/ professorleonard A constructive approach to Slope Fields and how they work. Individual exploration with a Computer Graphing application is highly recommended.
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 :)
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
Sitting through ads just to support a channel does more good to Google than to the professor, unfortunately :q There are better ways to support him more directly without Google and their advertisers running off with most of the loot.
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.
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.
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.)
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.
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.
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
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.
Check out the section "Advanced Circuit Analysis" in the book "Fundamentals Of Electric Circuits" by Alexander/Sadiku; that section explains a lot of stuff about Fourier Series, Fourier Transforms and Laplace Transforms.
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?
I think its because some differential equations cannot be integrated based on the techniques we learned in calc 2(which is why we have to use things like taylor seres to approximate the integrations)
How is this different from constructing direction fields for a given differential equation that only has one variable. For example, consider the differential equation y' = y(4 - y), where y' = dy/dt.
Bit late, but if anyone else is wondering, the only difference is that you need to use just one variale to determine the slope. in your example equation, the slope will be the same for any particular y for all x.
Retired Professor Dr. Gilbert Strang on the MIT website is the godfather of Linear Algebra. Jhevon Smith on the CCYN( City College of New York) website is also great.
@@ProfessorLeonard is there a way for students to make a one time donation? Patreon's model of a monthly charge is off putting to some. That being said, $12 a freaking year is absolutely NOTHING.
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 :)
Show him you appreciate by watching the ads and/or donating $1 or more on Patreon.
i came here to learn diff EQ and i left wanting to work out more
damn my dude
looking swol
saaaaame
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
$1 from each person who benefits from these amazing lectures would help a lot more.
@@davekes856 i feel too lazy to enable and disable adblock repeatedly
@@davekes856 I wonder if there is a one time payment instead of $1 or $250 every month
Sitting through ads just to support a channel does more good to Google than to the professor, unfortunately :q There are better ways to support him more directly without Google and their advertisers running off with most of the loot.
you still poor now?
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.
what is a dislike?
Taking diff eq online due to COVID-19 and your videos have helped me so much!
same here!
This helped me understand slope fields for our differential equation unit for Calc 2. Thank you professor Leonard
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.
When this dude kicks someone's ass, it's calculated.
These videos make Calculus infinitely easier.
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.)
exceptional absolutely amazing
Hello Professor Leonard, do you any chance have any studying material for workout routine but for students? Serious question!! Thanks!
Thanks, waiting for some videos about function series .
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.
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.
This is amazing
I take it "slope field" is just another name for "direction field"?
yes, same thing :)
How about a low frequency inversion field? :) (In case you didn't know, it's a name of one of the soundtrack for the movie "π" ;) )
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
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.
DID YOU COME TO O.C.? I SAW SOMEONE THAT LOOKS JUST LIKE YOU AT A COFFEE SHOP NEAR CAL STATE FULLERTON
Are you gonna having Partial differential equations in the future videos?
Thanx sir u r great us I'm from India ❤️❤️❤️❤️❤️
Do you have a book that you reference/use to do the lectures or any practice problems besides the ones presented in the video?
Please do tanks next, professor! Thank you for your videos.
Basically, the idea behind the slop field is the solution of DOE may be presented by many functions.
thank you sir!
Wow. Thank you!!!
Perfect !
A savior!!
Can this idea be extended to higher-order ODEs?
Professor, I really like your hairstyle !
Thanks!
are you gonna cover laplace transformation in this series?
thank you
Yes please. I need Laplace transforms for my upcoming exam! :)
Check out the section "Advanced Circuit Analysis" in the book "Fundamentals Of Electric Circuits" by Alexander/Sadiku;
that section explains a lot of stuff about Fourier Series, Fourier Transforms and Laplace Transforms.
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?
I think its because some differential equations cannot be integrated based on the techniques we learned in calc 2(which is why we have to use things like taylor seres to approximate the integrations)
Does anybody know what book he is using?
How is this different from constructing direction fields for a given differential equation that only has one variable. For example, consider the differential equation y' = y(4 - y), where y' = dy/dt.
Bit late, but if anyone else is wondering, the only difference is that you need to use just one variale to determine the slope. in your example equation, the slope will be the same for any particular y for all x.
What if there is no x
please do linear algebra
Gilbert Strang is your man
Retired Professor Dr. Gilbert Strang on the MIT website is the godfather of Linear Algebra. Jhevon Smith on the CCYN( City College of New York) website is also great.
Finding an approx. curve with slopes makes me think of the game Battleship
25/39 videos are on my first exam :O
I'm definitely allowing all ads on this channel. T_T
Thanks!
@@ProfessorLeonard is there a way for students to make a one time donation? Patreon's model of a monthly charge is off putting to some.
That being said, $12 a freaking year is absolutely NOTHING.
This man is a GOD
I love you
Bro, what’s your stack? Your physique is sick
DA MUSCLY GOAT
First!
laplace transformation needed
*25 like sir*
What a hottie professor.
30:00
plot twist. He doesn't actually teach to students live.
Professor Trenbolone
sir please make videos of full trigonometry base to advance humble request
Thanks
Can you pleaes make a Differential Equations II series?
11:48, you're welcome
logistics explain sir
Your shirt looks like a slope field ha ha