From aae00025bd8bff04de90b22b2472aed8a232f476 Mon Sep 17 00:00:00 2001 From: Navan Chauhan Date: Tue, 26 Mar 2024 18:21:29 -0600 Subject: post testing latex extra --- docs/feed.rss | 60 ++++++++++++++++++++++++++++++++++++++++++++++++++--------- 1 file changed, 51 insertions(+), 9 deletions(-) (limited to 'docs/feed.rss') diff --git a/docs/feed.rss b/docs/feed.rss index 12e9f8d..12b90df 100644 --- a/docs/feed.rss +++ b/docs/feed.rss @@ -4,8 +4,8 @@ Navan's Archive Rare Tips, Tricks and Posts https://web.navan.dev/en - Thu, 21 Mar 2024 14:27:28 -0000 - Thu, 21 Mar 2024 14:27:28 -0000 + Tue, 26 Mar 2024 18:20:37 -0000 + Tue, 26 Mar 2024 18:20:37 -0000 250 @@ -557,9 +557,7 @@ creating a DOS -

$$ -y = ax^3 + bx^2 + cx + d -$$

+y=ax3+bx2+cx+d

Optimizer Selection & Training

@@ -584,9 +582,7 @@ $$

Our loss function is Mean Squared Error (MSE):

-

$$ -= \frac{1}{n} \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2} -$$

+=1n∑i=1n(Y_i−Y_i^)2

Where Yi^ is the predicted value and Yi is the actual value

@@ -726,7 +722,7 @@ $$

How would you modify this code to use another type of nonlinear regression? Say,

-

$$ y = ab^x $$

+y=abx

Hint: Your loss calculation would be similar to:

@@ -3186,6 +3182,52 @@ values using the X values. We then plot it to compare the actual data and predic ]]> + + + https://web.navan.dev/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html + + + Quadratic Formula Derivation + + + Quick derivation of the quadratic equation by completing the square + + https://web.navan.dev/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html + Tue, 26 Mar 2024 15:36:00 -0000 + Quadratic Formula Derivation + +

The standard form of a quadratic equation is:

+ +ax2+bx+c=0 + +

Here, a,b,c∈ℝ, and a≠0

+ +

We begin by first dividing both sides by the coefficient a

+ +⟹x2+bax+ca=0 + +

We can rearrange the equation:

+ +x2+bax=−ca + +

We can then use the method of completing the square. (Maths is Fun has a really good explanation for this technique)

+ +x2+bax+(b2a)2=−ca+(b2a)2 + +

On our LHS, we can clearly recognize that it is the expanded form of (x+d)2 i.e x2+2x·d+d2

+ +⟹(x+b2a)2=−ca+b24a2=−4ac+b24a2 + +

Taking the square root of both sides

+ +x+b2a=−4ac+b22ax=±−4ac+b2−b2a=−b±b2−4ac2a + +

This gives you the world famous quadratic formula:

+ +x=−b±b2−4ac2a +]]> + + https://web.navan.dev/posts/2022-08-05-Why-You-No-Host.html -- cgit v1.2.3