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The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines

Dr. Trefor Bazett
482K subscribers
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89K views 4 years ago
MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)   Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs What do differential equations look like? We've seen before the analytic side of differential equations, solutions, initial conditions, and so forth. That is, the side involving functions that we differentiate or integrate. In this video we see the geometric side. The geometric version of an ODE is called a slope field or a direction field, and it tells you the slope at any given point. We can sketch these using the method of isoclines which are curves of constant slope. Finally an integral curve is a curve that matches the slope of the slope field and goes through the initial condition. The geogebra to plot slope fields: https://www.geogebra.org/m/z9c3ndaf 0:00 Intro 1:44 Slope Fields and Isoclines 5:00 Integral Curves 7:35 Analytic vs Geometric Story OTHER COURSE PLAYLISTS: ►DISCRETE …...more
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The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines
3.3KLikes
89,990Views
2021Feb 11
MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)   Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs What do differential equations look like? We've seen before the analytic side of differential equations, solutions, initial conditions, and so forth. That is, the side involving functions that we differentiate or integrate. In this video we see the geometric side. The geometric version of an ODE is called a slope field or a direction field, and it tells you the slope at any given point. We can sketch these using the method of isoclines which are curves of constant slope. Finally an integral curve is a curve that matches the slope of the slope field and goes through the initial condition. The geogebra to plot slope fields: https://www.geogebra.org/m/z9c3ndaf 0:00 Intro 1:44 Slope Fields and Isoclines 5:00 Integral Curves 7:35 Analytic vs Geometric Story OTHER 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...   ►LAPLACE TRANSFORM:    • How to solve ODEs with infinite serie...   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 & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography  

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Dr. Trefor Bazett

482K subscribers