你幫它糾錯，就是在提供反饋免費訓練它。假以時日，它就越來越厲害了

絕大多數人類的ego太多，沒法訓練。所以General AI才有希望

我剛問了它一個問題。 回答漂亮的像是從書上抄下來的。 就不知道哪一本

how to visually understand cauchy integral

 

 

The Cauchy integral can be understood visually by considering complex analysis as a generalization of real analysis to the complex plane. In real analysis, a path integral of a function over a closed curve can be thought of as the total change of the function as you travel along the curve. In complex analysis, the Cauchy integral generalizes this idea to complex valued functions and complex paths.

One way to visualize the Cauchy integral is to consider a function defined on the complex plane, and to imagine a small circle centered at a point in the domain of the function. The value of the Cauchy integral over this circle will be proportional to the average value of the function inside the circle. By considering a series of smaller and smaller circles centered at a point, one can obtain a better and better approximation of the value of the function at that point.

Another way to visualize the Cauchy integral is to consider the complex plane as a two-dimensional surface, and to imagine a function as a surface in this space, with its value at each point determining its height. The Cauchy integral can then be thought of as the total change in the function along a particular path, or the amount that the function "flows" along the path.

In either case, the Cauchy integral is a powerful tool for understanding complex functions, and provides a way to connect geometry and topology with complex analysis.

所有跟帖： 

• 所以，第一個，往往有優勢。 -trimtip- ♂ (0 bytes) () 02/10/2023 postreply 16:39:58