What scientific calculations can python do?

Python's characteristics in scientific computing: 1. The science library is complete. (Recommended learning: Python video tutorial)

Science library: numpy, scipy. Cartography: matplotpb. Parallel: mpi4py. Debugging: pdb.

2. High efficiency.

If you can learn numpy(array feature, f2py) well, your code execution efficiency will not be much worse than fortran and C, but if you can't use array well, the efficiency of the program written in that way can only be hehe. So after getting started, please spend enough time to understand numpy's array classes.

3. Easy to debug.

Pdb is the best debugging tool I have ever seen, and there is no one. Give you a paragraph directly at the program breakpoint, which can only be done by text interpretation language. It is no exaggeration to say that it only takes Fortran110 time to develop programs in python.

4. others.

It is rich and unified, not as complicated as the library of C++ (like various distributions of pnux), so python can do scientific calculations by learning numpy well. Python's third-party libraries are complete, but not miscellaneous. Python is easier to develop on a large scale than fortran because of its class-based language characteristics.

In numerical analysis, Runge-Kutta method is an important implicit or explicit iterative method for solving nonlinear ordinary differential equations. These technologies were invented by mathematicians Carl Runge and Martin William Kutta around 1900.

Runge-Kutta method is a high-precision single-step algorithm widely used in engineering, including the famous Euler method, which is used to solve differential equations numerically. Because of the high accuracy of this algorithm and the measures to suppress the error, its implementation principle is also complicated.

Gaussian integral is widely used in the unification of probability theory and continuous Fourier transform. It also appears in the definition of error function. Although the error function has no elementary function, Gaussian integral can be solved analytically by calculus. Gaussian integral, sometimes called probability integral, is the integral of Gaussian function. It is named after German mathematician and physicist C.F. Gauss.

Lorentz attractor and its derived equation were published by Edward Norton Lorenz in 1963. It was first proposed in the paper "Deterministic Aperiodic Flow" published in the Journal of Atmospheric Science, and it was simplified from the convection volume equation appearing in the atmospheric equation.

This Lorenz model is not only important for nonlinear mathematics, but also for climate and weather prediction. The atmospheres of planets and stars may show many different quasi-periodic states. Although these quasi-periodic states are completely determined, they are easy to mutate and appear to change randomly. The model clearly describes this phenomenon.

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