Differential Equations - Full Review Course | Online Crash Course

[@MathTutor1]

Topics line up Part 1 - First Order Differential Equations 1) Intro 0:00 kzbin.info/www/bejne/j3nbc5SFqdl-ebc a) Verifying solutions 6:04 2) Four fundamental equations 29:26 kzbin.info/www/bejne/a6GzonappN12d8k 3) Classifying differential equations 33:14 kzbin.info/www/bejne/fJ-tp6J6eJ6Mgrs 4) Basic Integration 47:52 kzbin.info/www/bejne/iKCqcphjh7iSb7s a) Table of common integrals 1:02:06 kzbin.info/www/bejne/mpapk4mIatp6hM0 5) Separation of variable method 1:02:08 kzbin.info/www/bejne/aIG2op6Xqs2thJY 6) Integration factor method 1:12:13 kzbin.info/www/bejne/nZi1oGl9bM50sK8 7) Direct substitution method 1:29:38 kzbin.info/www/bejne/Z6G4ioSphLdlmKs 8) Homogeneous equation 1:38:40 kzbin.info/www/bejne/a5m4c2l-h7l0hbc 9) Bernoulli's equation 1:49:03 kzbin.info/www/bejne/aXzRdYSLjp6ggdU 10) Exact equation 2:02:29 kzbin.info/www/bejne/jXutfI1-qt-kbJY 11) Almost-exact equation 2:21:13 kzbin.info/www/bejne/qoDHnamQpcmUodE All-In-One review 2:32:20 kzbin.info/www/bejne/e6LMaKCKeNKlbK8 12) Numerical Methods 2:32:56 kzbin.info/www/bejne/fojYkqGvh5JoiJI 13) Euler's method 2:34:20 14) Runge-Kutta method 2:46:12 15) Directional fields 2:50:54 kzbin.info/www/bejne/o6Tag5-Ioqpkeas 16) Existence & Uniqueness Thm 3:00:58 kzbin.info/www/bejne/d5jSZ3d5jtmMpbs 17) Autonomous equation 3:08:28 kzbin.info/www/bejne/hnjGk2Bsf76aoas Part 2 - Second Order Differential Equations 18) 2nd Order Linear Differential Eq. 3:18:09 kzbin.info/www/bejne/d6WaqK1thZ1nj5o a) Linear Independence 3:39:09 b) Form of the General Solution 3:44:14 19) Reduction of Order Method 3:57:25 kzbin.info/www/bejne/d32Wk3t7qL2Wj9E a) Reduction of Order formula 4:19:23 20) Constant Coefficient Diff. Eq 4:28:12 kzbin.info/www/bejne/iWOXimh4ib99qtk a) Complex Numbers Review 4:28:11 kzbin.info/www/bejne/pamlemyehtqKapo 21) Cauchy-Euler Diff. Equation 4:55:44 kzbin.info/www/bejne/n2GcoZyLmdOCb7c 22) Higher Order Constant Coefficient Eq 5:15:56 kzbin.info/www/bejne/Y5XUh6x_a72jfrs 23) Non-homogeneous Diff. Eq 5:33:42 24) Undetermined Coefficient Method 5:39:24 kzbin.info/www/bejne/pGK3nZeMpb2japo 25) Variation of Parameters Method 6:14:52 kzbin.info/www/bejne/bqjcZZWXmb-Li9k a) Formula for VP method 6:33:57 Part 3 - Series, Laplace Transforms & Systems 26) Series Solution Method 6:40:22 kzbin.info/www/bejne/babRooago8SepK8 a) SeeSaw method for series kzbin.info/www/bejne/larPfmB8q5hpoqM 27) Laplace transform method 7:22:28 a) Find Laplace transform 7:25:33 kzbin.info/www/bejne/oH3LYqGvfMh5g80 b) Inverse Laplace transform 7:37:9 kzbin.info/www/bejne/fYDPlmaQeMyBeaM c) Cover-Up Method kzbin.info/www/bejne/hISQfJqCrLmgpc0 d) Solving Diff. Equations 7:59:47 kzbin.info/www/bejne/rXfdlXaqd8t-pK8 e) Convolution method 8:13:30 kzbin.info/www/bejne/imXTgod9r6x5l5I f) Heaviside function 8:28:55 kzbin.info/www/bejne/ommVhJaIrbaKhKs g) Dirac Delta function 8:50:12 kzbin.info/www/bejne/fJi2nJJsf8qMrJI 28) System of equations 9:04:08 a) Elimination method 9:06:44 kzbin.info/www/bejne/Z6WmqKOEfbyLa6s b) Laplace transform method 9:22:23 kzbin.info/www/bejne/Z6WmqKOEfbyLa6s c) Eigenvectors method 9:32:47 kzbin.info/www/bejne/rp2wZISBd6-MbKc d) Shortcut method for 2 x 2 kzbin.info/www/bejne/aKOkpmBrZ7Gibpo e) Shortcut method for 3 x 3 (repeat) kzbin.info/www/bejne/fn-no4eCqqeMoNU f) Shortcut method for 3 x 3 kzbin.info/www/bejne/hJuyhnSAobdoaZY List of typos ------------------------------------------------- at 21:28, it should be dy/dt = ky at 22:38, it should be dy/dt = -ky at 4:38:50. The equation has -3 in it, not +3.

[@salkhan2138]

Excellent collection for Diff Eq.

[@tıbhendese]

Thanks for the great effort. where is the important integrals table / video ?

[@MathTutor1]

@@tıbhendese You can find that in the playlist. Please let me know if you cannot find it. Thank you.

[@MathTutor1]

Here it is kzbin.info/www/bejne/mpapk4mIatp6hM0

[@02vLxcZF]

The first two "typos" are quite egregious. Casts doubts on the rest of the lecture

[@peteranderson7578]

The most comprehensive diff eq review ever. This needs much more attention. Well done sir. Thank you.

[@MathTutor1]

Glad it was helpful!

[@MathTutor1]

List of typos ------------------------------------------------- at 21:28, it should be dy/dt = ky at 22:38, it should be dy/dt = -ky at 1:38:00 question, there should be 1/2 tan⁻¹(u/2) instead of tan⁻¹(u) at 4:38:50. The equation has -3 in it, not +3.

[@diegofutgol87]

Agreed

[@isacdaimary9908]

Kindly pin this comment,,, It might create chaos to new learners

[@thepro351]

Please check at 2:27:53 as well, instead of y and x you are using (delM/dely) and (delN/delx) respectively. Why? Am i missing something?

[@Will-Ch]

[@Justaguy-d4n]

My man! My Goat! My hero! I finished this course in two weeks (i studied everyday) , the exams are in 13 weeks lol😂...Now i am just doing more exercises. Getting ready for the academic comeback!!! RAH

[@MathTutor1]

Great to hear. I'm sure you will be excel in academic and others. Did you see the Laplace transform "Nine problems" video? That may be something you should see next. Good luck.

[@joeyGalileoHotto]

This deserves far more views.

[@MathTutor1]

Thank you.

[@salkhan2138]

I agree. Good work.

[@HujakAdynCykaNahujj]

i had a 3 year gap after my fisrt year in undergrad i was so lost that i didnt even knew what questions to ask in other words ,, i dont even know what i dont know '' . i had to jump straight into advanced ODES and this video is saving me from failing my class. God bless !

[@MathTutor1]

I'm glad that it helps you. Good luck with your studies.

[@johnsaylor1583]

Thank you for this! This is quite comprehensive, and you go at a perfect pace. Know that you have made people's lives easier with your work, even if this video doesn't have that many views on KZbin!

[@ashlynoconnor5876]

30 minutes of this and I already learned more than however many weeks of class, thank you

[@jan-willemreens9010]

...This excellent Differential Equations on ODEs course has saved me a lot of blood sweat and tears, for which I would like to thank you very much, and last but not least for your unwavering commitment to education in general... Much appreciation and many thanks, Jan-W

[@MathTutor1]

I'm glad that it helps you. Please spread the word about this course and let's help few more of your friends too. I'm sure you may have done so already. Thank you.

[@samancarl9476]

Wow, wonderful. One stop shop for everything that I need to learn in this semester. Thank you sir.

[@MathTutor1]

Glad it was helpful!

[@georgesadler7830]

MR. Math Tutor ,thank you for an exceptional video/lecture on Differential Equations. The problems/examples are excellent, however there are a few errors in the exercises. At the 1 hour and thirty-five minutes mark, you have the integral of du/u^2 +4 equal to Arctan u +c. The correct answer is 1/2 Arctan(u/2) + C. At the 5:51(Five hour and fifty minutes) mark you have y'' -y' -2 instead of y''-y'-2y=0. Finally at the 9:16 mark, you have 3/7 instead of 3/7t. Please correct these errors in the video.

[@MathTutor1]

Thank you very much for pointing these out. I have listed some of them in list of typos section. Unfortunately, youtube does not let me make any changes other than cutting out certain parts. This is a feature YT should think about, especially for educational videos. I'll update the list with your findings. Thanks again.

[@crispclean6028]

This video has me looking forward to my Diff Eq. Course starting next week!

[@MathTutor1]

This has everything you are going to learn in the course. You can learn them ahead of time with plenty of examples. Good luck with your studies.

[@enderwidder2500]

Thank you homie this was a lifesaver 🙏

[@Jamesfrazer01]

Was scared of my MAT202 course but after watching your video sir, I went into the exam hall with a 100% confidence and got an A. Thank you so much sir, your video really helped in my exam.

[@MathTutor1]

Very glad to hear that. Please tell your juniors about this course. Thank you.

[@erictrump5540]

Wow!

[@christianrosado8838]

Thank you! Ill surely need this for my future electrical courses!

[@MathTutor1]

Glad, it will help you.

[@Daniel_ElegantUniverse]

At 6:06:02, you should get -6Dsin(2T) - 2Dcos(2T)= 0 as there is no canceling sin(2T) factor for this in the expression “6 + 8e^(-2T) - 4cos(2T)”. So, to get the expression -6Dsin(2T) - 2Dcos(2T) = 0, it is D that must = 0, and C=2/3

[@MathTutor1]

Not really. As explained in Step 5, we are only equating coefficients of linearly independent terms. So, we only pick sin (2t) terms in this case. There are no cos (2t) terms. I have seen that many students do the same mistake. I hope it is clear now.

[@Daniel_ElegantUniverse]

@@MathTutor1 Yeah, I totally understand what I did incorrectly at the time. I completely missed it at the time, and after finishing the course and going through it a second time, it’s just so obvious to me now. Thank you!

[@Daniel_ElegantUniverse]

@@MathTutor1 I must also ask in regards to this part 6:20:17 , where did those two equation in (3) come from? Thank you.

[@Raga_Sandeep_Reddy]

Just what I needed Thank you very much ! You definitely deserve a sub!

[@MathTutor1]

Glad that it helps. Thank you.

[@renatopintoreveggino3813]

this man is a savior

[@salkhan2138]

Excellent resources for students. Keep up the good work.

[@uditakatugampola]

Thank you.

[@samancarl9476]

Totally agree.

[@kyzumii5]

for example 5/2k+5=24(2)/7 that means 2.5k+5=2.85714286 so now -5 its gonna be 2.5k=1.85714286 k=0.364583333 but because of the Einstein's shortcut, we can get the answer just by using mental math, r2 cannot be parallel with the angle Z in a symmetrical shape, so that means that each corner has to be 2.9946233?

[@edwardblack9263]

You are such a bloody winner. Thank you kindly, thank you SO much!

[@pluggmankth942]

4:38:50 Mistake. With this you get -3 not +3 (: so you get complex roots

[@MathTutor1]

Thanks for pointing that out. I was planning to write -3 in the equation, but wrote +3 instead. Sorry for that.

[@palak0707]

At 1:38:00 question, there should be 1/2 tan inverse u/2 instead of tan inverse u

[@icaneatapackofchipswithout3488]

I am also wondering about that.

[@MathTutor1]

Yes, you are correct. Thank you for pointing out. That helps.

[@meghachandran3955]

Yes

[@azizullah6524]

I like your "good"at every point

[@muskaanmohalik]

I have my first test tomorrow and this video has made me feel extremely good about my prep

[@MathTutor1]

Good luck with your studies.

[@ghaidsaeed1744]

Sir, In minute 9:04:00 why is it 2√5 in x(t) and not 8/√5 ?

[@albertgandhi7104]

The best diff eq review ever. Thank you.

[@MathTutor1]

Glad you liked it!

[@MathTutor1]

Related videos ---------------------------------- Illegal Math: kzbin.info/www/bejne/f5XHZqqjqq-ooZY Laplace Transform Method kzbin.info/www/bejne/fnXPiWmugc2errs Solving y'=y/x in Seven Ways kzbin.info/www/bejne/eYuxmXSbbcuBl7s Evaluating ∫ sec⁴ θ tan³ θ dθ in eight ways! kzbin.info/www/bejne/fGLcfWucr5KNj9k Thank you for watching!

[@thirat5173]

Thank you for the wonderful tutorial Sir...By the way , you already have some videos about differential equations Sir...Which videos do we want to learn ??...Only this video is enough to gain complete knowledge on differential equations or do we need to go through them also Sir ??

[@MathTutor1]

This video is a summary of what you learn in other videos that provide details information. It would be enough to watch just this if you are looking for an A for a undergraduate level ODE course. Thank you.

[@thirat5173]

@@MathTutor1 Thank you so much Sir

[@MrSajikhan]

Excellent Work. Is it possible to get a pdf file of solved practice problems?

[@gamerkumar3427]

4:27:23 how is it linearly independent when y2 is not 0 in general that does not show c1=c2=0

[@MathTutor1]

Good point. Let x = 1, this shows c1 = 0. Then take x = 2 to see that c2 should be 0. The idea is, if it is linearly independent at a one point (non-trial), then it is lin. independent in their domain of definition. L.I is a property of the function and it does not depend on the interval of consideration (in general). .

[@gamerkumar3427]

@@MathTutor1 I get it. Thank you sir!

[@Dina-he1uc]

hi! I had a question about something that has been confusing me very much.. an example is at 8:32:20 . s + 3 as a numerator got separated into 2 fractions, is it allowed to separate a polynoial like this? Dont we need to use partial fractions?

[@MathTutor1]

That's a great question. Yes you can separate the polynomial in this case and you don't need to use partial fractions in this case. This is like writing (1+3)/5 = 1/5 + 3/5. Partial fractions are used when there are more than one factor in the denominator. Even if you try to use partial fractions for this case writing (s+3)/(s^2+4) = (As + B)/(s^2+4), you will end up with the same answer. Could you do it for me and let me know what you got? Thank you for raising this great question.

[@athiba5945]

You did such an amazing work sir unfortunately you are so underrated😔

[@MathTutor1]

Please spread the message. Let others know about this free resources. Thank you.

[@Simon-xh8ki]

learning a lot watching this video, thank you!

[@harryderick9916]

Question: 28:19, shouldn’t it be dy/dt = ky and for the others it is also the wrong variable?

[@MathTutor1]

Yes, you are exactly correct. Sorry for the typo.

[@harryderick9916]

It’s fine, thanks for the quick response :)

[@MathTutor1]

@@harryderick9916 I also listed them in the description. Thank you.

[@abaduker9818]

Please make a video on calculus of several variables

[@MathTutor1]

That's a good suggestion. I'll make a video on those topics soon.

[@MrSajikhan]

I made PDF nodes from the slides for my personal use. If anyone needs these please let me know.

[@MathTutor1]

Thank you very much for doing it.

[@humphreyomito1861]

send me please

[@derricknanayaw8721]

I need it please

[@brann6761]

Please help me with your resources

[@mohammadmousa2625]

In topic 2 four fundamental medel equation, growth and decay , the d. e. Should be dy /dt =Ay and dy/dt =_Ay.

[@MathTutor1]

Yes, it is a typo and mentioned in the typos section in the description. I wish KZbin let me fix it. Unfortunately, there is no option for that. Thank you for pointing this out.

[@yopenzo]

11:35 should be: ... + 4C2.e^2t

[@MathTutor1]

Yes, you are correct. That's a typo. Sorry for that. In the same line, 4 is coming from twice differentiating e²ᵗ.

[@HDitzzDH]

36:00 How do you pronounce the ∂ symbol? 😂

[@MathTutor1]

It is pronounced as "dabba". It may also be pronounced simply "dee", "partial dee", "doh", or "die" depending on where on earth you live.

[@MathTutor1]

en.wikipedia.org/wiki/∂

[@MathTutor1]

I know you also asked this great question: "Regarding the homogeneous/non-homogeneous classification, aren't all differential equations homogeneous since you could just move all the terms to one side make it equal 0?" There are two answers related to the term: 1. Unfortunately, there are two type of differential equations that we call homogeneous; one that can be written as dy/dx = F(y/x), that is a function of y/x. We solve this using y = vx. 2. The second is your question. That is a differential equation that does not have a term of the independent variable only. So, you concern is can we put any diff. equation into homogeneous form? The answer is NO. The reason is we try to write in the standard form which has all the y terms including derivatives on the left and all terms with only independent variables on the right. So, if there is a term only of the independent variable, we cannot bring that to the left. If we do so, it is not in standard form. So, the classification is w.r.t. the standard form. For example, y''+3xy'−y+x = 0 is not homogeneous since there is a term x of independent variable only. I hope it is clear now. Thank you. PS: For some reason, you second question did not appear in comments. So, I rewrote it here. Thank you for asking this great question.

[@kendalwilliams5128]

thank you!

[@lefterissoulas4039]

Nice job dude. You make diff equations really simple to understand. I am at my MEng at Electrical and Coomptuter Engineering now and i struggle so hard at diff equations. Would be nice tho if u included Riccati equation.

[@MathTutor1]

I'm glad that it helps. Good luck with your studies.

[@karldionisio8290]

@1:00:35 how the x value became -1 instead of 1? Is it an error? While using the IV. Thanks for the reply

[@karldionisio8290]

Ohh it was solved @1:01:54 🤣

[@MathTutor1]

@@karldionisio8290 Thanks for noticing it.

[@KenMinhLim]

Skip 7) 9) 10) 11) 12) 13) 14) 15) 16) 17) 19) a) 21) 22) 24) 25) a) 26) (based on personal study curriculum)

[@yuzhongxaldouz7220]

Wish you good health and wealth

[@gamerkumar3427]

Sir, I have a doubt about homogeneous equations as you said if there is a no independent variable then there it is homogeneous eqn but my book says that the degree of each term should be n for it to be homogeneous eqn ?

[@MathTutor1]

Good point. Unfortunately, there are completely two different concepts meant by "homogeneous" First one is the same as you mentioned. Then there is another one that has 0 as the term of independent variable. Then, once you bring all terms with dependent variable, the right hand side becomes zero. This is a main concept learn in any diff eq course. I hope it is clear now. Thank you.

[@Sunny-qe5el]

For Autonomous equation (around the time 3:10:00) Are there any relevance between critical points and local/global maxima/minima?

[@vsxvp]

This is soo good, but I think it needs Systems too.

[@MathTutor1]

Thank you. It has systems as well (Part III) and adopted elimination method, Laplace transforms and also eigenvalue-eigenvector methods. Please refer to the list of topics in the description. I hope this helps.

[@rogersbrolin7784]

Does the video include PDEs also sir?

[@MathTutor1]

No, this is mainly about ODEs. Solving PDEs video will appear soon.

[@mightypill]

The state should give you a check to help humanity thrive at this point

[@gustavosh.5147]

10:49 Shouldn't it be 9Ce^-4t ?

[@MathTutor1]

Yes, it's been fixed later. Thank you for noticing it.

[@gustavosh.5147]

@@MathTutor1 no problem, i was just confirming, for myself. Thank you

[@BraydenDufield]

saving me diff eq final review, Thank you

[@NaturesSerenityStudio864]

Thank you so much sir.

[@harryzebeast9282]

How far can someone get into this video without having studied linear algebra?

[@MathTutor1]

That's a good question. You may cover part I without any issue. Linear algebra is used in part 2 and part 3. Even if you haven't taken it, you should be able to understand the lectures without difficulty. The concepts you need is linearity in part 2 and eigenvalues and eigenvectors in part 3. I hope this helps. Thank you.

[@justinbieber5195]

@@MathTutor1 Thank you. I studied the entire course without any difficulty. I'm taking full linear algebra course now and can recall some of the topics discussed here, for example, linear independence and linear systems and eigenvalues and vectors.

[@hermionegranger8833]

@@justinbieber5195 omg Justin Bieber studying mathematics 😂!!! Big fannn

[@Its_your_Aashiq_Yaar]

Sir is it contain syllablus of csir net

[@MathTutor1]

Yes, it covers all the topics.

[@Mikebigmike94]

Hi is the full 9 hours in English does anybody know? I’ve started many courses before and it turned out is wasn’t all English. Thank you in advance

[@justinbieber5195]

The easiest way to find out this is to check at several random places. Did you do that?

[@DatoelMatilda]

Thanks for the tutorial

[@ปาริชาติแซ่ย่าง-ค4ฝ]

Differential is made easy to get mind

[@ahmettanka4283]

Hii I like to know which book you are using for reference? Is it Boyce's?

[@MathTutor1]

That's a great question. I used my own notes for most of them and selected some questions from Boyce's, Zill and my own book. I hope this helps.

[@chrisbroward]

Very nice

[@athiba5945]

Thank you so much .

[@MathTutor1]

Thank you.

[@loganreidy7055]

Horrible timing but I was passing a kidney stone while taking this final, let's just say the kidney stone hurt less than the final.

[@MathTutor1]

Yeah, at times things happen out of control. Facing them is the best we can do. Thank you.

[@yuzhongxaldouz7220]

Thank you sir!

[@unimportant372]

Up to 2:33:33

[@MathTutor1]

Keep going. You will learn a lot. Good luck.

[@ananyasood]

Sir is it enough for 1st year ?

[@MathTutor1]

Yes, this covers all the topics needed for a undergraduate Diff Eq course. You may look at the description for more detailed lectures. Thank you.

[@MathTutor1]

Calculus II - Practice Final Exam kzbin.info/www/bejne/qaScg51qnt2daMk

[@azizullah6524]

You are great sir

[@emmanuelowusu-ansah2625]

I'm going to have paper by 6 hours time. I don't know why any mf sent us this amazing course like a months ago but chale I'm leaving everything to God by now walaahi

[@surprisingmathematics6792]

Thanks a lot from deep of heart to you sir From Bangladesh ❤️

[@ajaysuresh1240]

Thankyou so much

[@MathTutor1]

I'm glad, it helps you.

[@satyam8242]

Good👍👍👍👍

[@MathTutor1]

Thank you.

[@quanghungnguyen6630]

Do you have the cheat sheat for the final of this course?

[@justinbieber5195]

You plan to cheat in your exam?

[@sejalsangole2527]

@@justinbieber5195 lol cheat sheet is the list of important points and formula...like the entire course in a page or two.

[@skullypac4497]

Thank you.

[@posljednjilist4400]

7:22:00

[@MathTutor1]

Derivatives Review (All topics) kzbin.info/www/bejne/Zp3Npqlrg7ycq80

[@VndNvwYvvSvv]

10 hours is a full course, not a review

[@MathTutor1]

Thank you. You may find the full course at the description.

[@Trigger9994]

Nop, for these one you will need at least 1 hour for every review hour in the curse. A full curse on this subject could last 50 to 100 hours

[@maimounchokri1135]

Thank you

[@MathTutor1]

Thank you.

[@MathTutor1]

Calculus II - Practice Final Exam kzbin.info/www/bejne/qaScg51qnt2daMk

[@yashkumarjha5082]

28:10

[@MathTutor1]

Yes, there is a typo and it is mentioned in typos in the video description. KZbin does not allow me to edit that part. Sorry for that. The first two differential equations should be: dy/dt = ky and dy/dt = -ky. (with ending y) Thank you for pointing out this again.

[@MathTutor1]

Solving a differential eqn in 7 ways at kzbin.info/www/bejne/eYuxmXSbbcuBl7s

[@MathTutor1]

Illegal Math (Or Common mistakes) kzbin.info/www/bejne/f5XHZqqjqq-ooZY

[@Will-Ch]

:V

[@AshetuTesfayeBoru]

Very good

[@ElifArslan-l9g]

thank you