Syllabus
1. In the beginning: concept of derivative and its direct applications.
2. Carbon dating.
3. Textbook examples of applications of differential equations: population growth, spread of a disease, polluting; geometric problems: parabolic mirror; selected applications of DE in economy; circuits; orthogonal and izogonal trajectories;
4. Motion of celestial bodies - exact calculations and computer simulation. Dating of historical events.
5. Mass, space and time - geometry of real space.
6. Remarkable applications of differential geometry.
7. Partial differential equations: basic classification, boundary conditions, applications of PDE. Heat equation - simulation in Mathematica.
8. Simulation of flows - pump, wings. Infinite dimension spaces.
9. Weather and chaos. Strange behavior of solutions of some differential equations.
10. Architecture and geometry. Shell constructions.
11. Beams and bridges.
12. Statistics: scientific data evaluation; statistics and press canards.
13. Algorithms in calculators.
14. Image processing, focusing and other effects - digital photos. Signal transmission.
15. Equations with impulses - artificial heart.
Annotation
In the first three years of the teaching branch of study in mathematics student gains valuable knowledge of theory - this is a good base for starting to get acquainted with real applications - with concrete examples of adoption of mathematics. This seminar is a good platform for computation, simulation or simply familiarization with applications.
No preliminary knowledge of physics is required.