First of all, the understanding of infinitesimal is clearer than before. I used to think "infinitesimal" was "limit" After reading it this time, I realized that infinitesimal is also a variable, which can be "arbitrary, as small as possible", "with zero as the limit" and "can be artificially conceived". Knowing the concepts of "infinitesimal" and "limit", it is not difficult to understand that function learning can be transformed into "comparative study" of function and limit and infinitesimal. So it is easy to learn "continuity and discontinuity" and "derivative and differential".
The focus of derivative learning is to focus on the "five-point drawing" method of "function curve" and practice more diligently. Because this is the improvement of derivative ability and the basic application of derivative. The essence of derivative is "rate of change". The application of derivative is not only to multiply it with the increment of independent variable to get the change of function when the independent variable is slightly deformed, but also to solve the approximate value. The most practical place of derivative is to make the derivative zero, find the "stagnation point" and "non-derivative point", and then find the extreme value, maximum value and inflection point together with the two endpoints of the curve (the starting point and the ending point of the continuous function curve) to judge the monotonous interval of the function. And "guide" yourself to draw the curve diagram of the function, which is convenient for you to analyze the statistical data of production management and operation.
This edition of Advanced Mathematics is an old edition, and many concepts are expressed in Chinese. For example, many Chinese expressions of "derived formulas" are easy to understand and remember, which are many times more intimate than the so-called "pure mathematical language" written by "worshiping foreign things and obsessing foreign things". After reading this book, I suddenly understood some calculations such as "invariance of differential form", "derivative of complex number" and "derivative of implicit function". Those real scholars and educators who think that the editor of this book is really "kind and loving" really make me respect.
A book is like a person's speech. Whether the content of a book is easy to understand and detailed can show whether the author of this book is amiable, approachable, full of sense of mission and responsibility. Reading this book reminds me of my favorite teacher when I was a student. At this moment, I want to express my deep gratitude to the author of this book and give my memory to the teacher …