Junwen Wayne Peng - 台大 NCTS 數學組研究員

Psudocode of transformation from any quadratic form to a normal form

Posted on April 15, 2024 · 1 minute read

Idea [Read More]

Transformation & Change of Variables

Posted on April 10, 2024 · 1 minute read

[Read More]

Calculus III overview

Posted on April 04, 2024 · 1 minute read

graph LR A --> B C -.-> D E ==> F [Read More]

Spherical Coordinate

Posted on April 03, 2024 · 1 minute read

Spherical coordinates, also known as spherical polar coordinates, are a system of coordinates used in three-dimensional space. They are especially useful in fields such as physics and engineering where problems often involve three dimensions. In spherical coordinates, a point in space is represented by three values: the radial distance from... [Read More]

Note for an unfinished computation in today’s course

Posted on April 03, 2024 · 1 minute read

We’re considering a change of variables where

x = u^{2} - v^{2}

and

y = 2 u v

. We aim to express the solid

E = {(x, y) 0 \leq y \leq 2, \frac{y^{2} + 4}{4} \leq x \leq - \frac{y^{2} + 4}{4}}

in terms of

u

and

v

. Let’s examine the following graph to better understand what we’re trying to achieve. We are seeking the area on the left-hand side... [Read More]

Psudocode of transformation from any quadratic form to a normal form

Transformation & Change of Variables

Calculus III overview

Spherical Coordinate

Note for an unfinished computation in today’s course

Triple Integrals

Polar Coordinate

Double Integrals, Iterated Integrals, and Type I & II Regions

Counterexamples of Fubini theorem