Battlefield on the internet, infinite small method PK (ε, Delta) Limit Theory

When talking about calculus, many college graduates are a little embarrassed, indicating that all their calculus knowledge at school has been returned to the teacher. To put it bluntly, the knowledge of calculus is almost completely forgotten, and there is a lack of confidence in calculus. How did this happen?

Do not speak in circles. It is best to be straightforward and not to hide. The essence of the 6.18 infinitely small release plan for the Internet is: to open a battle on the Internet (Battlefield), the infinite small method should be "more true" than the traditional (ε, Delta) Limit Theory ". This "true" is the comprehensive confrontation between the infinitely small method and the (ε, Delta) Extreme theory, rather than using the infinitely small as an atomic bomb. The so-called "Comprehensive confrontation" refers to the comprehensive confrontation between the infinitely small calculus and the (ε, Delta) Extreme theory calculus. That is to say, the entire line is one-to-one "Pk ".

It can be seen that how to put the theoretical system of the infinitely small calculus on the internet, let the majority of calculus beginners as referees, fair "showdown" is the key to the problem. Relatively speaking, this "more realistic" front line is long and has a large span. Therefore, the text transcription of the teaching materials of the infinite calculus is a "bottleneck ". The transcription quality is too high and must be retried. For example, section 1.6 of J. Keisler basic calculus has a very poor transcription quality, which can be described as "cutting corners" or "self-destruction of the Great Wall". I will notify relevant personnel to bring it back. Leave the convenience of reading to the majority of readers, rather than the convenience to yourself. This is our principle of doing things.

After the layout on the Internet, people will be surprised to find that: "the infinitely small calculus is not playing the cards according to the general rules, the super real number playing the front, the derivative first, continuous, after the points, trigonometric function and exponential function pressure array (Chapter 1 and chapter 8). The infinitely small method is always the main line.

In the traditional (ε, Delta) Limit Theory, the situation is not optimistic. Knowledge is outdated (many concepts come from the enlightened knowledge in the middle school stage, which is not clear enough), and theories are outdated (for example, the definition of functions). This makes it easy for readers to forget. Is everything true? As the saying goes, it's just a horse pulling out of the Internet.

The evaluation of the infinitely small method can make a fair conclusion only in the process of fully expanding calculus. It is impossible to make a discussion of the infinitely small solution alone. For example, an infinitely small box is like Pandora's
Box), and then let it fly to the Internet.

Honestly, J. keisler's basic calculus ebook is an encyclopedia of calculus, with nearly 1,500 "knowledge points" (or basic mathematical concepts ), it is very beneficial to comprehensively improve the scientific literacy of Chinese college students. Therefore, releasing endless possibilities on the Internet is not unnecessary. Although the school wall is the last barrier of traditional calculus, the infinite devil will still be able to see the Internet access to the campus through optical fiber, effectively promoting the reform of calculus.