Viewing advanced numbers from the perspective of vector space (1) -- a series introduction

introduction

In College , Most of the high mathematics students have to take the exam , Learning progress is too fast , There is no time to immerse yourself in understanding advanced mathematics , Later I learned linear algebra , Then a whim occurred , Can we use the idea of vector space in linear algebra to interpret high numbers , So there's this series , Try to use the visual image of three-dimensional interpretation of abstract high numbers , Of course, perhaps the interpretation is not comprehensive , If there is a mistake , I hope you guys can correct me .

Content overview and guide

For high numbers （ Tongji Edition ）, We will find in the outline that , It's coming up function and limit , Then introduce differential and derivative Relationship , Let me introduce a little more integral （ Indefinite integral and integral ）, And then there was Differential equations . The first volume is basically about these contents , The second volume is about space Analytic geometry And Vector algebra , Next is Multivariate function differentiation , Then the Multiple integral 、 Curve and surface integrals , There's one left Infinite series .

Look at this , It doesn't seem to have much content, does it , I learned function in high school , The rest of the whole revolves around the limits 、 differential 、 The integral turns three times , Then add some analytic geometry and series , It constitutes all the contents of the high number .

Content arrangement sequence

Because this article will interpret high numbers in the form of vector space , So the content arrangement , Will make some adjustments , Let's start with the content of vector space , This part was also learned in high school , So it should be easy to understand , Then introduce the concept of function and limit , Look at differential and derivative , And the content of the integral

（1）— Vector space and equations and their applications