Newsletter #4 - Lagrange Multipliers

Learning resources for Lagrange Multipliers, an important tool in calculus and optimization.

Welcome to the fourth issue of the Aleph 0 newsletter! This issue, we’re covering Lagrange Multipliers, an important tool in calculus and optimization.

Learning Resources

This week’s topic is Lagrange multipliers. The core question Lagrange multipliers answer is: how do you find the maximum and minimum values of a function, subject to a constraint?

Here are some resources to learn the subject:

1. Check out this video by Khan Academy:

   If the voice in this video sounds familiar, it’s because the video was made by Grant Sanderson (of 3blue1brown fame!) during his time at Khan Academy. This is easily one of the clearest explanations of Lagrange multipliers out there!

2. Here are some online notes by Paul Lamar: https://tutorial.math.lamar.edu/classes/calciii/lagrangemultipliers.aspx. These notes are quite comprehensive, so it’s probably best to watch the video before diving into the notes.

Challenge Problem

A sequence consists of 2022 terms. Each term after the first term is 1 greater than the previous term. The sum of the 2022 terms is 31 341. Determine the sum of the terms in the odd-numbered positions. That is, determine the sum of every second term starting with the first term and ending with the second last term.

See here for the solution to last week’s problem. (Shoutout to Andrew Glatten from Saint-Petersburg, Russia whose solution is being featured this week!)

Feedback

If you have a solution to the above challenge problem, submit it here for a chance to be featured in the next issue of this newsletter.

If you have any learning resources that you think would be valuable for readers, or if you have any general feedback, let me know here and I’d be happy to incorporate it.

Thanks for reading and happy learning! Until next time,

Adithya