@@Rahul-cb4jb I'm actually a full-time university student. I have a few nice things but I'm pursuing my education along the way. Not rich by any means, but thanks for the compliment though!
When I can repay you in a monetary sense I will. You've saved my life, quite literally. School has been rough and my professors are awful (they've "given up," and you haven't) l, you've made an immense difference in my life and I can't thank you enough, I hope your family is doing well.
Thats awesome! I actually made a goal for myself that when im done with school and working, I will make a large donation to prof leonard. I have only experienced very few professors that care enough to put this much effort into their students. Prof leonard goes above and beyond because we arent even in his class, yet hes here to help. Amazing.
There are no stupid students. There are only teachers who can not teach. Good teachers make you feel smart, bad teachers make you feel stupid. You are a really good teacher!
Facts. I only made it through this course because I found a very patient tutor and this channel to compensate for my terribly fast professor, who thinks everyone in the class should already know the material before lecture starts.
Sir... your lectures are really very helpful for me. Please do more videos on the remaining topics of the differential equations like orthogonal trajectories... envelopes... singular solutions and equations solvable for p, y and x...... I am waiting for these lectures....
Hello Professor Leonard just want to thank you for the amazing lessons on Math such as Calculus and Stats you gave me throughout my college career. I am getting my Bachelors in Math this Spring 2019. You are by far the greatest Math teacher I have witnessed, so much knowledge and details goes into your craft. Hope all is well!
Education is the key to success in life, and teachers make a lasting impact in the lives of their students. The guru's aim is only the salvation of the disciple. It is the supreme art of the teacher to awaken joy in creative expression and knowledge.
Thank you for all your great lectures! For people who are asking, Professor Leonard just had a baby, and family is always first! I know it is not easy but you are doing a great job! Currently taking Differential equations right now, and just subscribed to your Patreon account! I wish all of you the best of luck!
Don't comment much, but have watched all your videos, full length, from Calc I to III, and now EDOs. Literally in this pandemic i've learned it all with your videos, it's my go-to everytime. Kinda sad to think i wont have you in the next courses
Prof Leonard YOU ARE MY HERO. Thanks for doing awesome lecture videos for all these years. Thank you for helping me to transition from a math enthusiast to a math major!!!
Hi, sir I really salute your dedication for teaching and I'm one of those whom you have helped through your videos. I would really appreciate it if you would have some videos regarding 2nd order DE and higher-order DE's. As well as finding its particular solution. I'm having a hard time on those topics. Thank you, Sir. Love from Ph ^_^
Many thanks for this marvelous teaching and explanation actually none of online tutors have explain it in right way , please can you post videos in the other 3 cases when the differential equations are not exact thanks
I was in Calc 3 when our university went online and my professor literally had us read out of our books and then test us on what we taught ourselves. Thank GOD I found your videos. You really helped me get through with a high level of understanding. I'm currently taking Diff and again, you provide the WHY behind a lot of the math. I'm an engineering student, and I thrive on the theory. Thank you for all of your videos.
No way, he made you read out of your BOOK? That thing that explains all the material in great detail, and provides examples/exercises? What a monster, that man is.
Thank you Professor Leonard. These must take a lot of work to prepare for, so just want to say I really appreciate your time and effort. You don't know me, but you've been a mentor in math (and honestly sometimes life) for years.
Very lucid explanation. Helped me in understanding the fuzzy areas in the basics of exact differential equations. Partial derivatives on a general function is sometimes a complex path to understand the proof. Thanks a lot professor.
man you make my day i have been watching bunch of you tube videos on exact DE topic but could not understand you make this topic simple and understandable thumbs up
I encountered exact differentials 40 years ago as an engineering student. I have been tutoring math and physics for years partly for pleasure and partly for spending money. A junior in HS just asked me to help her in Differential Equations. I thought it would be somewhat basic, but when I saw the curriculum, I said “Yikes!”. Her textbook is very comprehensive. My old textbook (Engineering Mathematics - Kreysig) was awful and I never understood exact differentials. As usual, when I encounter a problem, I go to TH-cam. You’ve done a great job. Thanks.
I LITERALLY CANNOT THANK YOU ENOUGH! THE BEST ONLINE PROFESSOR EVER! I learn absolutely nothing in class everything is rushed and my hand only writes so much at a time, so don't take notes at all. However, that was/is no solution for me because end up not having anything to study with for quizzes and exams but your videos are honestly grade savers! THANK YOU PROFESSOR LEONARD!!!!!
I am so grateful that we start learning English already at around age 7 in Sweden, so that I can understand exactly what Professor Leonard is saying without any problems. 8-)
Thank you from the bottom of my heart. I was looking for the thoery, my teacher jumped to the exercises without explaining the basic, he taught good but I was curious to know why this is happening. Thanks a lot again.
Professor Legend (sorry autocorrect). Thank you for your simple explanations and going through questions in depth to embed the concept. I passed calc 1 and 2 through your videos and I am certain I will get through DE and calc 3 with a breeze. Thank you again!
My calc 3 professor taught us a shortcut to find the potential function of a vector field. The process was very similar to this and I have started applying it to solving these kinds of exact equations and it seems to work all the time. Basically, you integrate M with respect to x and N with respect to y and then combine them, making sure that the same term is not repeated more than once, then just add the C on the other side. For example: if the integral of Mdx=xy+x and Ndy=xy, the answer would just be xy+x=C.
Hi Prof. Leonard. Why are exact differential equations considered ODEs, when there seems to be multiple independent variables (x and y in this case) and their partial derivatives involved? Is it perhaps because this is an instance of breaking down a PDE into ODEs?
Professor Leonard I don't know if you read these comments but I just want you to know these videos practically saved my life when it came to my DE tests. These explanations are just so in depth, thank you so much.
I've literally read 3 of my professors notes about this topic and none of them seemed to explain as half as good as the first 15 minutes of this video. Thanks professor Leonard! Literal life saver!
Heyy sir, I have got a slight quibble, its been years I dont know if you'd respond but this is bugging me. You said if the function and its partial is continuous and differentiable then the mixed partial should be equal, it makes it a necessary condition, but is it sufficient? Only then you can use that condition to solve the equation isnt it? Please do respond sir this is really keeping me up at night. 😒
Professor Leonard, I had to replay the whole little bit at 11:30 like five times, but it actually made sense in the end! Thank you so much. It took a lot of thinking.
Me, who just went through all about level curves and surfaces in Leonard's calc 3 playlist, and is now seeing this in the differential equation *oh yeah it's all coming together*
I don't understand the derivation at 4:33. All I know is that the derivative of f with respect to x is the derivative of f with respect to x. The addition of the second term confused me. It would only make sense to me if the derivative of f with respect to x only equalled one of those two terms.
I don't have money to support Dr. Leonard so I let ads play through entirely so he gets ad revenue. Plus, it gives me a break so I can review my notes.
hey, this is really out of left field, but any students, esp professor leonard students, remember the name of the...grid? for foiling out functions raised to a power?
Another really cool trick my professor showed: Take an integral with respect to x for M and get : F(x,y) = (integral of function M) + g(y) Take an integral with respect to y for N and get : F(x,y) = (integral of function N) + h(x) Now, since these should be equal, anything with both x and y in the term "cancel out". Then you look for anything with just y's and that's your g(y). Look for anything with x's and that's your h(x). So the final solution will be F(x,y) = (integral common terms) + g(y) + h(x). Hopefully I explained that well.
Professor you prolly an amazing teacher..... watched tons of youtube videos I still didn't get it. After watching yours I got to know why we are learning EXACT DIFFERENTIAL EQUATIONS. Couldn't be thankful anymore!
I come across this situation on my own (dM/dy = dN/dx). there is not an exercise or textbook problem is just me playing with some equation of motion. my question is, given the above situation and no more information on M or N (they are the unknown of the equation and of motion), is it safe to assume that exist an F such that dF/dx=M and dF/dy=N , forces are not conservative, but N, M are not the forces either, so this is not so much an issue
Very neat and comprehensive lecture!, simply awesome! Just a question: Why not just integrate M and N, and find the common terms and the only-x's and only-y's terms to come up with the solution?
Hey Professor Leonard, We are currently doing reduction of order in our diff eq class and it looks like you have something similar to it on your channel (Reducible Second Order Differential Equations missing x and y). But I am not sure I am certain we will cover that stuff eventually since we just started our higher order section. If its not up yet I would greatly appreciate it, also would embedded derivatives help me out with that stuff? Thanks!
totally understood the technique but I am a little confused about what is this 2 variable equations that we get. I mean I understand that this obtained equation satisfies the differential form but in terms of it being the solution to the differential equation I'm not sure I get it. I guess what confuses me is that it is a 2 variable function and until now we only got solutions with one variable...Does that mean that from the beginning we consider the "x" and the "y" as being two unknowns functions and not just a variable ? Hahah sorry if its not clear I think it's not clear for me what I don't understand :p
Thank you, my online teacher's videos are impossible to read, and her voice is one of those that are incredibly annoying to listen to. I needed your videos in my life.
thnak you for taking the time to teach us and believe in us, I believe you should start a business where you can teach teachers how to teach. I always send good vibes your way doctor
Hey Professor, firstly thanks. You've been saving me every semester. Any chance for an intro to in depth video series for Trig? From finding Trig Functions, the Unit Circle, Graphing, Right Triangles, even just the basics of introducing sin,cos, and tan?
Been a fan of yours since I took Calc 2! Right now I'm taking Differential Equations and they're not really explaining where everything comes from, so I really appreciate your videos and explanations!
When I don't understand a topic related to calculus from my lecturer and textbook, I always find the answer at this channel. You have made it understandable, Thank you.
These are the best lectures on Differential Equation I have ever come across over my forty plus years dwelling on the subject from high school to post graduate studies and beyond.
the virgin khan academy vs The Chad Leonard
lmfao what?
Rahul I think it was just a joke bro. We all know that they’re both good sources of information
@@Rahul-cb4jb Its a meme. It just shows the dichotomy between the two and their differences. Nothing against either
@@Rahul-cb4jb I'm actually a full-time university student. I have a few nice things but I'm pursuing my education along the way. Not rich by any means, but thanks for the compliment though!
Professor Leonard is ideal for in-depth and super-pedagogical math.
Khan Academy is ideal for a little bit of various decently explained subjects.
When I can repay you in a monetary sense I will. You've saved my life, quite literally. School has been rough and my professors are awful (they've "given up," and you haven't) l, you've made an immense difference in my life and I can't thank you enough, I hope your family is doing well.
I'm glad to have helped :)
Things are going well here and family is doing great!
Agreed!
Thats awesome! I actually made a goal for myself that when im done with school and working, I will make a large donation to prof leonard. I have only experienced very few professors that care enough to put this much effort into their students. Prof leonard goes above and beyond because we arent even in his class, yet hes here to help. Amazing.
Can you provide a life update? Did you ever support the professor via pateron
There are no stupid students. There are only teachers who can not teach. Good teachers make you feel smart, bad teachers make you feel stupid. You are a really good teacher!
No stupid students? You are incorrect.
Uhh I have definitely met some stupid students throughout the years. Stupidity does in fact exist. It's not some urban legend or mythical creature lol
Wisdom
Facts. I only made it through this course because I found a very patient tutor and this channel to compensate for my terribly fast professor, who thinks everyone in the class should already know the material before lecture starts.
And lazy on both sides
professor, i owe for my good grades in Calculus 1, 2 and 3. Love your work so much, i keep suggesting your channel to many people
Sir... your lectures are really very helpful for me. Please do more videos on the remaining topics of the differential equations like orthogonal trajectories... envelopes... singular solutions and equations solvable for p, y and x...... I am waiting for these lectures....
Very handsome...I'm just saying....and smart. He's a math genius. I learned so much from him...
I'll be taking differential equations in two semesters. Thank you in advance you son of a gun.
th-cam.com/video/Xr4-yJLD0Gs/w-d-xo.html
th-cam.com/video/Xr4-yJLD0Gs/w-d-xo.html
@@SriHarshaAcademy not cool
@@SriHarshaAcademy no
just no
Got the notif while watching champions league, turn to studying now, yeaaah
Hello Professor Leonard just want to thank you for the amazing lessons on Math such as Calculus and Stats you gave me throughout my college career. I am getting my Bachelors in Math this Spring 2019. You are by far the greatest Math teacher I have witnessed, so much knowledge and details goes into your craft. Hope all is well!
Education is the key to success in life, and teachers make a lasting impact in the lives of their students. The guru's aim is only the salvation of the disciple. It is the supreme art of the teacher to awaken joy in creative expression and knowledge.
I wish I had discovered you when I was a freshman, not just for grades, but for calculus.
Henry Cavil tells you about exact differential equations
Thank you for all your great lectures! For people who are asking, Professor Leonard just had a baby, and family is always first! I know it is not easy but you are doing a great job! Currently taking Differential equations right now, and just subscribed to your Patreon account! I wish all of you the best of luck!
Thanks Thomas!! I appreciate your support and kind words :)
Don't comment much, but have watched all your videos, full length, from Calc I to III, and now EDOs. Literally in this pandemic i've learned it all with your videos, it's my go-to everytime.
Kinda sad to think i wont have you in the next courses
Forgot to say thank you, Thank you a lot.
Prof Leonard YOU ARE MY HERO. Thanks for doing awesome lecture videos for all these years. Thank you for helping me to transition from a math enthusiast to a math major!!!
You deserve more viewers just because you are so enthusiastic about what you teach.
This guy is a genius. Thank you for making learning fun.
Hi, sir I really salute your dedication for teaching and I'm one of those whom you have helped through your videos.
I would really appreciate it if you would have some videos regarding 2nd order DE and higher-order DE's. As well as finding its particular solution.
I'm having a hard time on those topics.
Thank you, Sir. Love from Ph ^_^
Many thanks for this marvelous teaching and explanation actually none of online tutors have explain it in right way , please can you post videos in the other 3 cases when the differential equations are not exact thanks
I was in Calc 3 when our university went online and my professor literally had us read out of our books and then test us on what we taught ourselves. Thank GOD I found your videos. You really helped me get through with a high level of understanding. I'm currently taking Diff and again, you provide the WHY behind a lot of the math. I'm an engineering student, and I thrive on the theory. Thank you for all of your videos.
No way, he made you read out of your BOOK? That thing that explains all the material in great detail, and provides examples/exercises? What a monster, that man is.
Thank you Professor Leonard. These must take a lot of work to prepare for, so just want to say I really appreciate your time and effort. You don't know me, but you've been a mentor in math (and honestly sometimes life) for years.
Omg you are teaching differential equations. I am literally going to pass all my classes this semester.
Very lucid explanation. Helped me in understanding the fuzzy areas in the basics of exact differential equations. Partial derivatives on a general function is sometimes a complex path to understand the proof. Thanks a lot professor.
This mans passion for math is infectious and man does it make him a good teacher
Grinding to someday be as yolked and genius as this man. Professor Legend
does anyone had said you that you look like henry cavil
I was looking for exact equations yesterday and couldn't find them. Perfect timing for midterms in 2 days!
Professor, please type 'dance lessons for mathematicians' in google images.
Those son of a guns are copying your maths moves!
man you make my day i have been watching bunch of you tube videos on exact DE topic but could not understand you make this topic simple and understandable thumbs up
I encountered exact differentials 40 years ago as an engineering student. I have been tutoring math and physics for years partly for pleasure and partly for spending money. A junior in HS just asked me to help her in Differential Equations. I thought it would be somewhat basic, but when I saw the curriculum, I said “Yikes!”. Her textbook is very comprehensive. My old textbook (Engineering Mathematics - Kreysig) was awful and I never understood exact differentials. As usual, when I encounter a problem, I go to TH-cam. You’ve done a great job. Thanks.
I LITERALLY CANNOT THANK YOU ENOUGH! THE BEST ONLINE PROFESSOR EVER! I learn absolutely nothing in class everything is rushed and my hand only writes so much at a time, so don't take notes at all. However, that was/is no solution for me because end up not having anything to study with for quizzes and exams but your videos are honestly grade savers! THANK YOU PROFESSOR LEONARD!!!!!
I have watched a million videos and I wasn't getting it until I watched this...
Thanks professor
I am so grateful that we start learning English already at around age 7 in Sweden, so that I can understand exactly what Professor Leonard is saying without any problems. 8-)
I got 40/40 on my quiz today, that's because of your help, thanks!
Thank you from the bottom of my heart. I was looking for the thoery, my teacher jumped to the exercises without explaining the basic, he taught good but I was curious to know why this is happening. Thanks a lot again.
Professor Leonard is the awesome dude! I could finally understand those topics of diff I couldn't within the entire semester all thanks to him
I'm one of those who asked for this topic. Thank you so much for responding to us.
Great video and explanation
This man is almost singlehandedly guiding me through my math degree. You're a wonder-factory Professor Leonard!
Professor Legend (sorry autocorrect). Thank you for your simple explanations and going through questions in depth to embed the concept. I passed calc 1 and 2 through your videos and I am certain I will get through DE and calc 3 with a breeze. Thank you again!
thank you sir, your channel is the only place where i find DE understandable...
My calc 3 professor taught us a shortcut to find the potential function of a vector field. The process was very similar to this and I have started applying it to solving these kinds of exact equations and it seems to work all the time. Basically, you integrate M with respect to x and N with respect to y and then combine them, making sure that the same term is not repeated more than once, then just add the C on the other side. For example: if the integral of Mdx=xy+x and Ndy=xy, the answer would just be xy+x=C.
If you follow this process for the first example, you end up with the same answer. It works because many of the terms end up cancelling out either way
Why doesn't this have hundreds of thousands of views? This is the clearest explanation of this topic that I've found. Thank you
Hi Prof. Leonard. Why are exact differential equations considered ODEs, when there seems to be multiple independent variables (x and y in this case) and their partial derivatives involved? Is it perhaps because this is an instance of breaking down a PDE into ODEs?
Professor Leonard I don't know if you read these comments but I just want you to know these videos practically saved my life when it came to my DE tests. These explanations are just so in depth, thank you so much.
I've literally read 3 of my professors notes about this topic and none of them seemed to explain as half as good as the first 15 minutes of this video. Thanks professor Leonard! Literal life saver!
what?
You're throwing out the words like differential, level curve and expecting me to get whatever you're trying to say. Bruh this is confusing
Heyy sir, I have got a slight quibble, its been years I dont know if you'd respond but this is bugging me. You said if the function and its partial is continuous and differentiable then the mixed partial should be equal, it makes it a necessary condition, but is it sufficient? Only then you can use that condition to solve the equation isnt it? Please do respond sir this is really keeping me up at night. 😒
This really helped. Thank you.
E: I actually really understated that. This video was a god send. Thank you. I was confused for days.
lim(taking university classes) = failure
t->infinity
lim(professor Leonard's lessons) = success
t->infinity
Could u upload laplace and fourier series soon? My final is in 2 weeks :)
Laplace Transform and Fourier Series are advanced topics in Engineering Mathematics. I am not sure he is also teaching them.
@@canman5060 rip my grades
عظمه فشخ
تمام كده يا دنيا
Professor Leonard, I had to replay the whole little bit at 11:30 like five times, but it actually made sense in the end! Thank you so much. It took a lot of thinking.
Me, who just went through all about level curves and surfaces in Leonard's calc 3 playlist, and is now seeing this in the differential equation
*oh yeah it's all coming together*
You really saved my life. I'll be grateful to you forever. Keep up the good work!
we are going to discuss EXACTly what that means... LOL!
I don't understand the derivation at 4:33. All I know is that the derivative of f with respect to x is the derivative of f with respect to x. The addition of the second term confused me. It would only make sense to me if the derivative of f with respect to x only equalled one of those two terms.
I don't have money to support Dr. Leonard so I let ads play through entirely so he gets ad revenue. Plus, it gives me a break so I can review my notes.
hey, this is really out of left field, but any students, esp professor leonard students, remember the name of the...grid? for foiling out functions raised to a power?
This is why math is hard, lol. Every video begins with "you should probably go back to so and so video" lol
I love you so so much. Not even homo, just a desperate student! Your explanation is brilliant.
This reminds me a lot of trying to find f from Delf from calc 3 (line integrals thorugh conservative vector fields)
wish thee was more that 24h in a day so that i could watch more of the vids, they help me a lot. thanks
Clean notes, great explanation delivery, well dressed. Lucky students
Thank You so much.. You are my favorite Mathematics Professor.
Thank you so much professor Leonard! most patient and handsome professor.haha
you are truly a SUPERMAN! GREAT EXPLANATION :)
Arabic taught from you, your explanation is really awesome
like is not enough for your work. THANK YOU SO MUCH
Thnak you so mcuh for breaking it down your an amazing professor
Yay! Glad to have you back Professor! And just in time for my midterm too! Thank you so much! I don't know what I'd do without your videos.
Thank you
Daddy Superman thanks for the knowledge!
you are a hero to college students out there thank you very much professor
Since Z=F(x,y), then isn't it simply that dz=dF?
How are the fucking haters disliking such human
Another really cool trick my professor showed:
Take an integral with respect to x for M and get : F(x,y) = (integral of function M) + g(y)
Take an integral with respect to y for N and get : F(x,y) = (integral of function N) + h(x)
Now, since these should be equal, anything with both x and y in the term "cancel out". Then you look for anything with just y's and that's your g(y). Look for anything with x's and that's your h(x).
So the final solution will be F(x,y) = (integral common terms) + g(y) + h(x).
Hopefully I explained that well.
Professor you prolly an amazing teacher..... watched tons of youtube videos I still didn't get it. After watching yours I got to know why we are learning EXACT DIFFERENTIAL EQUATIONS. Couldn't be thankful anymore!
The conceptual part of this lesson made way more sense than whatever tf my professor taught in class. Thank you so much !
36:35 Prof. Leonard is hyping me up!
I come across this situation on my own (dM/dy = dN/dx). there is not an exercise or textbook problem is just me playing with some equation of motion. my question is, given the above situation and no more information on M or N (they are the unknown of the equation and of motion), is it safe to assume that exist an F such that dF/dx=M and dF/dy=N , forces are not conservative, but N, M are not the forces either, so this is not so much an issue
Thank you so much professor Leonard! You quite literally replaced my instructor, everything is just so clear when you explain it!
Very neat and comprehensive lecture!, simply awesome! Just a question: Why not just integrate M and N, and find the common terms and the only-x's and only-y's terms to come up with the solution?
thanks professor that is what calling explanation
Hey Professor Leonard,
We are currently doing reduction of order in our diff eq class and it looks like you have something similar to it on your channel (Reducible Second Order Differential Equations missing x and y). But I am not sure I am certain we will cover that stuff eventually since we just started our higher order section. If its not up yet I would greatly appreciate it, also would embedded derivatives help me out with that stuff?
Thanks!
This video is must! Otherwise one would solve exact DEs like robot based on some formulae.
Fantastic explanation concept is now clear. Thanks Prof.
totally understood the technique but I am a little confused about what is this 2 variable equations that we get. I mean I understand that this obtained equation satisfies the differential form but in terms of it being the solution to the differential equation I'm not sure I get it. I guess what confuses me is that it is a 2 variable function and until now we only got solutions with one variable...Does that mean that from the beginning we consider the "x" and the "y" as being two unknowns functions and not just a variable ? Hahah sorry if its not clear I think it's not clear for me what I don't understand :p
It's not that Professor Leonard never makes mistakes. It's that the equations are too scared of being put in a chokehold and solve themselves.
Thank you, my online teacher's videos are impossible to read, and her voice is one of those that are incredibly annoying to listen to. I needed your videos in my life.
Okay, but seriously you’re saving my life right now. Because you are the real Professor. I mean it. Thanks a lot for teaching us across the ocean.
Thank you.
I like how you explained where M and N come from, instead of just going directly on to how we can solve them. It helped me a lot. Thanks
This man is seriously saving me from failing my online math classes with crappy teachers who don't know how to teach online during COVID
tell me why this man look like a free trial version clark kent
thnak you for taking the time to teach us and believe in us, I believe you should start a business where you can teach teachers how to teach.
I always send good vibes your way doctor
You're a life saver!!! THANK YOU!!!!
Hey Professor, firstly thanks. You've been saving me every semester. Any chance for an intro to in depth video series for Trig? From finding Trig Functions, the Unit Circle, Graphing, Right Triangles, even just the basics of introducing sin,cos, and tan?
Yep, fairly soon after Differential Equations.
You are the man, look forward to them. Thank you in advance.
Thank you sir. You made things very clear and was able to understand what's actually going on here.
Been a fan of yours since I took Calc 2! Right now I'm taking Differential Equations and they're not really explaining where everything comes from, so I really appreciate your videos and explanations!
When I don't understand a topic related to calculus from my lecturer and textbook, I always find the answer at this channel. You have made it understandable, Thank you.
These are the best lectures on Differential Equation I have ever come across over my forty plus years dwelling on the subject from high school to post graduate studies and beyond.
Professor Leonard You've been so helpful for me and I like you so much that I really like to see you in person and try the meals you cook!