Infinitely small calculus to seize Internet classrooms

The important period of basic knowledge acquisition in life is the university age. Recalling college life is always sweet and hard to forget.

Chinese college students are not optimistic about the actual situation when learning calculus. They lack a modern calculus tutorial. In the classroom, I am suffering from the spirit of the teacher's traditional old ideas, and my mind is filled with seemingly non-conventional dogmas.

Professor J. Keisler, a well-known modern mathematical logic model theory scholar, wrote the basic calculus textbook which is very suitable for junior college students. The contents of this book have been carefully arranged and selected. The contents (contents) are as follows:

Preface

Chapter 2
Real Number and super real number

Chapter 2
Differentiation Method

Chapter 2
Continuous Functions

Chapter 2
Integration Method

Chapter 2
Ultimate, analytic ry, and approximation methods

Chapter 2
Set credit application

Chapter 2
Trigonometric function

Chapter 2
Exponential and logarithm Functions

Chapter 2
Infinite Series

Chapter 1 vector

Chapter 1 partial Differentiation

Chapter 1 multiple points

Chapter 2 Vector Calculus

Chapter 2 Differential Equations

Postscript

The preface and postscript of this book are the most brilliant and have high academic value. The teaching content arrangement sequence is unique. For example, the differential method is arranged before the continuous function, and the limit is arranged after the integral method. The trigonometric function and exponential function are placed in the second half of the teaching material. In the traditional calculus view, this kind of content arrangement is incredible.

In fact, from the perspective of the calculus theory system, this content arrangement sequence is fully logical, especially suitable for the level of understanding of lower-grade students. Forty years ago, the Calculus Teaching Reform Experiment in Chicago, United States has proved this. This calculus textbook can be considered as a classic book that has withstood the historical postgraduate entrance exam. Our current job is to bring it to the Internet classroom in China, so that the majority of college students can share the basic knowledge of modern calculus, accept the tao of modern mathematical theory, and broaden their horizons, distinguish between right and wrong, grow up and become talented, and better serve our country.