Junwen Wayne Peng - 台大 NCTS 數學組研究員

Homework 2

Posted on May 14, 2024 · 1 minute read

Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If $f$ is a scalar field and $F$, $G$ are vector fields, then $fF$, $F\cdot G$, and $F\times G$ are defined by [Read More]

Area of Parametric Surface and Surface Integral

Posted on May 03, 2024 · 1 minute read

Area of Parametric Surface [Read More]

Divergence (continuous), Parametric Surface and Their Application

Posted on May 01, 2024 · 1 minute read

Divergence and its connection with Green’s theorem [Read More]

Curl and Divergence

Posted on April 29, 2024 · 1 minute read

Common notation [Read More]

Calculus 4 Homework 1

Posted on April 29, 2024 · 1 minute read

This exercise demonstrates a connection between the curl vector and rotations. Let $B$ be a rigid body rotating about the $z$-axis. The rotation can be described by the vector $\mathbf{w}=\omega\mathbf{k}$, where $\omega$ is the angular speed of $B$, that is, the tangential speed of any point $P$ in $B$ divided... [Read More]

Green’s Theorem

Posted on April 26, 2024 · 1 minute read

Green’s Theorem is a fundamental concept in vector calculus that establishes a relationship between a line integral around a simple closed curve and a double integral over the plane region it encloses. Named after the British mathematician George Green, this theorem serves as a vital tool in physics and engineering... [Read More]