Differential Equations: Lecture 1.1-1.2 Definitions and Terminology and Initial Value Problems
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- čas přidán 16. 06. 2024
- This is an actual classroom lecture. This is the very first day of class in Differential Equations. We covered most of Chapter 1 which is mainly definitions, terminology, and initial value problems. Just tons of theory here.
Here is the book for the lectures amzn.to/4ajOMyW (affiliate link).
There are lots of notes and tons of definitions in this lecture.
Summary of Some of the Topics
- Definition of a Differential Equation
- Motivation for Differential Equations
- Types of Differential Equations
- Order of a Differential Equation
- Linear versus Nonlinear Differential Equations
- Solutions to Differential Equations
- One parameter families and two parameter families of solutions
- Particular Solutions
- Explicit versus implicit solutions
- The trivial solution
- The General solution
- Singular solutions
- The interval of definition
- Initial Value problems
If you enjoyed this video please consider subscribing for more content: czcams.com/users/themaths...
Please leave any comments or questions in the comment section below. Thank you:)
The difference b/w you and other professors is that you can keep students awake and interested for a full one hour. Enjoyed your enthusiasm.
Thx👍
Not only that, but he keeps the lecture based! He doesn't talk about stuff the students do not have a clue about. It means he genuinely wants to teach, not just show off his brilliance as some teachers do.
Keeping students engaged for 1 hour is easy and many have done it before but I don’t think so much managed to keep students engaged while talking for an hour in one subject!!
But the camera can’t keep up.
@@aliAlyacoubYep, as a math major myself I know exactly what you're talking about. I don't know what the teachers accomplish by doing that exactly.
my professor posts your videos, so he doesn't have to teach :^) congrats on your new job at my university!
Oof, I'm sorry. What a garbage professor. This is a good series, but they should still do the work you're paying so much for. I'm glad there are people like this putting their work online and speaking in more easily understood terms than the text.
@@VeritasEtAequitas He prob use in-class time to do research anyway.
It's better than not so intuitive lectures. And now your professor can help you out whenever you need.
@@VeritasEtAequitas I mean I'd personally rather pay to take a test based on these lectures or professor leonard's, seems like 80% of professors at universities are terrible at keeping students engaged.
IMO if I can basically completely replace your lecture with reading the textbook, why should I bother to show up to lecture?
@@fdsmanMost students are also terrible these days who got all As in high school and think college is the same.
you are an electric teacher, and funny too😂
I'm amazed how in the comments we see students from "prestigious" universities claiming these lectures helped them more than their professors... People pay thousands and get in life long debt for a fake and forced education whereas professors like the one from this series of videos are barely recognized. Congratulations Math Sorcerer, your honesty in teaching is what makes you so genuine and successful at what you do!
Gabriel
Thx man
I learned EVERYTHING in 1 hour. And learned nothing for the past 10 hrs in a week of lecture😂😅. Thx daniel👍
Lol
literally bro
Wow. I almost didn't recognize you because of the hair. I took an algebra class with you many years ago and now I find myself back here finishing my last differential equations course before completing my CS degree. Still to this day the best professor I've had.
Wow Diego!!!!!!!!!!!!!! Long time!!!!!!
cool !
What school?
What is The Math Sorcerer's real name?
@@carultch his real name is Mr. The Math Sorcerer
I'm glad there are people like this putting their work online and speaking in more easily understood terms than the text.
Been following since Calc and now I am in DE. You and professor leonard have helped me so much for my engineering major. Literally feel like I took the class with multiple professors everytime. You have no idea how thankful I am :)
Wow, you're the best math professor I've ever seen! Your enthusiasm, depth of understanding and engagement with the class is fantastic!
It must not feel intimidating at all for students to ask you questions because you're such a genuine dude! Please don't ever change!!
You're a great lecturer, very engaging and animated. Having recently done some public speaking for the first time in my life I've realized how difficult it really is. You're not just going through material, you're constantly taking the temperature of the group for signs of being lost, trying to learn and remember names, etc. and that's if you can get past the performance anxiety of talking to a group of strangers. Teaching really is a high CPU use activity. I should reach out to some of my professors who made attending lectures enjoyable.
The pandemic has taken me out of the classroom, but this professor made me miss being in one. Really top notch explanations, thanks prof!
OMG!!! incredibly, explicitly comprehensible record ⏺ highly appreciate it... I am currently taking Math 202 and my instructor is Okay.... but I believe this instructor is much more better than any math one had taught me. I am certain that I am going to continue the course with these high quality records. God bless you !
I had full math course at my college and I can tell you there was not a single teacher that had 10% of your energy nor enthusiasm. You are the type of teacher that lights up the classroom and for whom students love going back to classes no matter the subject.
For every instance when social media is criticized for being the digital crack that it has evolved to be, I will think of this professor and those like him and their content and be grateful that I live in the digital age. Knowledge in this format will basically be preserved in perpetuity and benefit mankind accordingly. Let that sink in for a bit.
I'm an Engineering major and my professor(really a TA) this semester for Diff Eq. is useless with online school. I've been using your videos to help me. Thank you so much
You are welcome😃
Thank you for teaching me what I couldn't learn from my actual professors, you are so passionate about math, you remind me why I became a math major!! I wish I could take your class!!
Not a dull moment. I have not studied this in decades. I am getting the hang of it again. Thanks.
Excellent!
I just want to express my gratitude towards this lecture. You deserve the best for it! I paused the video just to post this comment when you said "I can't solve this. People solve this for a living". This is the context that I have been asking throughout all of my education. Just put the difficulty in context! This is so important. It saved me years of questions and ponder. Thank you!
Your love of math really give others the enthusiasm to study.
Thank you for being a great teacher.
Amazing sir, I have been struggling with taking online classes and my DE grade was terrible. I'm normally a high grade student but online format has made me suffer. Thanks to your lectures on DE, my grade is rising and I'll be able to do good in the course. I appreciate it a lot!!!!
excellent!
stumbled across this gem and im glad i did. massive respect for the way of teaching, made it all look so easy.
He gives me the summary and I like that 😿💕, I don’t know why other teachers doesn’t do that too ... like this is how you should do it don’t repeat what in the book , That shows you don’t even know what is 🔥
Your enthusiasm is contagious! Great class! Awesom problem driven energy. I cant wait watching more of your classes.
I love this professor he seem very happy when explaining he really love his job not like others ,wish he teach me ,and thank youuu i really understood it .
👍
46:25 f(x,y) = some stuff with x und y is probably the best and simplest explanation that i ever heard of.
it's been nearly 15 years since I learned this stuff in my postgrad economics course, and I thought I'd already forgotten it all. I am amazed I still remember :) ODEs, PDEs it's all coming back :)
A weeks worth of lectures did not get me as far as this hour video. Awesome work!
Love how enthusiastic you are! Great teacher
Wow! I watch a lot of your videos when I get time MathSorcerer (esp the book reviews - love those!), but this is the first lecture one I've seen. I would've never guessed you had such a hyped and energetic classroom manner. Very refreshing.
I was thinking of taking some time off from mathing for a wee while, but the CZcams algorithm served me this, and within a minute I was hooked. This is a blast. Love it! ❤️
You may think that no one watches these onsite lecutre videos you've made, professor - you cannot be any more wrong. I absolutely love these videos you've made; they make me feel like I'm one of your students in the class (especially with the cam that follows you around😂)
Thank you.
im taking math 1b at uc berkeley and this has really helped me!! i found that after watching your videos, i was really able to test my knowledge and get a+'s on my tests :) thanks!!
Watching this as I start my calc journey to get to D.E. Wish me luck.
I want to sincerely thank you for your video lectures and studying tips. I've fallen behind my studies severely due to multiple reasons, the pandemic being the catalyst for making things so much worse. I still try to cope with my failures and defeated mindset. I've been having a hard time as I am unable to attend classes at my university and I am going there only to take exams.Thank you so much for your help. You are giving me guidance with the material, hope and motivation for trying again.
I used to love solving differential equations in college back in 1970. Now I'm 77 and have forgotten it all...plus calculus, and a lot about algebra.
It's alright. ❤ 😊
Awesome and the best professor teaching the subject!
I have been struggling in D.E. lectures of my university since the last few weeks, but just one hour of your video(lecture) made things clear and approachable for me. Much love & support from Northeast India ❤️
❤️
Why on Earth didn't I find these Lectures before? You are so great, thanks!
I just completed my bachelors last year in computer science. You make me want to go back to major in math! Awesome teaching!
the camera quality is INCREDIBLE. i love how clear the video is and ur explanations actually make sense!
Hi, I was in the process of self studying "Introduction to Linear Algebra" by Strang and I've been stuck at section 6.3, "Differential Equations" for about a week now.
Maybe it's a prerequisite issue, maybe I'm dumb but every line feels like a gigantic logical leap and I was ready to give up on math altogether.
That's when I found your lecture videos.
Your clear explanations and dedication to ensuring class comprehension has been incredibly helpful.
Your energetic and dynamic teaching style keeps me awake despite my focus issues.
You sir, saved my math career.😤
Strang is overrated. He doesn't teach too well.
Wow just figured out you have lecture playlists. Just started D/E this week...think I'll follow along with these for an alternate viewpoint as I go. Enjoyed the first one!
I am taking this class and you are bounds better a teacher than my professor. Thank you so much for this! I will be watching this in the next coming week to be super prepared later on in the semester and get an A.
Awesome!
The math teacher I've always wanted...
And now I have!
❤️
Wow!! I love mathematics and you sir have just made me fall in love with it all over again
It’s a very smart class. When I took DiffEq in my undergrad, half of my classmates were wearing helmets and the other half were chewing their crayons during the lecture.
I was having a hard time with DEs, but after this very class, it all seemed much more clear
A M A Z I N G
Excellent!!!
Hello again Math Sorcerer, always great to get your excited perspective that I don't ever get in the classroom. I was especially struggling with the difference between linear and nonlinear D.E.'s so your explanation really helped! I've been sharing your channel with everyone I can that is interested in math because your enthusiasm really rubs off, even if it has been 3 years since the lecture. Keep up the good work:) 🐴
thank you!
@@TheMathSorcerer Also kinda nostalgic that my class is in the exact same room where this was filmed
Thank you so much for your videos! You make learning Diff EQ so fun!! I've been binge watching your videos all day so far!
Awesome !!
Hi.
I'm from the Philippines.
I'd just like to say thank you for your lectures. They are very helpful. Listening to your lectures is also relaxing because you seem really kind teacher.
Yours is my favorite mathrelated channel.
thank you so much!!
In my diff eq class we are now solving D.E’s that are separable, linear, or exact. I realized i needed to come back to this part of Diff eq to be able to identify wth they are before i can use a technique to solve them haha thank you so much.
Profesor usted es un rifado, gracias por los videos en verdad son de mucha ayuda para todos los que queremos entender al 100 el curso, saludos desde México
Saludos! Me alegro que Este video te ayudo👍
You have become my favorite CZcams math person!
This is fun. I only took DE about 50 years ago, so I needed a bit of a refresher.
love it so much when the professor loves his job and it shows very well
taking de next year, so this helps a lot in advanced reviewing
@@rohanpagapulaan5676what's your age?
It has been an stand-up comedy not just a math lecture .
Thank you for your work it was very helpful for me.
Lol!!
0 dislikes. Way to go who can dislike this professor? No one.
❤️
Love his teaching style.
carajo mi amigo nunca habia visto un profe tan bueno con tanta pinche energia, eres un crack hechicero de la matematica
Without the pressure of seeing Differential Equations for the first time (1982) along with my Physics Courses, watching this it great fun!
Wow 1982!! So cool!! Ya it's always way more fun when there is no pressure😁
I love his teaching style🥺
I spent lot of time during 2002 by reading books , very difficult in India, few clever students could only understand. Now everyone can attend classes from best teachers. Thanks to the evolution of Technology
I wish I could take your classes. You are so dedicated and enthusiastic. Thanks for posting.
Aww thank you. You are welcome😃
I just finished calc 2 and im going to take doff eqs and calc 3 next ssummer. Thank you so much for posting these lectures
probably the best math teacher on CZcams.
We need more ppl like you sir
Good presentation. I can now enjoy O.D.E lecture. Thanks so much
After watching professor Leonard up to calc 3, your going to teach me the higher math! Thanks. Love your vids
Edit: Dang, I thought you had a lecture playlist of Real Analysis :(
Wish you were my prof. I've already gone through diff eq, but I came to watch just cause you're so entertaining!
Thanks! 😃
Wow you really are an Amazing teacher
you are such a fun teacher! I see a few empty seats near your desk, plz don't mind if I occupy one of those in one of your lectures😅. I wish my teachers taught me like this. All they did was provide a mathematical definition (which I barely understood and they didn't bother explaining in a simpler way), a few formulas and some practice exercises. No further explanation about how it relates to the past chapters or how are they used in real life etc etc. Recently I started studying maths out of personal interest and sort of a hobby and the first youtube channel I visited was yours. Took your advice and suggestions, revisited the precalculus topics and now I'll be starting with calculus next week.
Thanks for the motivation!
This camera system is nice, it’s like being there in class with the other students!
This makes me miss college a lot. I graduated over a year ago with an EE degree. I got a pretty good job but I feel like doing graduate studies in applied math. Probably would have to take some remedial courses though (Advanced calc, etc). Wish more universities offered night classes for workers :/
I love your energy and your humor!!! Is the homework available somewhere? I want to take your course for fun and the challenge!
Thank you!! It is not sorry.
Absolute baller professor. Wish I had this guy
❤️
Wonderful enthusiasm.
I think everyone passes through here should do like and subscribe.. thank you doctor/professor!! I don't know
I really like you.. I wish that I could be part of your students in the class. They're lucky!
Great and Every Intresting class to learn D.E .I like the way of Teaching. Thank you very much sir
Thanks and welcome:)
🎉🎉 you make the laborious task so celebrative 🎉🎉
I would hire this guy on the spot!
This is the funniest lecture I’ve ever seen. Thanks for teaching me what my actual teacher hasn’t been able to do in over 4 classes
:)
This is great! You’re an amazing and passionate professor!
Thank you!
Your energy is awesome, math is supposed to be fun
I am a mathematics education student. Thank you sir for the video. I hope there is a translate into Indonesian. 💕 and i love all your videos sir. ☺
Amazing course thanks!
You are welcome!
This lecture is awesome
amazing video. straight to it
I haven't started any calculus course but I understood the lecture,you are incredible Sir
Excellent
I really appreciate you sir
The best teachhhher ever ❤
thank you:)
summer prep for DE with the math sorc, huzzah!
Hehe
27:11 I think it's called family instead of set because a set can't have repeated elements while a family can
Encouraging professor to average students!!!!!!
The difference between your videos and those in my channel is that you'r are a brilliant guy😂
You are amazing thank you so much!
You're so welcome!
Amazing just amazing 🤩
Thank you ❤️❤️❤️❤️
this was pretty good thanks :)
Rectangular b/c the asymptotes are at right angles.
Thanks for doing these. Hard to find good DE videos.
My pleasure!