Course: Mathematics for Students of Physics I

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Course title Mathematics for Students of Physics I
Course code UFY/MAF1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the summer semester.
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Fuciman Marcel, Mgr. Ph.D.
Course content
Content of lectures: Mathematical theory of below mentioned parts of maths and examples of its use in physical problems: 1. Complex numbers, operations with complex numbers, trigonometric expression of c.n. 2. Techniques of integration (by parts, substitution), integration of rational functions and trigonometric functions 3. System of linear equations and matrices, rank of matrix, Gaussian elimination, Determinant 4. Scalars, vectors, dot and vector products, norm, linear combination, orthogonality and basis of a vector space 5. Eigenvalues, eigenvectors, diagonalization of a matrix 6. Taylor series, Fourier series 7. First-order linear differential equations 8. Second-order linear differential equations 9. Multivariable functions, vector functions Content of practical: Students actively solve mathematical and physical problems connected to topics discussed in corresponding lectures.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Practical training
  • Class attendance - 39 hours per semester
  • Preparation for exam - 11 hours per semester
  • Preparation for credit - 15 hours per semester
  • Preparation for classes - 12 hours per semester
Learning outcomes
Provision of mathematical readiness for courses of Physics II to IV, Theoretical Mechanics, Quantum Mechanics etc., aiming on practical abilities to solve mathematical part of problems in physics.
Student will intensify her/his knowledge of selected parts of mathematics and above all exercise solving of mathematical problems (including application on problems in physics) with relation to courses of Physics II to IV (Fyzika II to IV) and other courses with physics theme. (QM, Theoretical Physics etc.)
Prerequisites
For the course, only high school level knowledge of mathematics is expected. It's advantageous to absolve courses of Calculus I and/or Linear Algebra.

Assessment methods and criteria
Written examination

Student will graduate from the course by taking written test (solving of mathematical problems) with minimal success rate 60% (i.e. for mark 3).
Recommended literature
  • Daniel Turzík a kol.: Matematika I ve strukturovaném studiu, VŠCHT Praha 2005.
  • J. B. Fraleigh: Calculus with Analytic Geometry, Addison-Wesley 1990.
  • Karel Rektorys a kol.: Přehled užité matematiky I a II, Prometheus 2010.
  • Mary L. Boas: Mathematical Methods in the Physical Sciences, 2006 John Wiley & Sons, Inc..
  • Zuzana Došlá, Petr Liška: Matematika pro nematematické obory s aplikacemi v přírodních a technických vědách, Grada publishing 2014.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester