Introduction to Slope Fields (Differential Equations 9)

A constructive approach to Slope Fields and how they work. Individual exploration with a Computer Graphing application is highly recommended.

[sk]

Hello Professor, I'm a freshman in calc 3 and I've done quite poorly on my first exam... however upon reviewing the first 15 minutes of your Calc 3 videos it has helped a lot. I'm sure all your viewers including myself, would like you to know that we really appreciate what you're doing and this has really eased up my self-doubt, anxiety and feelings of depression from that score. Again, thank you :)

[immanuelsuleiman]

i came here to learn diff EQ and i left wanting to work out more
damn my dude
looking swol

[ChristianRoland]

I watched an entire ad just for you and when I make good money I will donate fat amounts of money to you to do whatever the hell you want.
For now, I'll remain poor xD

[realking]

How these videos have any dislikes is beyond me, this guy is helping thousands of ppl around the world actually LEARN some of the most difficult subjects there are to TEACH.

[Rick_Sanchez_Jr.]

This helped me understand slope fields for our differential equation unit for Calc 2. Thank you professor Leonard

[enb]

Taking diff eq online due to COVID-19 and your videos have helped me so much!

[georgesadler]

Professor Leonard, thank you for an awesome introduction to Slope Fields in Ordinary Differential Equations. From watching this great video/lecture and doing problems from multiple Differential Equations books, I finally understand Slope Fields and their impact on Differential Equations. Mathematica is an exceptional software that can be used to draw Slope Fields.

[Peter_]

These videos make Calculus infinitely easier.

[TheHisisi]

When this dude kicks someone's ass, it's calculated.

[taekwondotime]

I take it "slope field" is just another name for "direction field"?

[rupendrakushwah]

Thanx sir u r great us I'm from India ❤️❤️❤️❤️❤️

[pipertripp]

sagemath is free and very useful for exploring differential equations (and loads of other things). It has built-in slope field plotting so you can generate slope fields quite easily.

[taekwondotime]

Would it be advantageous to have the X and Y axis labelled the same on both the table and the graph?
(That way you can draw the slope lines along the same diagonal as the values in the table.)

[MikeySTN]

Hello Professor Leonard, do you any chance have any studying material for workout routine but for students? Serious question!! Thanks!

[chriscockrell]

Interesting. Slope fields were not covered when I took diff eq at NIC. I'll have to pull out my textbook and see if it is there and we skipped working problems. I was looking at control theory for stability in the electric power grid and came across bifurcation theory. This video seemed a good starting point.

[bonbonpony]

01:30 How can we tell whether a differential equation cannot be solved because we don't know the right technique yet, or it cannot be solved because there is no solution possible whatsoever? Are there any differential equations with no possible solutions? How can one prove then that that's the case for a particular differential equation? How about equations that do have solutions, but those solutions are some crazy functions that are not made of any functions that we know of, and we're just lacking that one special crazy function that solves it? Are there any methods to find the "domain of functions" that might possibly be the solutions to a differential equation?

[tobeornottobetobeornottobe]

Basically, the idea behind the slop field is the solution of DOE may be presented by many functions.

[AmateurRadioSouthAfrica]

Hello sir, If you have time at some point, would you mind doing Convolution? I struggle with it but its too late for me, I just know you would help out a lot other people in engineering.

[AkhilKumar-cipb]

are you gonna cover laplace transformation in this series?
thank you

[taekwondotime]

What if it's NOT a 1st order differential equation?
Do we have to be able to rework it into a 1st order DE to be able to use slope fields?

Ex: y'' = x^2 + 2y^2