



The course Mathematical methods in natural sciences will cover basic topics of mathematics necessary for
understanding fundamental physical theories such as classical mechanics and Maxwell theory of electromagnetic
field, as well as topics relevant for chemistry and biology.
Last update: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)



Credit for the course is based on the tests taken during the semester (60%) and final “takehome” problem (40%). Last update: Houfek Karel, doc. RNDr., Ph.D. (02.05.2023)



1. J. Nearing: Mathematical Tools for Physics, http://www.physics.miami.edu/nearing/mathmethods/ 2. G. B. Arfken et al.: Mathematical Methods for Physicists, Academic Press (2013) 3. D. J. Griffiths: Introduction to Electrodynamics, Cambridge University Press (2017) 4. lecture notes Last update: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)



1. Differential calculus. Elementary functions. Derivatives, their properties and applications. Taylor series. Partial derivatives. 2. Integral calculus. Indefinite and definite integral. Geometric meaning. Methods of integration. 3. Euclidean geometry. Coordinates. Points, curves, surfaces. Geometric vectors, scalar and vector products. 4. Linear algebra. Vector space, basis, dimension. Rows, columns, matrices. Linear operators. 5. Differential equations. Classification. Solution, its existence and uniqueness. Linear ODEs with constant coefficients. 6. Surface and volume integrals. Differential operators. Gauss and Stokes theorems. Last update: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)
