TabletClass Math www.tabletclass.com learn the basics of calculus quickly. This video is designed to introduce calculus concepts for all math students and make the topic easy to understand.
I took Calculus in High School. Got a D. Had to take it again first semester of college. Got a D. Had to take it again second semester. On my first day in class second semester, the TA asked me to meet him after class. He asked why I was having problems. I explained that I could do the math, but I didn't know what I was doing and why it was important. This led me to using the wrong rules on problems. He explained essentially what you show here, but only in about 5 minutes, since he knew I could do the math, but just had to understand the why. I never went back to class. Never cracked a book or studied. Just showed up for the tests. I got a B. Unlike the full professors I'd had in my previous classes, this TA knew how to teach. He simplified the subject matter in 5 minutes that two full professors couldn't teach me in a year. Nice job here.
I had the same problem in college. The prof did NOT know how to teach. There's an art to teaching, and at research schools, many profs have no desire to teach to undergrads, nor do they care to learn the art of it.
I was given 25-35 formulas to memorise and plug them with techniques result was I did not understand what the f is happening I could not understand the purpose of all this others around me just stuffed and spat out on paper it was an traumatic experience 😢
Same. I could do the math, plug in numbers and letters into where they needed to be, follow the order for the formulas, and do everything right to come out with a correct answer, but I never understood why it was important or what I was even calculating; I did math without it making sense. Because nothing made sense to me, none of the formulas would stay in my memory and I was always confused when doing it on my own. Each individual lesson I'd get passing marks on my homework and in-class assignments but then four lessons later during a test I would bomb every section as if I'd never learned any of it, because I kind of hadn't...
People get intimidated by math. I know I did. I’m a professional engineer, graduating from UC Berkeley in the late 70’s, I had a very successful 40 yr career. I took 4 years of math in High School, it wasn’t pretty, I just couldn’t truly understand it. I took A2, Trig, Analytic Geometry, and 4 calculus classes in college. Many people, especially boys’ brains aren’t developed enough to fully grasp math. Plus they tend to be restless and don’t have the required patience (If this is you, don’t worry, you are very normal). So they start to doubt themselves and hate math because of it. It happened to me. However, once I got to college, I was ready to tackle it. Don’t get mad at math, get even… when you are ready. I graduated at 23 with an Engineering degree from Cal because I didn’t give up. You haven’t failed until you stop trying. Of Course I had to go to JC first, but you do what you have to, to achieve your dreams.
I'm in that exact same spot. I'm a meteorology major & have to take 3 Calculus classes and the 3 prerequisite classes to get my degree, and I'll be honest, this first class already has me thinking about withdrawing.
Thank you for this. I'm 79 yrs old. I took up through Trig in high school but have never known what was involved in Calculus. I understood what you were saying, I appreciate it. It's not scary at all. lol Never too late to learn.
IF NORMAL lesson period is 70 minutes like at my school then the same lesson length at TabletClassMath the lesson would actually be 147 minutes if TabletClassMath time units are a CONSTANT right?
I'm a 9th grader here from India. Mathematics, physics, and astronomy are all very interesting to me. I will study harder to know more than anyone can at my level and make a significant contribution to the unanswered questions about the cosmos...
That's wonderful! Best of luck to you. And while you're at it, know that you will completely annihilate now, and later own every dopey American kid wasting their young lives on facebook and twitter.
I'm an retired engineer also and use calculus every day, for those who took classes before learn integration and derivation is not understanding calculus that is just algebra manipulation. When you understand calculus then you applied in everything you see just because you see what others can. Excellent video
Many years ago, I thought game development would require no math. Now, I'm having to learn calculus to put a blue and red circle around the planets for my space game.
@@Carlbarl. Indie dev, and it is not close to being done but I have worked for months and wrote 1,800 lines of code. When it's done, it will be released to the Steam store.
@@not.djkhalid6860 C# and a bit of HLSL. C# isn't bad when you get used to it, but HLSL is a nightmare no matter what. It's only used for shaders, though.
The derivative would actually be zero because derivatives calculate the rate of change of the variable in the function, so the derivative of any constant is zero. Another way to understand it, is to understand that the derivative gives the slope of a curve at a single point. Since the graphs of constants are horizontal lines with zero slopes, the derivatives will be zero.
@@vectork3 No we ait chilling! that dude need some education, let me make that clear: The derivative would actually be zero because derivatives calculate the rate of change of the variable in the function, so the derivative of any constant is zero. Another way to understand it, is to understand that the derivative gives the slope of a curve at a single point. Since the graphs of constants are horizontal lines with zero slopes, the derivatives will be zero. 😌
As someone who is interested in physics, only in middle school, and has never learned a thing about calculus, I appreciate this video very much. If only my math teachers could explain things like this.
I took Calculus twice 6 yrs ago. I can’t believe I have not seen this. Had I seen this, I wouldn’t have dropped the 2nd class. Well I’m going to attempt it again and I have a better understanding of it now. Thank you so much!
Never since the epic horror movie The Brain (and who the heck was the Brains behind that gem?) has a comment section been so monolithically predictable.
I have studied calculus from high school until I graduated from University with master degree in engineering, once I start working in my career I have never used calculus until today, it’s been 26 years since I got my master degree but calculus was not really hard class , all you need to do is to study Was another subject that I have ever hated called Probability all I remember about that class someone rolled a dice another guy flipped a coin while the third one had colored marbles trying to figure out which colored marbles he may pick!!!!!! Education is blessing no question about it To be proud of yourself, to be great asset to the society and to make your parents and loved ones proud of you I always wished there is some guidance to help the students to know how important the subject that you are studying will be towards your future career Sadly I have never got lucky with a teacher or a professor he was kind enough to help us learn more than he was enjoying seeing the whole class failing Lord have mercy the final exam he will be revenging from the students with kind of questions that we have never seen during the whole year and he will be proud of himself to see how many students had failed his class I pray to God no one on those days goes over what I went through
I have always had the deepest curiosity, respect and love for Mathematics. I graduated college in 79 with BS in Accounting. I left off at basic Calculus with a C. That’s because I got lost at derivatives and limits. Very frustrating because back then, math didn’t wait for you to catch up. And admittedly I’m a 2-dimensional slow learner. But after I saw your video here at age 63, I GOT IT. Thank you so much. My curiosity continues to burn on the language of the Universe. I’ll be able to move on in Calculus and beyond, now that I’m retired. Thanks!
I'm in my 50's and if we had RU-vid in the 70's and 80's...But we did not, but at least now, I have been able to teach myself the metric tensor., which has helped me to understand GTR. Just like you its something I will always love.
I blame your professors. They assumed that you already understood the principles because they did, or they never understood the principles themselves, just memorized the rules, and parroted them to their students without understanding the principles they were teaching. The reason I know this is because of the irritation and even anger my teachers expressed whenever I asked Why a certain formula worked, or how it was dervied. Shame on them, and shame on the school system that fostered that mentality. Even Carl Sagan said that when he was in high school and college, the math professors taught purely by rote, and the great physicist Richard Feynman claimed that he had to teach Himself math, and that if he had tried to learn from a college professor, he never would have understood math at all. He didn't have a high regard for school math teachers. It's very rare to find a math teacher who is able to explain Why math works, or even understands that students have the need to understand why it works.
I'm 77yo and I've been trying to learn calculus since I was 18. The first course I took in college was taught by a brilliant mathematician who lectured for 3 hours non-stop. If one of us asked a question at a first or second floor level the answer came back at the 106th floor level, only 3 kids in the class could understand him. It was an exercise in total confusion. Differentiation I learned from a physics physics professor at the U of Wis in the student lounge when I was a grad student in psychology a few years later. (I started out in chemistry). What he taught me, in 15min was essentially exactly what you said in your presentation, where were you when I was in school??? LOL. I've still got problems with limits and integration. I hope your lessons will help. Thanks for doing this.
Not all schools teach or mention calculus. My advanced liberal arts school was heavy on reading: English grammar, then after an hour, literature for an hour beginning with a couple weeks of Old English. Then Chaucer for a month followed by several Shakespear plays ( much to memorize) with the spelling and grammar and meaning. Moving forward to Hedda Gabbler, Hemmingway, and world literature. Every day. Then after lunch came 4 years of Latin, with a seperate Spanish or French class. General Science, biology, chemistry and physics in 4 years. Geometry, algebra 1, 2 then trig in 4 years. No mention of calculus. Oh 4 years of ancient, world and US history. And as seniors, we had a few weeks of classical Greek intro. We were well equiped to become history, latin and english majors. Sadly i chose engineering and was in trouble with calculus. Prof said here is the book. I am a prof. mathmetician researcher and it is an insult to be forced to teach freshman and i won't. Then slept through each class. I am not stupid, had a year of analytical and spherical geometry in the summer at a local college, with an A. Took me a long time to get calculus. The terms are misleading to an English major. Your class would have been the key to understanding. You gave your listeners more in 20 minutes then i got in a year with the arrogant fool of a teacher. Thank you.
Still think math is easy and I was an electrical engineering major with a math and cs minor. Currently a grad student in analog design. Calculus is the most basic thing to us
I'm trying to become a mechanical engineer and I'm terrified for college calculus, I had a rough teacher for precalc and it almost turned me away from a math major forever. I'm trying to get back to my love for math before I go to college and this video has helped me immensely
I love math too and a teacher completely ruined it for me, but I switched to homeschool when covid happened and I have my love for math back, I hope you do too. I'm also trying to become an engineer, but I'm debating on becoming a mechanic though. only because I love cars and stuff, but I know nothing about them haha.
FooBar Maximus I agree. I was lucky to have an AP Calc teacher in high school who would take the time to explain concepts in understandable terms to almost everyone. He cared about his students succeeding and would personally explain everything in detail but also simplified to those who didn’t get it. I can’t imagine how much harder it would have been with a teacher who only expects note-taking, problem solving, and a pass or fail on quizzes/tests/finals.
@@foobarmaximus3506 this is a very unfair comparison. Pre-school stuff is way easier to learn and teach. Teaching someone how to do 2x2 is not the same of teaching someone concepts and theorems of calculus, or algebra, or number theory.
@mabrown5000 You got that right. When I took calculus in college a long - long time ago, I learned that it's simply algebra with some additional techniques that can be used to find the area under a curve and a lot of other shapes that can't be solved with algebra. All things considered, if you have a decent handle on algebra then it's fairly easy. At least I thought it was. I also had a really good teacher that didn't teach from the textbook. He used his own notes that he had built up through the years of teaching to present the material in a way that made the concepts easy to understand. From that, doing the problems in the textbook weren't that difficult. Calculus was also the only math class I took in high school or college that I got an "A" in.
False, maybe basic calculus, but when you get into differential equations where you're solving PDE's or Probability Theory where you're using integration by parts to find the CDF, at that point its more than just algebra with tricks, but yeah, maybe calc 1, differential calculus is just algebra with tricks.
For those who got upset by the length of the video, he actually successfully explained it in around 10 mins. Somewhere around 11:57 he ended his explaination and followed with a second example. thats why its longer than it was said in the title.
But he didn't though. He spent about 10 minutes explaining that calculus can solve for area and volume and the rest of the video explaining that it can be used to find slope. 3 separate functions and it took much longer than 10 to get there. He even me toned that it was well over 10 minutes towards the end. Also... pretty good explainatio. I enjoyed the video.
@@thanosnoctem4473 exactly! That's what's frustrating. " I'll explain that in a minute- we'll get to that in a minute- but before we get to that- which will be too long to explain right now..." That type of filler talk is infuriating. It's a good video otherwise. But he has to work on his execution.
Nice work. I’ve dissed Calculus for 50 years after I got a D in it. Now I understand that I can calculate the slope of that unhappiness, if it could be quantified. I applaud this video. I was wrong, it’s not useless. My study habits were.
I did calculus at school but that was over 35 years' ago and now I'm teaching Maths. Your video was perfect for me! I'm British btw so when I say school i mean up to age 18 when I did A'level. Thanks a million!
Where the hell were you 50 years ago when I flunked out of college calc? With you as my teacher, I would have been able to make something of my life instead of just being a clerk all those years. I'm investigating math now because the failure in my youth still bothers me plus they say that exercising the brain helps ward off Alzheimer's disease. Maybe, if the Lord makes me come back to this world, some of this math learning will stick and I will be more successful in my next life. Glad I found your video. Now, it's just a matter of practice.
Actually I flunked out of basic math in 9th grade and by the time I was 22 was working in the field of Geodesy. Don't blame your teachers, your wasted youth or anything else, it's a matter of WILL.
35 years ago I passed Calculus but it still hunt me today that I never understood the "why". I just plugged in numbers on formulas that allow me to pass the class but never knew why. This was extremely inspiring and I feel that if more people understand the "why" or the application of math there would be a lot less "I hate math" kind of people. For those of you whining that the video was more than 10 min you are just looking for the easy way out in life. That's why you are where you at!
Absolutely spot on. My teachers can never tell me why? Only how to solve the problems. I have a hard time with college algebra and calculus because no one can tell me why that certain formula is and how you get the answer
I think I can finally say I understand calculus ! I was off school for 6 weeks just when they started calculus. I later learnt the steps to take to do the sums, but think I missed the explanation of what we are aiming to achieve i.e. the link between the steps we take, and why we do them ! Now it finally makes sense to the point where I think I actually understand when to apply calculus in scientific situations. Thank you so much.
At 63 with a a degree in applied sciences, I can repair electronics, set up computers from out of the box. I had a seventh grade education before going to a juco in my area. I kept asking myself, when will he plug in numbers to one of these formulas? I had a stroke 5 years ago and my mental capacities remained slow. Formulas look just like formulas, until you plug in numbers. I learned something. My curiosity is now peaked. I must learn more! Thanks.
What makes Calculus complicated is not understanding the basic fundamentals of Algebra and Geometry. The idea of Calculus is simple enough but it requires often understanding and solving rigorous Algebraic and Geometric problems. I took Calculus years ago and decided in Calculus 2 that I couldn't go on because I really didn't understand it, even though I got a B+ in the course. I decided to not pursue anything to do with Mathematics, even though I did like it. But as I reviewed Calculus over the years, I wondered how I even got as far as Calculus 2 after discovering my lack of understanding of the most basic Algebraic and Geometric principles. I guess I was able to follow the dots but I never was able to connect them. It doesn't do any good if you don't understand what you are doing because you will not be able to apply it. My advice is to understand Algebra. Mathematics is about building relationships. Some people just can't get beyond 1 dimensional thinking. You have to begin to look at simple relationships like the reason there is Pi is because the circumference is 3.14... longer relative to its diameter. It compares their relative lengths. As simple as this is, people have a difficult time understanding this simple relationship because they are unable to compare things and are fixated on a 1 dimensional level. Most people function at this 1 dimensional level very well. They say they they don't need Algebra but yet the doors to the Sciences, Technology, Engineering and Mathematics are completely closed to you. I always wished that Art was taught in conjunction with Mathematics in the Elementary schools. Art can nurture your mind to be able to imagine form better, as well as to improve imagination to allow yourself to be creative in your thinking by seeing Art also an exploration in relationship to go beyond that 1 dimensional thinking but that is another story.
In my brain, calculus is art🤔 and yet I also truly believe many people fail to realize they can go beyond level 1 dimension of thinking in calculus. We limit ourselves not knowing how intelligent we were made to be. We limit ourselves because we believe we have 1 dimensional thinking yet we don't. It's all a matter how you truly care for some thing. For me when I dont understand something regardless of how hard it is I keep pushing because I have to know for what ever reason, and I get it soon enough. So if you really care, you'll understand more than you thought you could know.
I appreciate the tutor's simple way of explanation. We could not see the points when he was plotting due to it's size and could not able to read his handwriting..
That was my main problem with learning all math, trig, geo, algebra and so on. I always knew that math has a deeper concept than just using formulas for certain equations. It has helped me so much in the long run, and understanding is such a cool experience. Sadly, not every teacher knows how to really "teach" so to speak
Thank you for a basic understanding. My daughter is minoring in mathematics, calc 1,2,3 while majoring in biology. Honestly I didn't know calc 2 and 3 was a thing! I am a blessed and proud dad and want to understand a bit of the math.
The thing that works for me is explaining integrals thusly: Take a fuction of velocity versus time. The area under the curve is the total distance the car has travelled. If the car is steady at 100 km/h, for 2 hours…. You multiply the height of the curve 100 by the width 2 … 200 km. Makes perfect sense.
You don’t understand it if you can’t recall it. What your saying is you’d rather have a surface level/big picture understanding of something (presumably because you’re too lazy to fully study the subject or you’re just not inquisitive enough to care or you’re simply not smart enough). It’s easy to watch a 20 minute video. Knowing how to do calculus is not easy. You can watch this video but if I asked you how to take a derivative, you wouldn’t be able to. That’s not understanding. Like another user said, that’s like thinking you understand how to ride a bike because you watched a video of someone doing it along with a short documentary on how a bike works.
@@mcbaggins12 You read a whole lot into what the OP posted... For me, getting the big picture first makes learning and recalling the details a lot easier. It makes the details much more meaningful compared to trying to remember lots of facts in isolation. People learn things in different ways. Don't know why you had such a harsh reaction to that...
@@jambaby4999 The OP said he doesn't want to learn. He wants to "understand." Of course you learn by getting the big picture first before the details. OP is saying he will get the big picture, then screw the details, and assume he "understands" a topic as a result. It's lazy, pseudo learning. Theres an implication that traditional classes and learning is bad because it has so much detail.. OP is likely just too lazy or not smart enough to learn calculus but thinks that watching these videos once means he would get an A in a Calc 1 class. He's the type to get a C and then blame the professor for it being too hard (when really calculus is just hard).
This was awesome. Thank you so much. Math was a passion of mine for most of my student life but I haven't needed it to this extent in quite some time. I appreciate your overview.
Americans When the trees start speaking vietnamese Russians when the snow starts speaking finnish Highschool students when the math start speaking greek
My college calc professor (two classes) taught in the same manner as you. Very relatable and understandable. I got an A in both, because of the professor being so good at explaining the concepts.
Lucky you! Unfortunately that was not my experience in my last year of high school, which led me to use my girlfriend's (she was in a private school whereas me in public) assessment paper (not exam based) and "reverse engineer" to understand how the conclusion was determined and then write my own assessment. I past calculus, however my best mate and his girlfriend were at the same school as me and took part in this exercise which led to our 3 papers being similar, resulting in the 3 of us being called individually into a maths''s review committee to explain our results. My mate's girlfriend was the only who failed because she couldn't explain how she had come up with her results. Cheers
No matter what commenters have to say. I really enjoyed watching your video. I don’t know how quickly the video passed. And I surely learnt from this. Thank you.
@@_IvanMichael Learnt however is more common in British than America and Canada and is considered informal. Learned or Learnt: ... Learned is used as a verb as well as an adjective but learnt (with a t) is only used as a verb.
One of the scariest moments of my life (including my military service) was being informed I had to take a Calculus class to receive my BS in Zoology. Thanks to a great professor who somehow made it understandable, I passed on the first try.
@@brendanhickey4955 Hi Brendan- The best advice I would offer someone that has a fear of math ( and I did- I took my last math class before college as a high school sophomore as all you needed to graduate was Algebra II/Trig) is to try and relax. That is the most important thing that college professor taught me. I would be so psyched out that I would almost have a panic attack taking quizzes and tests! Undergrad Calculus is basic, and you learn it a little at a time. So one needs to study regularly and consistently. DO NOT try the old “cram the night before the test technique,” Calculus is not a discipline where you can bs yourself through a test like a Sociology class. You either know it or you don’t. Take the medicine a small sip at a time and you will do fine. BTW, to all the Sociology/ Philosophy graduates that may read this, it was not my intent to denigrate your area of study. My point is the hard sciences (like chemistry, genetics, anatomy, physics, etc.) are not subjective. You have to be able to regurgitate the facts (solve and insert the answer), not go on page after page on an essay test.
If you were my calculus teacher in high school I would have probably been an engineer or architect! So clear and comprehensible -when taught well! Thanks for taking the time effort to demystify these concepts!
I agree too! Those public school math teacher just show up and draw a few things on the board without explaining what is it and gave us homework. I end up going to tutoring. I realized how they want you to be dumb down.
I am 22 years old I’ve been working for 3 years as a Web Developer and about 2 years as a Software developer now. I have no prior higher education but I am planning to go to college next year to get a bachelor in either Computer Science or Aerospace Engineering. All my life I was really struggling with math and wasn’t able to grasp how it’s important but now after about 5 years of experience as a developer and stumbling over multiple different complex topics I finally understood why it’s so important and that it’s just learning and applying rules to solve problems rather than pure number crunching. Thank you for creating this video!!
This is why, while I was good at other kinds of math in school, I never understood calculus fully, because apparently the integral of f(x) where x is a value representing my patience, x starts at ten, threatens to go on to infinity, and ends up having an actual value of 21.95
Fantastic explanation. I was introduced to calculus 50 years by a teacher called Mr Choduric in a school in East Finchley ,London called Bishop Douglass. He launched in, violently by presenting an equation and the rules to differentiate it. NO basic explanation whatsoever. He succeeded in scaring the crap out of the class. It took me 10 years to get over the shock. I wish Mr Choduric could have used your introduction. Mr Choduric took the fun out of maths for most of that class for ever. Thankfully I fought it and subsequently succeeded in engineering. Mr Choduric will be an old man now. If he reads this I'd like him to know how destructive his teaching method was.
Math is one subject that i always wanted to revisit. I am starting out again with grade 9 math and will pursue it all right through what is taught at bachelors level. Its fun to study something when the only compulsion is to enjoy whatever you learn.
Calculus is basically the study of two problems. The slope of the tangent through a point in a graph, aka the derivative. The area of a region in a Cartesian plane where one side is not a straight line aka the definite interval. The derivative and the definite integral are actually inverses of each other.
Well said mate! Me...I also love trying in my head to figure when rotations(or other transformations too) are done on a plane giving a 3D shape...then of course we get those cross sections at various angles which add a whole new level of fun!....
It's all about the teacher, struggled with basic algebra in middle school but once I had an amazing teacher in my freshman year of high school I had no issues all the way into ib calculus
@@user-hz5yt1kk7k Not really, generally middle schools end off at algebra 1 or geometry, they rarely go into trig or alg 2, and definitely not precalculus. Of course, all middle schools are different.
@@user-hz5yt1kk7k in what country? 😆 my 17 yr old took algebra.and algebra 2 required for high school graduation. for me, it was algebra 1 and geometry to graduate. im 35 now, back in school for Engineering and I'm JUST NOW learning TRIG/PreCal.
Thank you so much!!! I have always wondered about the value of calculus. You, Sir, have done a fantastic job of demystifying this branch of mathematics's basic concept and importance! Thanks again!!!
I was from a broken family setting where algebra and calc weren't talked about much but,,,,,,I wanted to become an architect and what I found out on my own is that you need to take calculus whether you like it or not. take it ,, that's all you won't regret one second if you stick with it and heck you might like it!!!
Thank you so much for this explanation, I am 12 and have had high math grades, this and a few more videos of yours helped me understand many ideas about maths, can’t thank you enough.
probably the best video on the internet for getting an intuitive layout of what Calculus looks like. now I have to jump to "probability distribution" to find out this "probably" !! 😛
I am a physician who has saved innumerable lives. I am the son of a mathematician. I am the brother of a physicist. 49 years ago I got a C in Calc 101. I was getting an F in Calc 102, until a police drug raid in my university led to riots and I was able to get a Pass (which to this day I'm very proud of) in Calc 102. Where the hell were you when I needed you?! I got my mother's mathematical gene set! To this day, my greatest academic failure, and there were no other failures, near failures, close to failures in my entire career, was calculus. It made no sense whatsoever! I'm going to repeat this video, and with God as my witness, I will be able to pass Calc 102 with flying colors before I leave this earth!
I dropped the engineering degree for a tech degree because of calculus. I worked 25 years as a designer including a large engineering design firm as senior designer and now have my own company, yet still feel the failure.
I'm an engineer with a strong background in maths and physics; I was watching this video since children were. I think this is one of the most simple and effective way of showing how derivation and integration in calculus can be a real example scenario, not just numbers or whatever theory could give an obfuscate understanding. Great explanation, everyone scared about derivates and integrals should dedicate some time to look at your work, impossible to end without having a clear vision of the basics..... and you know, getting rid of fears generated by strange symbols and similar things is the only barrier to destroy for a human race which starts his life playing three-in-a-row, rubrik cube and other logic games. We're mathematics by nature, sometimes scared by symbols, but these concepts are our alphabet to read our universe. Everyone knows how to read it ;-) Great job. PD for all commenting on video duration, useless observations in my opinion, time is relative and the deltas containing part of the matter can be an infinite amount of minutes.
Engineers and mathematicians do mot always see eye to eye. Thy (mathematicians) say we abuse their discipline; but we are just putting it into.goot use...
Spoken like a true engineer 😂 You are right though... the symbols can be a problem. Example: when I went to college I was forced to memorize the delta-epsilon definition of a limit. I didn’t lean a damn thing and got through Calc I by rote. My daughter’s AP Calc teacher taught limits first and only after the students got the idea of what a limit really meant... did he introduce the classic delta-epsilon definition. It opened my eyes to what calculus was really about. She has a BA in math and economics and I took every math course with her. I see the beauty in the Fibonacci numbers/Golden Ratio. I understand the usefulness of applied Fourier series. I might have actually stayed in computer science had it not been for that professor that saw no other way to teach but delta-epsilon.
I found it very useful when designing operational amplifier circuits. Probably why they are not used very often automotive circuits. I guess a few hundred thousands lines of code is lighter. But does it draw less current?
I'm a 12 yr old 8th grader who wants to be a mechanical engineer. And is learning calc early cuz I wanna be just like my fav Book character and cuz I like engineering.
This is my biggest fear like I'm focused as hell but when I looked on the other part of my phone and look back to the discussion it's already a crime scene.
