Slope Fields | Calculus

This calculus video tutorial provides a basic introduction into slope fields. It explains how to draw a slope field using an x-y data table given the differential equation. It also explains how to sketch the solution curves or the general solution of the differential equation on the slope field and how to verify the solution of the differential equation by integrating using separation of variables. Finally, this video explains how to match the slope field with the appropriate differential equation by finding the values of x, y, and the slope or y' at a certain point. This video contains plenty of examples and practice problems.
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Integration Formulas:
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Integration By Tables:
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Homogeneous Differential Equations:
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1st Order Linear Differential Equations:
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Bernoulli's Equation for Differential Equations:
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Slope Fields:
• Slope Fields | Calculus
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Converging & Diverging Sequences:
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Monotonic & Bounded Sequences:
• Monotonic Sequences an...
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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another amazing video/lecture on the Introduction to Slope Fields in Differential Equations. From watching this video and analyzing slope fields in Differential Equations textbooks, I fully understand Slope Fields and its impact on the solution to Differential Equations. This is an error free video/lecture on CZcams TV with the Organic Chemistry Tutor.

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All I had to do was watch till 3:48 and I knew how to solve the questions I just wasted 2 hours trying to learn from my prof's notes. Thank you!

[@americanexpress888]

past a few years, I wanted to review this and today finally did it and understood it correctly. nice work and thank you.

[@worldblazin4209]

Finished ap calculus bc in 2022 and understood that the equations compared to the slope because of AP daily review. But I never knew you could use Algebraic tables to perform slope fields I only thought of guessing and checking by fully integrating diff. Equations. Now I'm a happy camper! 😅😅🎉😂😂

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Cal 2
First Exam - 76
Watched OCT
Second Exam - 88
All I can say is Thank You.

[@farhanchowdhury6238]

Any link for when questions like this-
(In the graph, −3 < x < 3 and −3 < y < 3). This is the graph of the direction field of a
certain equation y
0 = f(x, y).
(a) Draw an approximate solution y with y(0) = 1.
(b) Draw an approximate solution y with y(1) = 0.
(c) Draw an approximate solution y with y(0) = −1.
(d) Is it possible that f(x, y) = y
^2?
(e) Is it possible that f(x, y) = x
^2 + y^2?

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ما شاءالله هذا عنده شرح كل شيء
Thank you

[@bonbonpony]

Can this be extended to higher-order equations? :q Because it seems to be working only with 1st-order ones :q

[@Lisa-wh8bu]

the slope feild is the shape of its solution! thats what i was missing thanks

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[@kc-99p]

thank you!

[@johnding5124]

how would you draw a slope field of trig functions? for example x^5 - tan x

[@anujpatel2121]

Everything was on point but the only thing I don't understand at @14:28 how the answer is that I am not getting the same

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excellent

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[@allistermi6014]

how to choose point to make the graph

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[@allistermi6014]

how to find the differencial equation according to the direction field?

[@JD-nu4pc]

Good luck on the exam tomorrow 😉

[@bolb6000commenterlol]

In the first example, shouldn't y be 1? (derivative of x with respect to y = 1 or 0)?

[@chrisgodsey8481]

Y would be x^2/2. You integrate x to solve for y. Y’ is a derivative to undo it you have to integrate

[@NehaKawatraOshiwara]

which video will have the solution of the differential equation y' = x-y . I am not able to find it.

[@sakshi-cm7rb]

Thankyou

[@windthorpe9628]

Why did you put a prime to x at 4:13? Thanks a lot!

[@Nightcomer]

It's not prime, its x^1

[@Sarah-ve3cd]

Which grade gets introduced to slope fields?

[@bdawes123]

Probably Calc BC which is a 12th-grade course. Or in my case, Ordinary Differential Equations which would be a college-level course around year 2 or 3

[@edward3709]

12 here AUS

[@sanjeetkaur4114]

shouldnt the solution to the differential equation have another term e^-x? solution : y=x-1+ce^(-x)....[as per your first order diff eq video]

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Wow this is so smart. Holy cowshit. Oke thanks i can really use this at my exam

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This comment is so underdressed for this video

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[@xKroos6]

You only live once 👏

[@ultralaggerREV1]

What if you chug in a C? And make dy/dx = f(x,y) and then f(x,y) = C

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The GOAT

[@John-lf3xf]

SUPER LOGIC

[@Shadhin52]

I have problem on deciding the angle of the slope by looking from y'. e.g., y'=4 who can i find out the angle of the slop without using trigonmetry?

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or maybe your input is too low

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[@carllouiscotacte2753]

How to determine the direction of the slop?

[@ES-qe1nh]

Slope does not have "direction". It is one dimensional

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[@ScienceDrummer]

First

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No that’s someone else

[@LaureanoLuna]

Disliked due to unbearable ads. Couldn't make it past them.

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focus on the fact that you're being taught something by a guy that spends his time to help us learn