Speaker：Shibo Liu（Florida Institute of technology，US）

Time：2022-12-11, 10:00

Location：Tencent Meeting ID：545-822-257（No Password）

Abstract:

We demonstrate why linearization is the fundamental idea of differential calculus by analyzing the inverse function theorem (I call it the fundamental theorem of differential calculus), as application we present our result on surjectivity of maps between Euclidean spaces, including a striking consequence saying that any vector valued function over a compact manifold possesses infinitely many critical points. Then we will discuss our proof of the change of variable formula for multiple integral, then derive the Brouwer fixed point theorem as a direct corollary. Finally, we derive the very useful coarea formula from physical consideration (due to myself). If time permits, a proof via ordinary differential equation will also be presented. This lecture is accessible (and helpful) to undergraduate students knowing linear algebra and multivariable calculus.