Introduction to Slope Fields (Differential Equations 9)

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  • Опубліковано 2 лип 2024
  • / professorleonard
    A constructive approach to Slope Fields and how they work. Individual exploration with a Computer Graphing application is highly recommended.

КОМЕНТАРІ • 78

  • @immanuelsuleiman7550
    @immanuelsuleiman7550 4 роки тому +53

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

  • @ChristianRoland7
    @ChristianRoland7 5 років тому +142

    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

    • @davekes856
      @davekes856 5 років тому +15

      $1 from each person who benefits from these amazing lectures would help a lot more.

    • @zakusa9891
      @zakusa9891 5 років тому

      @@davekes856 i feel too lazy to enable and disable adblock repeatedly

    • @-maver1ck
      @-maver1ck 4 роки тому +1

      @@davekes856 I wonder if there is a one time payment instead of $1 or $250 every month

    • @bonbonpony
      @bonbonpony 4 роки тому +4

      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.

    • @sydtabat8948
      @sydtabat8948 3 роки тому +8

      you still poor now?

  • @sk5213
    @sk5213 5 років тому +108

    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 :)

    • @Xopher30
      @Xopher30 4 роки тому +15

      Show him you appreciate by watching the ads and/or donating $1 or more on Patreon.

  • @realking4918
    @realking4918 3 роки тому +22

    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.
    @Rick_Sanchez_Jr. 5 років тому +18

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

  • @georgesadler7830
    @georgesadler7830 Рік тому

    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.

  • @enb19988
    @enb19988 3 роки тому +14

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

  • @TheHisisi
    @TheHisisi 4 роки тому +15

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

  • @Peter_1986
    @Peter_1986 5 років тому +3

    These videos make Calculus infinitely easier.

  • @tahy59
    @tahy59 3 роки тому +1

    exceptional absolutely amazing

  • @jacobalaichi123
    @jacobalaichi123 4 роки тому

    This is amazing

  • @rupendrakushwah
    @rupendrakushwah 3 роки тому +1

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

  • @logio7663
    @logio7663 5 років тому

    Thanks, waiting for some videos about function series .

  • @tanvirtscientist608
    @tanvirtscientist608 4 роки тому

    thank you sir!

  • @pipertripp
    @pipertripp 4 роки тому +3

    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.

  • @esthelaa5028
    @esthelaa5028 3 роки тому

    Wow. Thank you!!!

  • @user-xv9qk3iz7b
    @user-xv9qk3iz7b 4 роки тому

    Perfect !

  • @lixondarvish7334
    @lixondarvish7334 3 роки тому

    A savior!!

  • @taekwondotime
    @taekwondotime 5 років тому +6

    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.)

  • @taekwondotime
    @taekwondotime 5 років тому +50

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

    • @ProfessorLeonard
      @ProfessorLeonard  5 років тому +36

      yes, same thing :)

    • @bonbonpony
      @bonbonpony 4 роки тому

      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" ;) )

  • @NeverendingAbyss
    @NeverendingAbyss 5 років тому

    Please do tanks next, professor! Thank you for your videos.

  • @tobeornottobetobeornottobe974
    @tobeornottobetobeornottobe974 5 років тому +1

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

  • @Michael-jv2gf
    @Michael-jv2gf 2 роки тому

    Thanks!

  • @chriscockrell9495
    @chriscockrell9495 4 роки тому +1

    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.

  • @anasasim3856
    @anasasim3856 3 роки тому

    Professor, I really like your hairstyle !

  • @MikeySTN
    @MikeySTN 5 років тому +3

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

  • @AmateurRadioSouthAfrica
    @AmateurRadioSouthAfrica 5 років тому +7

    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.

  • @taekwondotime
    @taekwondotime 5 років тому +1

    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

  • @jpskiskate2000
    @jpskiskate2000 3 роки тому

    25/39 videos are on my first exam :O

  • @bonbonpony
    @bonbonpony 4 роки тому +3

    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?

    • @wnooristany539
      @wnooristany539 2 роки тому

      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)

  • @ccym9370
    @ccym9370 5 років тому

    Are you gonna having Partial differential equations in the future videos?

  • @foku9000
    @foku9000 5 років тому +2

    DID YOU COME TO O.C.? I SAW SOMEONE THAT LOOKS JUST LIKE YOU AT A COFFEE SHOP NEAR CAL STATE FULLERTON

  • @strongerwithstubsstretch3472
    @strongerwithstubsstretch3472 4 роки тому +1

    Finding an approx. curve with slopes makes me think of the game Battleship

  • @mateocamargo7437
    @mateocamargo7437 Рік тому

    Do you have a book that you reference/use to do the lectures or any practice problems besides the ones presented in the video?

  • @fernandomuro7007
    @fernandomuro7007 2 роки тому +1

    This man is a GOD

  • @mertkocabalalumni8109
    @mertkocabalalumni8109 5 років тому +15

    please do linear algebra

    • @aidangardner6538
      @aidangardner6538 4 роки тому

      Gilbert Strang is your man

    • @georgesadler7830
      @georgesadler7830 Рік тому

      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.

  • @bonbonpony
    @bonbonpony 3 роки тому

    Can this idea be extended to higher-order ODEs?

  • @AkhilKumar-ci6pb
    @AkhilKumar-ci6pb 5 років тому +17

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

    • @taekwondotime
      @taekwondotime 5 років тому +1

      Yes please. I need Laplace transforms for my upcoming exam! :)

    • @Peter_1986
      @Peter_1986 5 років тому +1

      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.

  • @japple314
    @japple314 4 роки тому

    I love you

  • @joseaguilar2561
    @joseaguilar2561 4 роки тому

    Does anybody know what book he is using?

  • @aldrinsantiago7873
    @aldrinsantiago7873 4 роки тому +6

    I'm definitely allowing all ads on this channel. T_T

    • @ProfessorLeonard
      @ProfessorLeonard  4 роки тому +11

      Thanks!

    • @davekes856
      @davekes856 4 роки тому +4

      ​@@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.

  • @alya410
    @alya410 5 років тому +4

    laplace transformation needed

  • @parkermilligan7503
    @parkermilligan7503 4 роки тому

    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.

    • @TechSpeaker-ih1yz
      @TechSpeaker-ih1yz 5 місяців тому

      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.

  • @KyubiCloaks
    @KyubiCloaks 10 місяців тому +1

    What if there is no x

  • @EricATena
    @EricATena 2 місяці тому

    DA MUSCLY GOAT

  • @kvnagendra5354
    @kvnagendra5354 5 років тому

    *25 like sir*

  • @user-dl8ux4up6m
    @user-dl8ux4up6m 5 років тому +4

    Bro, what’s your stack? Your physique is sick

  • @feilongish
    @feilongish Рік тому

    30:00

  • @AkarshBalaji
    @AkarshBalaji 5 років тому +1

    11:48, you're welcome

  • @jwjackflash
    @jwjackflash 5 років тому +2

    First!

  • @honeymural1729
    @honeymural1729 5 років тому

    sir please make videos of full trigonometry base to advance humble request
    Thanks

  • @JoshuaWorleyWindle
    @JoshuaWorleyWindle Рік тому

    Can you pleaes make a Differential Equations II series?

  • @vortexmonster6908
    @vortexmonster6908 3 роки тому +1

    What a hottie professor.

  • @FernandoRodriguez-et7qj
    @FernandoRodriguez-et7qj 3 роки тому

    plot twist. He doesn't actually teach to students live.

  • @user-dl8ux4up6m
    @user-dl8ux4up6m 5 років тому

    Professor Trenbolone

  • @ramlb8
    @ramlb8 5 років тому

    logistics explain sir

  • @coleabrahams9331
    @coleabrahams9331 2 роки тому +1

    Your shirt looks like a slope field ha ha