Using Lagrange’s Multiplier Method to Solve Mathematical Contest Problem

Using Lagrange’s Multiplier Method to Solve Mathematical Contest Problem

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Author(s)

Author(s): Maher Ali Rusho

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DOI: 10.18483/ijSci.2622 26 46 8-9 Volume 11 - Oct 2022

Abstract

“Most people study mathematics to satisfy some requirements .Some Study Math to learn the tricks of nature so they may find out how to make things bigger or smaller or faster or more sensitive . But a few ,a very few ,study math because they wonder -not how things work ,but why they work .They wonder what is at the bottom of things -the very bottom ,if there is a bottom . This paper will be very useful to them .”-M.A.Rusho. Remember when you first participate any math contest or olympiad maybe national or International you see some terrible function and the question state that you have to find this function maximum or minimum value. You become frustrated thinking I have to take the derivative first then equalising it to 0 , then find the optimal value of X blah blah blah……. . now it’s time to reconstruct your mind for solving this type of Mathematical problem in a suitably way . First we have to think that is the difference between School textbook math problem And Olympiad Math Problem . The core difference is problem solving . But you may think that in school mathematics we all solve problem . But this problem solving is different like you can solve it by GUIDE or may a teacher can help or this problem may directly solved by any standard formula like( a+b)^2 . But in Olympiad problem You are totally in a new place , totally difference problem you didn’t see it . But you have too slove it now Many people find this difficulty .BUT IT IS not difficult if you solve it by making some useful strategies . This paper although written for High School Student’s but those who will read it thoroughly they will understand it is for useful for undergraduate or beg gainer of a graduate student from engineering background . Though Calculus , linear algebra , partial differential equation is not included in Math Olympiad Syllabus . But if you are really a Math Enthusiast I believe you already learn it !!! If you didn’t don’t be hesitate . Learn It from any book or course . Then came here to read this thesis paper . Best Wishes to all !!! Happy Problem Solving !!

Keywords

Finding Maximum and Minimum of a Function, Real Analysis, Single Variable Problem, Partial Derivative, Topology, Complex Analysis, Lagrangian Transform

References

  1. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Thermodynamics_and_Chemical_Equilibrium_(Ellgen)/21%3A_The_Boltzmann_Distribution_Function/21.02%3A_Lagrange%27s_Method_of_Undetermined_Multipliers
  2. https://machinelearningmastery.com/a-gentle-introduction-to-method-of-lagrange-multipliers/
  3. https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/constrained-optimization/a/lagrange-multipliers-single-constraint
  4. https://www.thescientificteen.org/post/multivariable-calculus-lagrange-multipliers

Cite this Article:

International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

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Issue October 2022

Volume 11, October 2022


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