数学

数学

Method Of Lagrange Multiplier Under Equality Conditions

This article describes Method Of Lagrange Multiplier, a powerful technique for solving mathematical optimization problems.
2022.04.02

The Distance Between A Point And A Hyperplane

Derive the distance between a point and a hyperplane, which is the general form of the distance between a point and a line.
2022.04.01
機械学習

Derivation Of “Differentiate By Vector” Formula

When studying machine learning theory, we often see the operation of "differentiating a scalar by a vector. In this article, we derive the formula for "differentiating a scalar by a vector.
2022.04.01

Binomial And Polynomial Theorem Proofs

The binomial theorem is a very versatile theorem that shows up in a variety of places. In this article, we will discuss the binomial theorem and its generalization, the polynomial theorem.
2022.04.01
物理学

Proof Of Theory Of Helmholtz Resonance

When you blow on the mouth of an empty bottle, you may hear a "boing" sound. This phenomenon is called Helmholtz resonance. In this article, we will explain the mechanism of Helmholtz resonance.
2022.04.01

Taylor Expansions Of Two And Multivariable Functions, Simple Proofs

Extending the one-variable Taylor expansion, we derive a Taylor expansion for multivariable functions. We will first discuss Taylor expansions for two-variable functions.
2022.04.01

Maclaurin Expansion Of Exp, Sin, Cos

As a specific example of Taylor expansion, we will compute the Maclaurin expansion of e^x, sinx, and cosx. And finally, we derive Euler's formula.
2022.04.01

Explaining The Theory Of Taylor Expansion

Derive the Taylor expansion. The beauty of the Taylor expansion is that it allows us to express functions in polynomial form.
2022.04.01
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