F1422 Computing practice 1

Faculty of Science
Autumn 2024
Extent and Intensity
0/3/0. 3 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Ing. arch. Petr Kurfürst, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Ing. arch. Petr Kurfürst, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Ing. arch. Petr Kurfürst, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 17:00–19:50 F1 6/1014
Prerequisites
It is recommended to master basic operations of differential and integral calculus on the secondary school level.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Obtain routine numerical skills necessary for bachelor course of physics and applied physics.
Learning outcomes
Student will be able after completing the course:
- to master the derivation and integration of even more complex functions of one real variable;
- to understand the basics of vector and matrix calculus and calculating the bases of vector spaces;
- to solve ordinary differential equations of 1st, 2nd, and of higher orders;
- to solve the line integrals of 1st and 2nd type and to apply them to geometrical and physical situations in Cartesian, cylindrical and spherical coordinates;
- to solve the basic operations with scalar and vector functions of more variables, including partial derivatives, scalar potentials, and vector identities;
- to understand the basics of calculation of probability and statistics.
Syllabus
  • 1. Differentiation and integration of real functions of single variable, practicing of basic operations.
  • 2. Fundamentals of vector algebra in R-2 and R-3: vectors, vector calculus, scalar and vector product and their geometrical and physical interpretation, vector calculus in bases.
  • 3. Fundamentals of vector algebra in R-2 a R-3: transformation rules.
  • 4. Ordinary differential equations: separation of variables, first-order linear differential equations, physical applications (nuclear fission, absorption of radiation).
  • 5. Ordinary differential equations: linear equations of the second and higher orders with constant coefficients, physical applications (equations of a particle motion, harmonic oscillator, damped and forced oscillations).
  • 6. Simple systems of equations of motion.
  • 7. Curvilinear coordinates.
  • 8. Line integral: curves, parameterization, line integral of the first type and its physical applications (length, mass, center of mass and moment of inertia of the curve), line integral of the second type and its physical applications (work along the curve).
  • 9. Scalar functions of two and three variables: partial derivatives, directional derivatives, gradient.
  • 10. Scalar functions of two and three variables: total differential, existence of potential.
  • 11. Vector functions of two and three variables: definitions, Jacobi matrix, integral curves of the vector field (streamlines, field lines, ... ), differential operators.
  • 12. Combinatorics and fundamentals of statistical distribution. Random variables: the probability, discrete and continuous distributions, characteristics of the distribution (mean, standard deviation, median, ... ), distribution function.
  • 13. Random variables - applications: fundamentals of measurement results processing, physical problems.
Literature
    recommended literature
  • KURFÜRST, Petr. Početní praktikum. 2. vyd. Brno: Masarykova univerzita, 2017. Elportál. ISBN 978-80-210-8686-9. html PURL url info
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis). Brno: VUTIUM, 2006, 281 pp. Vysokoškolské učebnice. ISBN 80-214-2914-3. info
  • ARFKEN, George B. and Hans-Jurgen WEBER. Mathematical methods for physicists. 6th ed. Amsterdam: Elsevier, 2005, xii, 1182. ISBN 0120598760. info
Teaching methods
Seminar based on the solution of typical problems.
Assessment methods
Based on 'Studijní a zkušební řád Masarykovy univerzity', chapter 9, section 2 the attendance on schooling is required for students of full-time form of study, there is only one unexcused absence tolerated during the semester. The absences can be compensated by elaboration of additional exercise from the set of examples in the textbook "Kurfürst Petr, Početní praktikum, 2017", published on the website of the course, selected individually by the teacher. Deadline for additional homeworks is the end of the examination period, however, it is better to hand them over continually. Due to the current epidemiological measures can be the contact presence lectures changed to distant. Students will be informed about all such steps and changes in time by e-mail. Students gather points for lecture activity. Each lecture activity is evaluated with one point for correct and complete solution of any of pre-assigned example. Subject matter is divided into three particular tests, which are written during the semester, typically in the 5th, 9th and the last week. For each test student can obtain a maximum of 10 points. Student write fourth test from whole semester, if achieve less then 15 points. Time limit for each test is 60 - 90 minutes. At their own discretion, the already successful students can also improve their rating through oral examination. Students of combined form also write three particular tests or they can write one summary test during the exam period. Final grade will be determined from sum of all points gained by each student during the semester. All the detailed informations about the method of final classification, and others, are published on the website of the course on my website.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
http://physics.muni.cz/~petrk/
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
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