Drawing Slope Fields from Differential Equations - Calculus 2

In this video, I will show you how to draw a slope field, also known as the direction field, which can be drawn from a differential equation y' = F(x,y). A differential equation is an equation with an unknown variables and its derivatives. You also need the piece of information about the initial condition or the initial value, which is basically the starting point of the differential equation and can be used to draw the solution curve.
We'll delve into the fascinating world of direction fields, also known as slope fields, in Calculus 2. Direction fields allow us to visualize the slopes of solutions to differential equations and gain a deeper understanding of how functions behave. Join us as we unravel the concepts behind direction fields, explore their applications, and demonstrate how to construct them with practical examples. Whether you're a student struggling to grasp slope fields or a math enthusiast eager to expand your knowledge, this video will guide you through the intricacies of direction fields and unlock new insights in Calculus 2.
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[@roblox21242]

I wish you would also do Cal 3 topics, your channel will grow immensely since you're very good with explaining shapes, etc...

[@QuocDatPhung]

Hehe thank you! I can try to learn Cal 3 topics on my own :) It's not a required course in my program

[@brianna631]

You’re awesome, keep going man you’re helping so may people 🙏

[@QuocDatPhung]

Thanks Brianna! Don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@mica-ff6tp]

Nice video !
But I have still a problem. When I see your Slope field, I feel that there are other posibilities to draw the graph.
Is it normal or we should have only one graph in the direction field ?

[@QuocDatPhung]

Thanks Mica! You can draw an infinite number of graphs on a direction field. However, if they provide you with a point (e.g our function passes through the origin), then you will have to draw one graph that passes through (0,0). Let me know if that makes sense!

[@xc7525]

omg thank u

[@mhamudasik7713]

Many many tnx

[@QuocDatPhung]

You're welcome, Mhamudasik! Please kindly subscribe and share! Also you can find all of my Calculus II videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html