Mathematical methods in natural sciences - NSCI020

• Title: Mathematical methods in natural sciences
• Guaranteed by: Institute of Theoretical Physics (32-UTF)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2023
• Semester: winter
• E-Credits: 2
• Hours per week, examination: winter s.:0/2, C [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: doc. RNDr. Robert Švarc, Ph.D.; doc. RNDr. Karel Houfek, Ph.D.

Annotation

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

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.

Course completion requirements

Last update: doc. RNDr. Karel Houfek, Ph.D. (02.05.2023)

Credit for the course is based on the tests taken during the semester (60%) and final “take-home” problem (40%).

Literature

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

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

Syllabus

Last update: doc. RNDr. Karel Houfek, 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.