Numerical Methods (KMD/E-NMM)

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  • 6 credits
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1 [hours/week]
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.): Bc., Mgr.
  • Method of completion: Examination

Synopsis / description / annotation:

The course introduces numerical methods which can be suitable applied in construction of educational materials for mathematics. In the introduction, the basic concepts and properties of chosen mathematical problems are explained. These problems are further solved using the numerical methods. There are the approaches of differential and integral calculus. Further, the basic methods of optimization are presented for the purposes of an analysis of a course of functions. Chosen examples are implemented in MS Excel and Octave. The elementary essential techniques of programming are explained.

Requirements on student:

An active participation in the full-time form of the education, an active approach to solving tasks, the successful passing of the written test of the final exam.

Content:

  1. Basic concept of differential calculus – derivative of funcion, derivative of higher orders.
  2. Integral calculus – indefinite integral and analytic methods for integration, definite integral (Riemann integral).
  3. Basic concept of optimization – utilization for purposes of analysis of course of  function.
  4. Numerical methods for derivation.
  5. Riemann integral solved using numerical methods.
  6. Numerical methods of optimization for purposes of analysis of course of function.
  7. Elementary approaches to programming used in examples of numerical methods in MS Excel and Octave for educational purposes.

Time requirements:

  • Being present in classes - 26 h.
  • Self-tutoring - 30 h.
  • Consultation of work with the teacher/tutor (incl. electronic) - 5 h.
  • Preparation for an exam - 30 h.

Prerequisites:

The secondary school knowledge of mathematics is assumed.

Course results:

After finishing the course, in which an understanding of topics of the numerical methods is offered, students will have knowledge about the advanced aspects of these parts of mathematics. Student will have abilities to solve problems using a software support for mathematics.

Assessment methods:

  • Written examination
  • Continuous analysis of student’s achievements

Teaching methods:

  • Computer-based tutoring
  • Dialogic (discussion, dialogue, brainstorming)
  • Individual tutoring

Literature:

  • CHAPRA, S.C., and CANALE, R.P. Numerical methods for engineers. 6th ed. Boston: McGraw-Hill Higher Education, 2010. ISBN 978-0-07-340106-5.
  • RAO, S. S. Engineering optimization: theory and practice. 4th ed. Hoboken, New Jersey: Wiley, 2009. ISBN 978-0-470-18352-6.

Updated: 03. 10. 2022