Kinetics: Initial Rates and Integrated Rate Laws

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  • Опубліковано 21 гру 2024

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  • @ProfessorDaveExplains
    @ProfessorDaveExplains  6 років тому +714

    Hey everyone, UA-cam is deleting annotations, and there is an error at 5:41 that I had fixed with an annotation so unfortunately I must simply list the correction here! The values at the bottom right should read: 0.04 = k(0.01)(0.250) and k = 16/(M^2 * s), when making the video I forgot to square [NO] so please make that correction in your minds, sorry about that!

    • @tjvanderyacht9806
      @tjvanderyacht9806 6 років тому +11

      Professor Dave Explains thank you!

    • @towkirshuvo97
      @towkirshuvo97 6 років тому +3

      Sir do u mean 'top right'?

    • @Reforitor
      @Reforitor 6 років тому +5

      Towkir, play the video at the given time, not pause it. You'll see it on bottom right

    • @towkirshuvo97
      @towkirshuvo97 6 років тому +4

      @@Reforitor Thank you.

    • @Reforitor
      @Reforitor 6 років тому +5

      You're welcome bro

  • @_thismustbesam
    @_thismustbesam 6 років тому +1260

    how did i understand this in 10 minutes but couldn’t in two weeks, honestly professor dave u out here savin lives.

  • @thatguy5358
    @thatguy5358 4 роки тому +534

    5:31
    "the reaction order HAPPENS to match the stoichiometric ... but this won't always be the case"
    right there, professor dave has done what no fucking textbook in the fucking world has ever done. it has pointed out something that a student might mistake, by thinking the way a student might.
    hats off. well done. please write a text book or ten for students who wouldn't know any better and make that mistake. i'm a 30-something year old engineer, and i'm dead serious.
    you are the man.

    • @IbrahimKhan-lx3bm
      @IbrahimKhan-lx3bm 3 роки тому +5

      And i realllly like your reply u are dammm so correct

    • @thatguy5358
      @thatguy5358 3 роки тому +3

      @@IbrahimKhan-lx3bm thank you. i wish i weren't.

    • @WOG18
      @WOG18 3 роки тому +5

      This is exactly why I was getting my answers wrong because my teacher NOR the textbook explained that the reaction order was not in relation to the stoichiometric coefficients!!

    • @mohamadhanan5706
      @mohamadhanan5706 3 роки тому +2

      i have a question, so the overall order is the the third order?

    • @SVN391
      @SVN391 3 роки тому +1

      @@mohamadhanan5706 same doubt bro

  • @joanavillalobos2792
    @joanavillalobos2792 5 років тому +751

    I have my chemistry exam in 30 minutes and you just explained literally everything I need to know in ten minutes. Can you be my chem professor instead? 😭🙏🏽

  • @markkeith9055
    @markkeith9055 7 років тому +196

    I like Professor Dave. He tells it like it is. No messing around, pay attention type instruction in a clear and precise way. Very nice.

  • @cheriesshum
    @cheriesshum 3 роки тому +45

    2:30
    When the concentration is doubled and the rate then also doubles, the reaction is first order with respect to that reactant. When the concentration is doubled and the rate quadruples as a result, the reaction is second order with respect to that reactant. If changes in the concentration doesn't affect the rate, the reaction is zero order with respect to that reactant.

  • @raymondhee8239
    @raymondhee8239 2 роки тому +30

    I am a Chemistry lecturer and I find your videos very clear and concise. Well done!

  • @cameroncrowley9432
    @cameroncrowley9432 2 роки тому +8

    This man is a legend, taught me this in 4 minutes what my lecturer couldn’t in 3 weeks

  • @sanjivprasad6846
    @sanjivprasad6846 Рік тому +21

    You know you are at the right place when Jesus himself teaches you chemistry

  • @angelarose4799
    @angelarose4799 6 років тому +41

    Explained it better in ten minutes than my uni lecturers did in a week - thank you XD

  • @chocolatecrud
    @chocolatecrud 7 років тому +64

    Can always rely on this great channel for that extra bit of explanation, much appreciated

  • @mathyouforgot
    @mathyouforgot 6 років тому +12

    I have a pre-lab assignment due and the instructions were hard to understand. you saved my butt by being smart and teaching the way it should be taught. Thank you !

  • @panosr2135
    @panosr2135 6 місяців тому +2

    No joke this was a blessing. I understood more in 9 minutes than in a whole physical chemestry lecture. Thanks professor Dave

  • @taariqh.8608
    @taariqh.8608 8 років тому +185

    Very well done video you explained it good. I suddenly understand everything now which makes me again question why im spending thousands on tuition money...

    • @brian_mcnulty
      @brian_mcnulty 7 років тому +14

      You won't get that chem engineering job without that degree.

    • @paulnicholas1278
      @paulnicholas1278 7 років тому +44

      because you have to have proof that you've been educated lol. Go to class for the rep, go to UA-cam to actually learn.

    • @andrewthehope
      @andrewthehope 6 років тому +8

      paul nicholas This is the most true statement about college I have ever read!!

    • @cyen923
      @cyen923 6 років тому +15

      Elaphe Gutatta ehh not always true. Have you guys ever heard of repetition and familiarity? I know you have. Because I think learning really comes down to that. If we watched this youtube video before lecture, im sure the lecture would have made more sense versus when you watched a youtube video about that same topic. Now this does not mean there aren’t bad professors out there because there are...but I think one reason why you get a topic more after this video is because its PROBABLY your second time hearing about it. I think all we need is to learn a topic from DIFFERENT resources to actually understand or be ‘’more familiar” with anything... Thats what books, teaching assistants, tutors, youtube videos, khan academy!, homework assignments, worksheets, online simulations, etc., are for !😄

    • @fatelis
      @fatelis 3 роки тому

      @@brian_mcnulty you can just self employ dude, I did and now im making water treatment systems from scratch. materials and everything. no employment needed .... i I am certified by my local government. no degree needed. self taught via books, online websites, youtube. saved thousands on tuition fees. but only reason i'd go to university is if i want to be a doctor. the rest, no degree needed when self employing.

  • @joeysantana784
    @joeysantana784 5 років тому +187

    Crash course: Hey so I was walking my dog on alone with my family on Christmas in the summer, and lol chemistry rate laws XD. Dave: I’m Dave here’s chemistry

  • @millicentmagolego8101
    @millicentmagolego8101 6 років тому +5

    I'm writing my Chemistry semester test today and i had thought i'd have to sacrifice this chapter but thanks to Professor Dave i have a feeling that i'm going to nail it.

  • @elizabethlear7299
    @elizabethlear7299 4 роки тому +11

    I literally can't thank you enough, you make chem easy to understand

  • @Kamilaxx7
    @Kamilaxx7 3 роки тому +6

    I struggled with this for 2 years. And after those 9 minutes i understand it completely. I can't believe this..

  • @nihilo4796
    @nihilo4796 3 роки тому +2

    Turned a 3 hour lecture and at least double that of useless practice into 10 min of cohesive tutoring. Thanks a million

  • @Josh-zk7pf
    @Josh-zk7pf 6 років тому +18

    Man I love the intro i just have to hear it one more time before I start learning

  • @oceanbackwards1903
    @oceanbackwards1903 Рік тому +1

    you are literally one of the few teachers out there who can teach so much with so little
    love your stuff, ur saving my grades rn

  • @picoto1775
    @picoto1775 3 роки тому +7

    You have a small mistake in 5:48, the NO should be raised to 2 and the rate constant = 16

  • @swordmas7544
    @swordmas7544 8 років тому +73

    CLUTCH

  • @Roadways50
    @Roadways50 5 років тому +4

    He makes me understand the concept in just 9.10 minutes. What a great teacher. Hats off to you professor dave. 😃😃

  • @alephd93
    @alephd93 6 років тому +14

    A whole chapter explained in less than 10 minutes , thank you Professor

  • @Milkjust
    @Milkjust 6 місяців тому

    In the realm of academia, where complexity often obscures understanding, the illumination of knowledge is a beacon of hope. It is with profound gratitude that I extend my appreciation to the creator of the invaluable tutorial video elucidating the intricacies of rate laws. This heartfelt ode seeks to articulate the depth of my appreciation for the educational oasis they have crafted amidst the arid landscape of academic challenges.
    The journey of learning is often fraught with obstacles, and the domain of chemical kinetics is no exception. With its labyrinthine equations and abstract concepts, mastering rate laws can be akin to navigating a treacherous sea. Yet, thanks to the altruistic efforts of educators like the creator of this tutorial video, this voyage becomes less daunting, and the shores of comprehension draw nearer.
    The video's inception marks a pivotal moment in the quest for understanding. Its existence signifies more than mere pixels on a screen; it embodies the convergence of knowledge and generosity, serving as a testament to the transformative power of education. Through meticulous explanation and illustrative examples, the creator has bestowed upon us a gift-a beacon of clarity illuminating the path to mastery.
    Every frame of the tutorial video is imbued with intentionality, each word a stepping stone towards enlightenment. It is evident that the creator's dedication transcends the bounds of obligation; it is a labor of love, fueled by a passion for fostering intellectual growth and empowering learners to conquer the formidable terrain of chemical kinetics.
    Beyond the confines of the digital realm, the impact of this tutorial video reverberates through classrooms and lecture halls, enriching the educational landscape with its profundity. As students, we stand on the shoulders of giants, leveraging the wisdom imparted by educators to scale the peaks of academic achievement. The creator's contribution, therefore, extends far beyond the confines of their video-it is a catalyst for intellectual evolution and a cornerstone of scholarly excellence.
    In a world besieged by uncertainty, the constancy of knowledge serves as an anchor, grounding us in the pursuit of truth. The tutorial video stands as a bastion of stability amidst the tumultuous seas of academia, offering solace to weary learners and guidance to those adrift in a sea of confusion.
    To the creator of this tutorial video, I extend my sincerest gratitude. Your dedication to the dissemination of knowledge is a testament to the transformative power of education. Through your selfless efforts, you have ignited a flame of curiosity in the hearts of learners, illuminating the path to understanding and inspiring generations to come.
    As the curtain falls on this humble ode, let us reflect on the profound impact of educational altruism. In the creator's act of generosity, we find hope for a brighter future-a future where the pursuit of knowledge knows no bounds, and the flames of curiosity burn eternal. To them, we owe a debt of gratitude-a debt that can only be repaid through the pursuit of knowledge and the dissemination of wisdom.
    In conclusion, let us cherish the creators of educational content, for they are the unsung heroes of academia-the architects of enlightenment and the stewards of knowledge. In their tireless pursuit of educational excellence, they inspire us to reach greater heights and strive for a future where ignorance is but a distant memory.

  • @kirayoshikage1491
    @kirayoshikage1491 Рік тому +2

    Thank you Dave. I like many first found your channel because of your debates, love those videos. But whenever I get confused about a subject during dead week and get anxious I’ll fail, you’re there to rescue me. Thank you for the great videos

  • @HatlessMuffin
    @HatlessMuffin 2 роки тому

    I have spent weeks on these topics alike, haven't got them through, then the professor with his majestic magic of words and examples engraves it in my long term memory

  • @R.Bharathkumar2003
    @R.Bharathkumar2003 4 роки тому +2

    When ever I see your channel I relatively find some easy ways you are like my brother giving me an easy ways to get the information thank you bro I will remember you in my entire life

  • @nighthunterangel4319
    @nighthunterangel4319 2 роки тому

    You're an actual godsend, have an exam later and after weeks of scratching my head you made it make sense in 10min. Can't thank you enough!

  • @hielenaug
    @hielenaug 7 років тому +4

    AWESOME! ..come teach at my school! you taught me more in 9 minutes than my professor did in an hour.

  • @AJAYKUMAR-if6jv
    @AJAYKUMAR-if6jv 4 роки тому +8

    Hello sir I have exam tomorrow before I didn't listen this lesson properly now I understood very well thank you and thanks for saying

  • @kataraarts3027
    @kataraarts3027 2 роки тому +2

    I'm glad i didn't skip the comprehension questions, it really helped!

  • @aaliyahvarona5409
    @aaliyahvarona5409 2 роки тому +3

    Out here reviewing for my AP chemistry exam in May. Thank you! Very helpful!

  • @GrimLock666
    @GrimLock666 7 років тому +5

    Dude I can't thank you enough! freaking out about an exam tomorrow and this video really really helped!

  • @harshadasonawane7445
    @harshadasonawane7445 7 років тому +3

    Thank you Dave sir my child is really very happy as she got her topics cleared because of you

  • @ShanukaUditha
    @ShanukaUditha 5 років тому

    This is amazing. I didn't have any idea about Initial Rates and Integrated Rate Laws before watching the video. You are a miraculous savior. Thank you sir.

  • @nashleef
    @nashleef 6 років тому +2

    You have singlehandedly saved my chem 110 grade!

  • @TheQueenofNeckbeards
    @TheQueenofNeckbeards 2 роки тому +1

    literally my savior right now. thank you chemistry jesus

  • @anisa-mj6qs
    @anisa-mj6qs 6 місяців тому

    I have tired to figure this out for a whole year, and now the day before my exam, I GET IT! Thank you so much

  • @taaabby
    @taaabby 6 років тому +2

    Holy crap I’ve watched 4 of these videos and tried to understand but you put in such easy terms, thank you!

  • @juliavreugdenhil8050
    @juliavreugdenhil8050 6 років тому +2

    I really want to thank you for your wonderfull video's! Everytime when I'm losing my concentration on a subject I turn to your explanations which make the subject so much more fun to learn, thankyou!

  • @Micki007vids
    @Micki007vids 8 років тому +8

    Writing my IB Higher level chem exam in 2 weeks time, thank you so much for all the content!

    • @blebonick7088
      @blebonick7088 6 років тому

      I'm doing standard level, not all of his stuff is applicable but most is!

  • @francisgregoryku1689
    @francisgregoryku1689 6 років тому +8

    CLEAR CONCISE AND FAST. WASTED MY TIME WATCHING A 30 MIN VIDEO WHEN THIS VIDEO EXPLAINED EVERYTHING WITH EASE

  • @thegirlnextdork
    @thegirlnextdork 3 місяці тому

    Professor Dave, your table of the orders was so helpful. Thank you. It was glossed over quickly in my class notes, so I needed to see it laid out this way!

  • @arturoguerrero740
    @arturoguerrero740 7 років тому +109

    prof dave tight af

  • @practicaltheory7
    @practicaltheory7 Рік тому +1

    Hey professor Dave!
    I honestly love your channel, the writing, and editing style in [video] was a huge influence for me when I first got started!

  • @ladyinred396
    @ladyinred396 7 років тому +5

    Prof. Dave, you are AMAZING! So happy I found your tutorials online & it is soo helpful!!! Thank you you're always ready to help (xoxo)

  • @mrpickles1
    @mrpickles1 2 роки тому

    Hell, i dont even wait for the lecture anymore, let alone night before the exam. If i know a topic is coming up i go to Dave first to give me low down! I can pause Dave to take notes. I can't pause my professor.

  • @vijayasrip7724
    @vijayasrip7724 6 місяців тому +1

    2.20 was really what i wanted🎉🎉🎉🎉Thank u so much Dave ❤❤❤

  • @brian_mcnulty
    @brian_mcnulty 7 років тому +4

    This stuff is super helpful for test material review. Thank you!

  • @lia-hf8jq
    @lia-hf8jq 3 роки тому +15

    Guys, Jesus Christ came all the way down to teach us chemistry

  • @simranmalhotra3865
    @simranmalhotra3865 4 роки тому +3

    You are simply a phenomenal teacher Dave, thanks a million !

  • @2030games
    @2030games 7 років тому +2

    Wonderful video, thanks a lot! I wasn't feeling well in class when my teacher went over this and whew it was a lot but you made it very clear in a short amount of time :)

  • @Lizrinc7110
    @Lizrinc7110 2 роки тому +2

    For 5:42 , how come we dont square the concentration 0.100? Since NO reaction is 2nd order? Why isn't it 0.04=k(0.100)^2(0.250)

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  2 роки тому

      Yeah that's my bad, I pinned a comment citing this error hoping people would see it. Sorry about that!

    • @Lizrinc7110
      @Lizrinc7110 2 роки тому

      @@ProfessorDaveExplains Thank you so much for the explanation and quick response. You teach very well!

  • @howitfeelslike5381
    @howitfeelslike5381 5 років тому +2

    Oh my god sir!! ❤ I don't have words to thank you ! You just saved my life

  • @rawan4297
    @rawan4297 2 роки тому

    10 minutes and I am done with kinetics, it took me ages before. thank you

  • @akbarrahmatullah6701
    @akbarrahmatullah6701 6 років тому +1

    Very clear quite precise presentations on various topics. The videogame presentations are well timed which Keeps concentration consistent.

  • @akilakavisinghe7189
    @akilakavisinghe7189 8 років тому +9

    Thank You Professor Dave!

  • @kenneth5538
    @kenneth5538 4 роки тому

    its been 5 years and yet he saves my life

  • @westt3182
    @westt3182 9 місяців тому

    I've got my exam in a couple of minutes and this just helped me grasp the topic better..

  • @stevealapatt9499
    @stevealapatt9499 7 років тому +1

    Someone give this guy a promotion!! Thank professor (Dr., chemistry savior) Dave

  • @Badgal_seni
    @Badgal_seni Місяць тому

    8 years later, this information still valid.

  • @NeilHummer
    @NeilHummer Рік тому +1

    My class got the practice question right, Dave! Thanks Dave!

  • @leticiaavila5430
    @leticiaavila5430 7 років тому +3

    thanks Professor Dave for making everything so Clear!!

  • @thatrecord5313
    @thatrecord5313 3 роки тому +5

    *Professor Dave notices an influx of viewership at the end of the 2021 school year*
    Professor Dave: The AP exams are upon us!

  • @RadiantGamma
    @RadiantGamma 3 роки тому

    Thank you so much for helping me survive AP Chem with a teacher who doesn't teach :)

  • @andthen6066
    @andthen6066 4 роки тому +1

    Thank you sooo much. you are the only reason why I can pass chemistry.

  • @boddmonchu
    @boddmonchu 8 років тому +1

    5:50 is what I was looking for. Trying to wrap head around the relationships of all the variables. Thanks

  • @tomoguitaro
    @tomoguitaro 8 років тому +4

    Excellent video with precise wording that was very clear, thank you!

  • @jagnoork6013
    @jagnoork6013 9 місяців тому

    Thanks for summarizing an 80 min lecture in 9 mins!

  • @kellypaton2626
    @kellypaton2626 5 років тому +2

    I have been struggling with this and you have I really helped thank you! I love your videos, they're always clear and helpful

  • @MechanicalEngineer-c2u
    @MechanicalEngineer-c2u 2 місяці тому

    Professor Dave is the best guy in existence

  • @raplopez4258
    @raplopez4258 4 роки тому

    3:06
    I understand how individual reactants have an individual rate order. My question is how they "combine"
    So that means for:
    A^1 + B^1 = C
    The reaction is second order. That means as concentration increases for both, it proceeds at a quadruple rate?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  4 роки тому

      yep if a reaction is first in order in two different reactants then doubling both of their concentrations will quadruple the rate

    • @raplopez4258
      @raplopez4258 4 роки тому

      Professor Dave Explains ah. I appreciate your kindness in your reply. If I may follow up with another question, and you would answer it, I would be doubly grateful. I'm currently learning without a formal teacher.
      Background info from textbook:
      although we cannot deduce the rate law for an overall chemical reaction from the balanced chemical equation, we can deduce the rate law for an "elementary step" from its equation.
      E.g. for an elementary step:
      A + A -----> products,
      the rate law is necessarily k[A]^2
      Question:
      I assume then, that the only reason why you cannot deduce the exponent without experimentation (as you say at 3:25), is because the reaction may have "elementary steps".
      By extension, if the reaction were not to have any elementary steps (effectively becoming an elementary step), it's rate exponent can be determined solely by the equation.
      Is this reasoning valid?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  4 роки тому

      Yep! I’m pretty sure I have another tutorial right after this one that talks about mechanisms so check that one to reinforce the idea.

  • @alexfiennes5539
    @alexfiennes5539 2 роки тому

    oh god you have NO idea how MUCH i needed this. Thanks SO MUCH.

  • @Malasruroon
    @Malasruroon 3 роки тому

    i cannot beliece how easy you have made this

  • @rayenaouadi3190
    @rayenaouadi3190 Рік тому

    I didnt have enough time to study yesterday and my teacher didnt get through all of the units so here i am studying the morning of my ap exam 💪

  • @KristenGreen-il4sx
    @KristenGreen-il4sx Рік тому

    I can always rely on your videos to prepare me for an exam. thank you so much!

  • @CharlesMathison
    @CharlesMathison 2 роки тому +1

    Totally got it. I wish my textbook was written by you! Thanks Professor

  • @aleenasikandar5585
    @aleenasikandar5585 4 роки тому +1

    It is the second video I watched of u and it is worth watching I spent a whole hour finding a good lec..but ur ten minutes sums up everything.. May Allah help uh ❤️

  • @291ayl
    @291ayl 4 роки тому

    THANK YOU!!! I never took calculus (I did useless trig instead, regret that decision lol) so I have been scouring the internet for rate law without having had two semesters of calculus! AMAZING EXPLANATION!

  • @Kerwyn204
    @Kerwyn204 8 років тому +1

    best videos on youtube thanks a lot! love the comprehension ending. it really makes me understand

  • @Cat-xm4xw
    @Cat-xm4xw 4 роки тому +3

    I've always hated kinetics cos I didn't understand them but you've actually somehow made me enjoy them and reminded me why I love chemistry! Honestly, this is by far the most helpful video I've watched on this. Its enough for someone without much knowledge but not boring when explaining the basics! :) Thank you I'm gonna pass my exam cos of you!

  • @tealwalters990
    @tealwalters990 6 років тому +3

    So helpful man, thanks professor Dave

  • @isabellaashby1887
    @isabellaashby1887 Рік тому

    professor dave making more sense than a lot of science teachers

  • @jettj7585
    @jettj7585 8 місяців тому

    Took me a shit ton of practice problems before i got it, and understanding how to do the different problems actually helped me understand. Units are still tricky though

  • @canadianhaitian
    @canadianhaitian 8 років тому +30

    That was tricky because I thought clo2 was 2nd as well since rate quadruple

    • @thelostsaint1176
      @thelostsaint1176 6 років тому +2

      canadianhaitian how come it is first order?

    • @thelostsaint1176
      @thelostsaint1176 6 років тому +1

      Help me please

    • @maxineo1976
      @maxineo1976 5 років тому +3

      That’s exactly what I was confused on, can anybody explain why it’s not 2nd order please :(

    • @robertmiranda2709
      @robertmiranda2709 5 років тому +5

      @Majed Take the quotient of 2 concentrations of ClO2 and divide it by the quotient of the 2 rates, since the concentration quadruples and so does the rate 4/4=1

    • @someaussiekidd
      @someaussiekidd 5 років тому +11

      @Majed because he didnt double the concentration, and then get quadruple rate, he QUADRUPLED concentration THEN got QUADRUPLE the rate. Its equivalent to doubling the concentration and getting double the rate which is FIRST order. (:

  • @aneva_borden4683
    @aneva_borden4683 2 місяці тому +1

    How did calculate the rate constant in the end?? Thank you for video! This makes more sense than the past month in school

  • @LaviniaApple
    @LaviniaApple 4 роки тому +1

    Hi Prof Dave, I use this video in my A2 class in school. Helps a lot! Thanks!

  • @Reforitor
    @Reforitor 6 років тому

    To find the order, instead of remembering what Dave said, simply write down the rate law for various trials and divide the ones with same concentration of either reactant. The rate constants will cancel out and you'll have a sweet equation which can ne solved to get the value of the order of the reaction!

  • @paulnicholas1278
    @paulnicholas1278 7 років тому +4

    Prof. Dave, ALWAYS remember that you are a godsend!

  • @Chinemeremma99
    @Chinemeremma99 3 місяці тому

    Bro you're the 🐐

  • @kleinerflugel65
    @kleinerflugel65 2 роки тому +1

    as expected professor dave, you never fail me. thanks!

  • @nyebadr
    @nyebadr 3 роки тому

    god bless u. pls keep blessing us with ur videos. 2 lectures in uni were explained in less than 9 minutes. you rock!

  • @BillGriffin77
    @BillGriffin77 Рік тому +3

    Thank you Prof. Dave! I thought i was gonna take the L on my chem this week. You saved the day!

  • @johnrudd629
    @johnrudd629 4 роки тому +2

    well done, i liked these videos , easy and nicely explained, thanks Prof. Dave!

  • @MissIronToga
    @MissIronToga 5 років тому +1

    You just saved my exam.

  • @jayashrikulkarni5519
    @jayashrikulkarni5519 7 років тому +1

    Thank you sir for explaining in a simple way

  • @SmokyBigSmoke
    @SmokyBigSmoke 7 років тому +10

    Thanks a lot professor. Awesome video 😘😘

  • @stevendog40
    @stevendog40 7 років тому +1

    Dave is single handedly getting me through my sophomore year