Virtual Laboratory of Applied Mathematics

Fun and pedagogic experiments


1. The brachistochrone. The shortest path is not the fastest. It's crazy, but it's absolutely true! With knowledge of the integrals, the variational calculation, you will find that this trivial question lead to an amazing response and a lot of valuable information.



2. The unidimensional ballistic shooting. It was a classic problem in high school, but you will find that this variant - presented in a fun way - is useful.



3. The bidimensional ballistic shot. This is the improved version of the one-dimensional problem with a lot of new concepts such as bilinear interpolation, the grid ... and a lot of passion.



4. The Chinese remainder theorem. A problem dated from 2000 years but modeled as a game. You will understand why our ancestors came to solve very complicated calculations, and why now this knowledge is still useful.



5. The cycloid. Do you know the trajectory of the moon seen from… the sun ? And if the earth suddenly changes the direction of rotation around the sun? It’s not necessary to go to the sun, because the answer is here, in this exercise.



6. Djiskstra algorithm. Finding the shortest path in a directed graph is a classical problem but with many applications. One of the fastest algorithm is the Djiskstra, but its principle is not easy to understand. This exercise helps you to get rid of this trouble.



7. Elliptic curves. This is a fairly new concept and is the subject of many research since its application field is wide. What is interesting here is that a 2000 years old principle is used to solve problems in 2000.



8. Fractal.  Beautiful and vibrant images in nature or things around us such as blood vessels, the market changes are also subjects of  exciting mathematical research. These are fractal structures that are found here in this exercise.



9. The three laws of Kepler. They explain the movements of the celestial body in the universe. We will understand why our ancestors could to calculate the trajectories of comets with their semi-major axes greatly exceed the limits of our solar system.



10. Newton’s laws of cooling. This exercise presents a variant of a classic application of differential equation first degree, the problem of heat exchange between two and several different environments.




11. Leapsheep. This is certainlya very familiar game when you're little, but here is a little different. You must provide knowledge of numerical sequences, linear algebra ... and with all that, you will have less than 1% to win.
So! You try ?




12. Tris in main memory. We know (almost) linear sort but little on how to sort-merge. This exercise explain detailed way the steps of these two methods and animated diagrams clearly show the superiority of our method tri-fusion.



13. Calculation of extrema without gradient. This exercise explains detailed and graphic manner the steps to determine the extrema of functions of one variable by numerical methods.




14. Chain matrix multiplication. This is a very interesting topic in optimization. Not only because it shows an error that was always believed to be true, but it shows that the most powerful computers are still far behind the human imagination.



15. Finding roots by numerical methods. This exercise explains detailed and graphic manner the steps to determine the roots of functions one-variables by numerical methods.



16. Runge-Kutta methods. exercise explains detailed and graphic manner steps to solve the problem initial values ​​(or Cauchy problem) by Euler and Heun (improved Euler) methods.


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