Chapter 289 (1/2)

Chapter 292

Cheng Nuo's winter vacation officially began in the quarrel with Mu Leng.

After a busy semester in college, Cheng finally had time to rest.

After several days of lying dead like salted fish at home, Cheng Nuo had to get up again to start his learning process.

”Complex function” and ”ordinary differential equation” are two courses that need to be used in college students' mathematics competition, and Cheng Nuo should complete them by himself before the new year.

Taking a taxi, Cheng Nuo goes straight to the biggest bookstore in Qingcheng.

Originally, I wanted to buy only two books: complex variable functions and ordinary differential equations. However, I thought that all the things were coming. It was better to buy more books at one time. Cheng Nuo took more than a dozen books from the bookshelf and settled the account one by one.

Functions of real variables and functional analysis, abstract algebra, probability theory and mathematical statistics, topology, partial differential equations

These are the courses that mathematics department will learn in the four years of college.

He returned to his bedroom with a dozen books.

The hundreds of high school review books on the bedroom bookshelf have been cleaned up by Jiang LAN, and now it is a little empty. Cheng Nuo put more than a dozen books on the bookshelf in order and chuckled.

With his learning speed, it is estimated that the bookshelf will be filled again soon!

Study, Sao Nian!

After making a cup of coffee, Cheng Nuo sits at his desk and opens the title page of the book complex functions.

It is more difficult to learn a complex function than a natural function. This course is based on derivative and integral as the starting point, gradually developed.

As a branch of function theory, compared with real variable function, complex variable function takes complex field as an independent variable to carry out various function operations.

This textbook mainly explains the content of complex variable function through three aspects.

Analytic function, general mapping, Riemann surface.

Cheng Nuo had the manuscript in hand, reading and calculating the theorems in the book.

For example, Cauchy Goursat theorem means that a function f (z) has a theorem on the region u, G (z) is called the analytic primitive function of F (z) in the region u, if G (z) is analytic on u and G '(z) = f (z) holds everywhere on U.

After reading this theorem, Cheng Nuo did not directly look at the proof process of the theorem below, but directly proved it on the draft paper.

Let γ: [a, b] → C be a piecewise smooth curve with parameter equation γ (T), a ≤ t ≤ B. if f (x) is continuous on γ, then ∫ f (z) DZ = ∫ (a, b) f (γ (T) γ '(T) DT 】

after verification, Cheng Nuo opened the textbook for comparison. The idea is exactly the same.

Whoa, whoa, whoa! Sure enough, great mathematician Cauchy and I have the same idea!

Holding a happy mood, Cheng Nuo continues to look down.