISBN: 978-80-87865-01-9, Vyšlo: 2013/10
Teaching methods
Lectures:
• Lecture-based with discussion

Exercises:
• Application of knowledge, skills development
• Enhancement of thinking and practical applications
• Reinforcement of knowledge
• Automation of basic skills
• Understanding principles, not just formulas
• Development of logical and analytical thinking
• Application in economics

Modern Technology-Supported Methods – Motivation, Interactivity:
• Use of AI as a personal math tutor for visualization and interactive learning
Assessment methods
The course concludes with a credit and an exam. Credit: Requires a written credit test (minimum 60% success rate) and 75% mandatory attendance. Students with an Individual Study Plan (ISP) are exempt from mandatory attendance. Exam: Written exam (minimum 50% success rate).
Language of instruction
English
Follow-Up Courses
The course is also listed under the following terms Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (recent)
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