Modelling with Differential Equations Lanchester Square Collapse

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Create interactive math documents with MAPLE LEARN: https://www.maplesoft.com/products/le.... Thank you to MapleSoft for sponsoring today's video. • In this video we use mathematics to model war. We will see a system of differential equations that leads to something called Lanchester Square Model and helps explain the phenomenon of Lanchester Square Collapse, where wo armies that were originally relatively comparable end up having one side collapsing. We use a differential equations technique called eliminating t to derive hyperbolic solutions. This model is contrasted in Lanchester's Linear Model. • The paper using Lanchester Square Model to analyze the battle of gettysburg by Armstrong and Sodergren is here: https://onlinelibrary.wiley.com/doi/f.... I also used the mobile game 2D Battle Simulator for animations. • 0:00 Modelling Battles • 0:49 Lanchester Square Model • 6:48 Battle of Gettysburg • 7:36 Lanchester Linear Model • 9:22 Direction Fields • Check out my MATH MERCH line in collaboration with Beautiful Equations • ►https://beautifulequations.net/pages/... • COURSE PLAYLISTS: • ►DISCRETE MATH: • Discrete Math (Full Course: Sets, Log... • ►LINEAR ALGEBRA: • Linear Algebra (Full Course) • ►CALCULUS I: • Calculus I (Limits, Derivative, Integ... • ► CALCULUS II: • Calculus II (Integration Methods, Ser... • ►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivariable Calculus ... • ►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Calculus (Line In... • ►DIFFERENTIAL EQUATIONS: • Ordinary Differential Equations (ODEs) • ►LAPLACE TRANSFORM: • Laplace Transforms and Solving ODEs • ►GAME THEORY: • Game Theory • OTHER PLAYLISTS: • ► Learning Math Series • • 5 Tips To Make Math Practice Problems... • ►Cool Math Series: • • Cool Math Series • BECOME A MEMBER: • ►Join: / @drtrefor • MATH BOOKS I LOVE (affilliate link): • ► https://www.amazon.com/shop/treforbazett • SOCIALS: • ►Twitter (math based): / treforbazett • ►Instagram (photography based): / treforphotography

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