Infopaket

Special methods of programming and simulation in physics

ОК18

Обов’язкова дисципліна для ОП

Second

2022/2023

2 Semester

6

06. Choose effective mathematical methods and information technologies and apply them to research and / or innovation in physics and / or astronomy. 13. Create physical, mathematical and computer models of natural objects and phenomena, check their adequacy, study them to obtain new conclusions and deepen understanding of nature, and analyze limitations. 19. Know and be able to apply numerical and analytical methods for appropriate calculations in the field of medical physics. 20. Know and be able to use software to simulate the physical actions that occur in the human body.

Full-time form

• Know the basics of mathematical analysis, analytical geometry, linear algebra, differential equations, mathematical physics, and programming. • Be able to apply knowledge of mathematical analysis, differential equations, linear algebra to perform mathematical transformations and solve differential equations. • Have basic skills: computer skills, mathematical transformations, finding derivatives, and integrals.

The course "Special methods of programming and simulation in physics" studies the means of computer algebra system Maple for symbolic transformations of mathematical expressions, analytical and numerical solutions of equations and systems of algebraic equations, problems of mathematical analysis, analytical geometry and linear algebra, visualization and data analysis. Means of analytical and numerical solution of ordinary differential equations and their systems, partial differential equations and visualization of solutions by means of graphs, phase portraits or animations. Maple's programming tools, such as creating own functions and procedures, conditional statement, loops, writing data to a file, and reading, are also explored. In addition to mathematical problems, gaining work skills in Maple is consolidated by considering problems from different fields of physics or problems that arise in students’ graduate works.

1. Kuzmin A. V., Denisov S. V. Computer Algebra: Course of lectures and laboratory practice: teaching. manual / A.V. Kuzmin, S.V. Denisov. – K.: VOC "Kyiv University", 2017. – 281 p. 2. Wang F.Y. Physics with Maple. The Computer Algebra Resource for Mathematical Methods in Physics. – WILEY-VCH, 2005. – 605 p. 3. Meade D.B., May M., Cheung C.K., Keough G.E. Getting started with MAPLE. – John Wiley & Sons, 2009. – 233p. 4. Liengme B.V. Maple: A primer. – Morgan & Claypool Publishers, 2019 – 171 p. 5. Bauldry W.C., Fox W.P. Advanced Problem Solving with Maple: A First Course. – Taylor & Francis;CRC, 2020. – 347 p. 6. Borwein J.M. Skerritt M.P. An Introduction to Modern Mathematical Computing with Maple. – Springer-Verlag New York, 2011. – 216 p. 7. Betounes D., Redfern M. Mathematical Computing An Introduction to Programming Using Maple. – Springer-Verlag New York, 2002. – 418 p.

Lectures, practical classes, independent study of students

Semester grade: Fulfillment of individual independent assignments (40 points – practical classes, 20 points – lectures). At lectures and practical classes, students receive individual assignments that they must complete on their own in the Maple system and turn in these assignments. Final grade in the form of an exam: The exam is held in a computer class. The exam paper contains 8 practical tasks, each of 5 points, so the student can get a maximum of 40 points in the exam. Students have 1 hour to complete the tasks.

Ukrainian