Calculus Visualized - by Dennis F Davis
This 3-hour video covers most concepts in the first two semesters of calculus, primarily Differentiation and Integration.
The visual and animation style is intended to be informative and provide insights into the logical reasoning behind the rules and formulas in calculus.
Timestamps
0:00 Can you learn calculus in 3 hours?
2:23 Calculus is all about performing two operations on functions
3:32 Rate of change as slope of a straight line
5:37 The dilemma of the slope of a curvy line
7:04 The slope between very close points
11:30 The limit
15:36 The derivative (and differentials of x and y)
21:48 Differential notation
27:58 The constant rule of differentiation
29:15 The power rule of differentiation
35:36 Visual interpretation of the power rule
39:19 The addition (and subtraction) rule of differentiation
41:34 The product rule of differentiation
43:08 Combining rules of differentiation to find the derivative of a polynomial
44:53 Differentiation super-shortcuts for polynomials
48:03 Solving optimization problems with derivatives
52:46 The second derivative
59:59 Trig rules of differentiation (for sine and cosine)
1:05:54 Knowledge test: product rule example
1:06:32 The chain rule for differentiation (composite functions)
1:15:23 The quotient rule for differentiation
1:19:04 The derivative of the other trig functions (tan, cot, sec, cos)
1:20:55 Algebra overview: exponentials and logarithms
1:33:12 Differentiation rules for exponents
1:41:33 Differentiation rules for logarithms
1:45:32 The anti-derivative (aka integral)
1:46:21 The power rule for integration
1:48:32 The power rule for integration won't work for 1/x
1:52:37 The constant of integration +C
1:57:26 Anti-derivative notation
1:59:59 The integral as the area under a curve (using the limit)
2:12:05 Evaluating definite integrals
2:13:11 Definite and indefinite integrals (comparison)
2:15:30 The definite integral and signed area
2:18:10 The Fundamental Theorem of Calculus visualized
2:21:37 The integral as a running total of its derivative
2:24:25 The trig rule for integration (sine and cosine)
2:27:07 Definite integral example problem
2:32:53 u-Substitution
2:42:05 Integration by parts
2:56:03 The DI method for using integration by parts
PROMISED LINKS:
Binomial Expansion (with Pascal's Triangle): • How to expand (a+b)^n ...
Trigonometry Series (by me!): • TR-00: Introduction to...
KEY RESOURCES FOR PRACTICE:
Steve Chow: @blackpenredpen
100 Derivatives: • 100 derivatives (every...
100 Integrals: • 100 integrals (world r...
100 more Integrals: • 100 integrals (almost ...
DI Method for Integration by Parts: • integration by parts, ...
Other Great Calculus Resources
Grant Sanderson: @3blue1brown Grant is the grand master of math visualization
Essence of Calculus Series: • The essence of calculus
Michel van Biezen: @MichelvanBiezen (iLectureOnline)
Huge calculus playlist: • Calculus 1 CH 3 Deriv...
Mathologer: @Mathologer
Why is calculus so... EASY?: • Why is calculus so ......
The Organic Chemistry Tutor: @TheOrganicChemistryTutor
Learn Calculus Fast playlist: • Calculus 1 Review - B...
There are lots of good resources on KZread in addition to these.
Key Words:
Maths, differentiation, derivative, integration, integral, limits, tutorial, overview, proof, proofs, animated, animation, explain, explained, A-level maths, O-level maths, IB math, power rule, product rule, quotient rule, u-substitution, integration by parts.
Пікірлер: 322
Vote for calc 2 calc3
@megaanubis5362
Ай бұрын
Gradient and Lagrange 🥵🥵🥵
@alphazeta321
Ай бұрын
I wonder how this calculus might be so easy in a fun way. super explanations.
@antreaslouca726
Ай бұрын
Yes please
@keepgoing8252
29 күн бұрын
Calc2 Calc3
@L17_8
29 күн бұрын
God sent His son Jesus to die for our sins on the cross. This was the ultimate expression of God's love for us. Then God raised Jesus from the dead on the third day. Please repent and turn to Jesus and receive Salvation now before it is too late. The end times written about in the Bible are already happening in the world. Jesus loves you with all His heart ❤️ but time is running out.
What a fantastic video. My biggest regret in life is to be born and raised at a time where internet did not exist. I would have been a much better students earlier on. I struggled in school as a teenager. Now in my 50s I am having a blast learning on my own a bunch of math and physics classes. Thanks youtube, and all the wonderful teachers like yourself sharing their talent for free here.
@traveltoeurope007
Ай бұрын
I swear I was thinking the same thing 😅
@StudywithmeinPakistan
Ай бұрын
Me too 😢
@sunnythebridger7529
Ай бұрын
Pls, I don't think you want to be born with label "gen z" or "gen alpha" stick with your head
@traveltoeurope007
Ай бұрын
@@sunnythebridger7529 but you guys got the blessing man !
@azizulhaouqe4150
Ай бұрын
Don't regret it.with all the opportunities I couldn't utilizes
I am a math professor at a community college. From now on, I would like to give my 1st semester calculus students your video to watch at the end of the semester as the best way to bring together the techniques they have struggled to learn all semester. You did a very good job.
@DennisDavisEdu
Ай бұрын
Professor, Why not at the beginning? It would be like a running start.
@BarbaraRademacher
Ай бұрын
@@DennisDavisEdu Why not at the beginning? Because the students would be overwhelmed with with new material; they could panic and drop the class. However, near the end of the class, they will see how every topic fits together like puzzle pieces forming a picture. Showing the video at the beginning and end of Calculus1 makes perfect sense. Watching your video was a terrific experience.
@DennisDavisEdu
Ай бұрын
Thank you for your kind words. I wish you and your students the best!
@codename-abdullah
Ай бұрын
@@DennisDavisEducan you make a video about Vector Algebra?😢
@L17_8
29 күн бұрын
Jesus loves you ❤️
I'm a math teacher and general math junkie, and it is always such an immense treat to stumble upon videos like these of such incredible quality. Thank you kindly for sharing your hard work!
@L17_8
29 күн бұрын
Jesus loves you ❤️
Dude, seriously, thank you ! I'm self-teaching maths in an attempt to get to university level, and I use KZread a lot to help get overviews of new subjects before diving into exercises. I really appreciate the time and effort you put into these videos, the colour coding, choice of words, structure of the lesson and topics covered, visualisations… All of it ! It's amazing ! I feel truly blessed to live in a time when this type of content is available (for free no less !). I definitely rate you up there with the best maths teachers / “visualisers” on KZread at the moment. Keep it up and know that it really is making a positive impact on peoples lives ! Much love. Rowan.
@SplashIs_
26 күн бұрын
You’ll get there brother! I wish you the best in your studies.
@SymbioticSense
26 күн бұрын
@@SplashIs_ Thanks bro! You too ! We're learning more every day 😉
This is a masterpiece. One of the best videos that I've seen on KZread.
You are one of the heros of YT, I'm so grateful for your time and energy to put these out for all.
Your trigonometry series was absolutely fantastic and helped me a lot. I'm going to treasure this series as well.
@webgpu
Ай бұрын
"was"? so it isn't anymore?
@paulskvorc3627
Ай бұрын
@@webgpu yawn, are you seeking attention on KZread, of all places?
Man, you have the real talent to make complex things simple (and not simple things complex).
After your superb trigonometry series I am very glad to see you covering calculus!
Get this man to 100k already.
@digguscience
Ай бұрын
yup, This channel really deserves to reach it
@DennisDavisEdu
Ай бұрын
Haha I couldn't agree more! Maybe someday!
@L17_8
29 күн бұрын
Jesus loves you ❤️
This man is not just smart, he is a genius. His explanations and visuals are the best. .This video is a Masterclass in how to explain very complex ideas in a form that most people can grasp. Thank you Sir. I am putting you on my Christmas list . . Forever.
@DennisDavisEdu
2 күн бұрын
Thank you so much for your kind words!
@alexeyantoshin3433
Күн бұрын
+ totally agree
Man! I love you, you already saved my life with your amazing trig series.. Thanks a lot for calculus. You are the best teacher ever.
The world definitely needs you, I know you mentioned you can’t cover higher mathematics but if u can collaborate with someone or something and teach in this same way would be amazing, because this is the exact way our education system should teach these things. I shared this with everyone I know and watched it so thanks for this! I understand but I really wish u would go beyond this too with some other mathematical people to make this a thing !
Let us all take a moment to appreciate the brilliancy of colure code which made us understand everything hatts off to you sir. This requires lot of hard work and you made it
@DennisDavisEdu
Ай бұрын
Thank you! I would be embarrassed to tell you how long this took to make.
@owaisahmedkhan8293
Ай бұрын
@@DennisDavisEdu7 months. I guess...
@paulskvorc3627
Ай бұрын
@@DennisDavisEdu worth every exhaustive minute. Amazingly concise and comprehensible. Thank you.
@vijaylaxmi6720
29 күн бұрын
Yeah
I studied this at MIT but your explanation is outstanding!!!
30 seconds in, I like it. Some people need these subjects visually explained. I'm one of those people. You make it click. Subscribed. Thank you!
hi im from bangladesh where we have a reputation of teachers never teaching the basics and just doing practice problems. it's so bad that if you sit down to learn basics instead of solving board questions it is considered a waste of time. we have two very important exams ssc(in 10th grade) and hsc(12th grade). in ssc your trig series helped me so much in understanding the fundamentals. Like none of my friends understand trig like i understand trig all thanks to you(i regularly preach your channel to them 🙏). next year we have hsc and we have differentiation and integration and i was looking for a good calculus series. the timing couldn't have been any better 😭😭💗✨
I really gotta say it..... Thank you so much for this... Was struggling to catch up with my class because I had lost any interest to study and now because of you I'm ahead of the class.... Im able to solve most sums without much doubt or problems at all ..... Thank you thank you thank you
This is the most clear explanation about Calculus I have found in KZread so far. Thank you for you time and effort to make this amazing visual lecture.
I am pretty sure Calculus isn't gonna be difficult after watching Dennis Davis video.
When we needed him the most he returned 🙏
I too am a engineer, electrical. I took calculus at the university 55 years ago. If only this video aid and explication was available at that time . . . . great job, Dennis. I'll have to take a look at your other videos.
This was so crisp and concise, what a masterpiece of explaining difficult things with simple yet precise language. Thank you for your hard work and thank the God for giving you strength.
Mr. Dennis … I am a retired engineer. When I am bored of movies, I look for math and science videos on YT. These videos keep my mind active and take me back 50 year to my university days (which were a lot of fun and hard work). A “Back to the Future” experience 😊. I agree with many others - you are a ROCKSTAR educator! OMG, I wish I had access to this type of information and education so many years ago. Thank you Sir for your hard work in making an exceptional learning video. Your efforts will pay dividends to all of us, no matter where we live. Kindest regards.
Thank you, Dennis! I've finally got it thanks to your video. Your explanation was clear and easy to follow, making the complex concepts of calculus much more accessible. The examples you provided were practical, and the step-by-step approach helped me understand the material deeply. This video has been a game-changer for my learning process. Highly recommend it to anyone struggling with calculus!
The clarity of this overview is incredible!
great Dennis being on the same side of the coin your initial enrichment of the topic is highly recommended and commendable .
"Modern math lectures need to learn these teaching techniques. Wow, you made world students proud that we have Dennis F. Davis!"
Oh my goodness.I needed it.THE BEST CHANNEL I HAVE EVER SEEN
Simply the best calculus ever, and you are not assuming anything about the prior knowledge of the learner. A marvelous representation.
I'm Jameel Hussain Khokhar, sir your video on calculus helped me alot to understand related concepts. Being Math Teacher I share this in my radius of students. Sir Stay blessed.
@webgpu
Ай бұрын
and I'm We Bg Pu. Ni Ce To Me Et Ya.
ABSOLUTE LEGEND!!!
Engineer Davis, whoever you are, you know your stuff Man. I sincerely commend and salute you. With brotherly affection from KENYA🇰🇪
Wish I had this twenty years ago. Excellent presentation. Thank you.
😭Dennis always has what I'm desperately looking for but always lack to find (especially on KZread)🙏😭God truly does know my heart!!
Bro, thanks for the time you’re spending to create this awesome content and give it to us for free. You are a true legend. Respect.
This is as close to perfect instruction as I have ever witnessed. BRAVO!
I aced calculus in college 25 years ago in college. Now watching this video makes more sense than all those 3 years of college calculus combined. So whoever finds calculus difficult you have hope by watching excellent teaching videos like this. Thank you !
Thanks Dennis for the immense job you've shared. The explanation and combination of other things to give this output is absolutely nothing short of hardwork. Thanks for engineering it all!
One of the best Calculus videos EVER. Crispy Clear!
I've been bingeing the Trigo series last year. I don't know how to thank you enough for covering Calculus! Thank you so much for this Sir Dennis!
Omgg, I watched your trigonometry visualized video like, 4 years ago. I have now passed 12th grade and finished Calculas 1. I still use the concepts and flashcards you taught in trigo. Thank you so much for your hard work
Amazing to gave you back! Your trig course was a masterclass in education + presentation; I still go back to it. I am so looking forward to completing this video course,
This is so good it's tragic, I could have been in an entirely different career if I had had such a clear teacher as yourself some 30+ years ago. What a marvelous video that will elucidate the many minds out there looking for such explanation your guidance will alter the course of many persons understanding and in some small way change their lives via the confidence they glean from this video.
Thank you for the video Dennis, I will update you after I take Calculus in the fall. I am not so afraid of failing now. I love how well this video is organized and will definitely use it to supplement what we learn in class. I pray you will always be safe and that you take care of yourself as well so you can make it to retirement and be an amazing and inspiring professor.
@DennisDavisEdu
18 күн бұрын
Yes I'd like to hear how you do!
You made me understand Calculus in english, even my teachers couldn't make me understand Calculus to me in my native language . Can you please make a similar video on Vector Algebra? It will be really helpful for my engineering entrance exam preparation of JEE.
This is perhaps one of the most useful video that I've seen for an introduction to calculus. I've gotten the math of calculus but never really wondered why the math works. This video needs to be watched by every stem student as of now
@DennisDavisEdu
29 күн бұрын
Haha that would be nice but I don't know how to make it happen. Thanks for your kind words.
Thank you Dennis - so often I find the most difficult part of Maths is the unnecessary verbiage of the instructor, concepts that can be grasped from simple minimal statements seem to work best for everybody - your careful choice of words that encapsulate those concepts and the timing and placement of them elevate your videos above others.
I surely wish I had this video when I was learning Calculus in College !! This explanation is SO MUCH BETTER / CLEARER !!! Thanks !!
I'm a slow learner, but I've tried to learn calculus several times. This is an excellent step-by-step explanation.
Along all calculus YT videos i've watched, this is the most intuitive one. Thank you so much po sir! From Philippines
Thank you for this remarkable video! Really enjoyed watching and learning from it! 🙏🙏🙏
one of the best explanation of the subject. Super high quality. Thank you very much.
Thank you Dennis, just so brilliantly understandable, esthetically insightfull, pleasing and interesting, the way you explain the principles, it captures the mind to enable beter understanding. Thank you dearly for sharing your knowledge, in a calm collective manner.
I love this kind of vid. When i was in high school i wish this type of videos exist so i can understand under the hood of math and physic, and now as a 3rd year comp sci undergraduate i get the privilege watching this as i am retaking my cals class😂. Thank you very much sir
People like you are incredible. Thank you for your time and effort!
I finished your trig series a few weeks ago. You are godsent! Thank you for this.
Thanks for this amazing video!!! Visualizing works(for me) so much better then abstract textual explaining! Looking forward to your new material!!! Thanks again
Really impressive presentation and exposition on calculus. Anyone can have a good understanding of calculus basics. Thank you.
Perfect visualizations ! Use of dark background and colors makes it so much easier to look at and learn.
Most videos start with these slices of an area under a slope and then making them smaller and smaller and then...calculus formulas! That's really frustrating. I'm so glad you did the slope calculation with a width of h step by step and came up with the derivative for a parabola, as if you were inventing it for the first time. I'll watch the rest of the video later. I want to savor this eureka moment first.
one of the greatest videos on youtube
Very important and interesting videos with all important topics and points putting together. Thank you very much for your hard work.
My prayers have been answered!
What a wonderfull video. So much content in one video, and with so much quality. Wonderfull work! Congratiolations !!
What a boss Newton was. ... Created calculus to figure out gravity. "This math I have is trash! I'll just create a whole new math that will work!" ... Mass respect 🤜🤛
@rutgersmit3383
Ай бұрын
Huh huh, mass... gravity... Hey? 😉😉
I literally just finished Calc 1 which made me prepared for Calc 1. I am redoing it for my own prep for Physics snd Calc 2. I needed to "see" this so badly, so thanks!!
My respect to you Sr. Thank you for sharing your powerful knowledge. The class and your voice is music to the ear. As extensive and complex numbers and formulas can be, I can easily come back to re listen such a golden video of you. Thank you!
@DennisDavisEdu
Күн бұрын
Thank you sandravasquez you are making me blush.
Outstanding! I am glad I found your Channel today.
Thank you so so much!~ I haven't watched this video yet, but I always recommend your channel to others after your incredible Trigonometry series !
You made this so straight forward. This is good…
Im about to take AP Calc AB and I think your video is going to help me a lot! Thank you so much.
amazing instructions . so much logical . even people hate math who like me can't refuse the tuition
Where's that guy who says to wake up to his *babe* because Dennis has dropped new video?
@squarerootof2
Ай бұрын
Don't expect to see that idiot around here.
@sassygrl5018
Ай бұрын
Good one 😁
@issasalifou5635
Ай бұрын
😊
@funnyguy4766
Ай бұрын
Its is a big waaao...I have downloaded this video...
Outstanding teacher in this video and all your videos. Keep up the great work
You explain it so well, I appreciate the learning!
Wow ! You're fantastic ! Your voice, visualization, explanation, .... so so good !.
This video breakdown is crazy!!!🔥🔥🔥🔥 Fantastic work!!🥂🥂
Thank you for your amazing explanation! This is the only video that gave me understanding of basic principles, despite me being a clinician that didn't t know anything about differentiation and integration 😅
this is beautifully narrated
I have watched your trigonometry videos and this video, just like them is absolutely incredible. The explanation in these videos is what i was looking for when i was learning(still learning). It's nothing short of a miracle that i stumbled upon your channel, It's a gem ❤. I have a request, can you please make a video about functions and limits just like this one, and also about linear algebra in context of computer graphics.
So happy to find this video, thank you so much
Most difficult thing to do is make things simple and this video did it extremely well. I watched this after 20 years of learning calculus and everything just made sense now. One request is, you have the class of problems which is solved by differentiation in the middle. If this can be made as introduction, it would help on why we need to learn this question.
Sir you made me to fall in love with maths❤❤❤❤❤❤💖💖💖💖💖💖
I wish I could such big work for other ppl
Going to do today what I’ve failed to do for 8 years: learn calculus. Went from thinking I wasn’t good enough for math to now thinking it’s just two more hours (already watched the first one 53:18 and understood all of it) Can thank the creator of this video but won’t. I’ll pay it forward someday in some way. But boy I’m just two more hours away from conquering my freaking demons
This is fantastic. More of this and more like it.
Your trigonometry videos helped me so much, thanks man
Best video I've watched so far
Wow, it's really good. It's very attractive and the AD is very interesting
Wow, great piece of work, thanx!!!
Thank you for educating us!
I have just started watching your video on Calculus. Based on the comments, I'm watching it with lots of anticipation and excitement. Just wanted to thank you for creating this fabulous video. Any future comments that I make should be considered as constructive criticism. My first comment is that you state that the course will start with differentiation, as do most other Calculus courses, but you don't explain why you're starting with differentiation. Even an explanation as simple as "we have to start with one or the other and differentiation lost" would suffice. But I suspect there is a deeper reason for starting with differentiation.
It is so good. Wish I had a teacher like that.
Yo man i am 14 and You made me intrested in science and maths and understanding calculus and TR
@DennisDavisEdu
Ай бұрын
That's fantastic! You gave me a boost for the day! I think you can learn anything you want for free online. I'm so glad you are taking advantage of your opportunities. With self-directed motivation you can learn anything and go far. Best wishes and good luck with your studies!
I enjoyed a lot learning from you.
Fantastic course, thank you!
ohhhhhh my gooood, that's extremely helpful, thank you very much to infinity ♾️
Man, you should start teaching all mathematical concept Including Algebra, Geometry, Linear Algebra. I mean the mathematical syllabus we need to complete engineering at university. Thanks for the straightforward scripts with great visualization