I watched your Calculus video's over the summer and I got 105%, 103%, 99%, and 90% on my exams over the quarter in Calculus 1. I can't explain how helpful your videoes have been to me in learning math. Thank you so much, I can't wait until I can become a patron!!!
I feel college algebra is more appropriate content, compared to differential equations. Students in college algebra are just at the beginning of their actual college math journey and they need the most help, as compared to someone in a differential equations course(they at least took Calculus 2). These are great content and I am sure they will help people for years to come, thank you for all that you do.
Professor Leonard, thank you for a clear explanation on How to Graph with Transformations. I realized that your method is not in any textbook, however it is really helpful in all levels of mathematics..
Please do not delete these videos. This is one of the most in-depth and helpful mathematics lessons on the internet, even better than attending college, due to the fact it's learn at your own pace. But i've got one question, do you have or can you find a way for users to be able to download all your content in case of RU-vid problems, seeing as videos can go missing after a while in some instances?
Professor Leonard i really want to say to you from my bottom of my heart thank you for your videos and your hard work and thank for you still uploading videos for 5 years ، i started my college this year and i found your channel it just amazing. I wish if it will be like a reference for the students in the future, i literally can find all what i need here, and the most important thing that you focus about the concept behind the subject, there is no word can express your great job!
...Good day Professor Leonard, First of all let me say that your presentations are all crystal clear. One comment to this presentation: Given at time 26:40 g(x)= 2SQRT(1-x) + 3, one could also first determine the domain of g(x) by setting 1 - x >/= 0 --> x
Finished your algebra, Calc 1, Calc 2, statistics and halfway done with you Calc 3 course. DiffEq is next, followed by Linear Algebra (which should be posted by the time I’m done with DiffEq). I use the lower level courses for training my guys in the lab. This precalc course should be a good substitute for trig.
@@ProfessorLeonard I respect your decision but as you started differential equations first, shouldn't it be given more priority?Also differential equations is way tougher so it would take time for you to record and for us to digest so it would be great if you please upload them asap as many people are taking it next sem..
@@ammishtandon4961 There are people who are new to calculus to like me, its not only for people who are doing calculus So its really helpful for people like us too
A very Merry Christmas and Happy New year to you and your family ... Sir !!! ... God always bless you all with joy , peace , contentment , togetherness and love ... 🎄🎄🎄 🎅🎅🎅 🎁🎁🎁
Professor, I love your lectures. You think you will be done with linear before February? I am taking it next spring. Without your lecture I will get a C. Please save me Mx
@9:00 How come the transformations did not apply to the origin (0,0)? If we shifted up and to the right, the origin becomes (3,2). But then when you compress by 1/2 shouldn't the origin be at (3,1), and following the reflection be at (3,-1)?
Mark Quennell thank you, I was going about it the wrong way; I had never learned it before as making the ‘fake’ x/y axis that he does in this video and I keep trying to recall the way I used to do it and it was incorrect.
Hey Professor love your videos just one question. I'm struggling to figure out how you got the outputs for the cubic graph at 16:25, I understand the transformations, but I don't understand the output of -1/3 because wouldn't you still have to subtract the one from -1/3 making it -4/3? Thanks for all your videos you are a tremendous help!
these graph transitions confuse me, how does this fit into the order of operations? specifically the left/right shift, yes I watched the previous video
so, for the first transformation: -1/2⎮x-3⏐+2 are we not suppose to reflect over the actual X-axis? so the point of the "vertex of the final transformation would be (3,-1) ? I know this comment is really late, Im just a bit confused.
hi community,for the second example, if i want to find the x intercept, i set the function equal to 0, i get -2.4425.can anyone show me the working out please? thank you
The lecturer Chris Tisdell has several great videos on PDE problems. He is just as likeable as Professor Leonard, and has just the same passion for teaching.
I think this will have quite a few. This playlist will include college algebra/trigonometry, this is intended to bring students to a appropriate level before taking calculus
@@bigshaqsmathematicalinstit3318 I would say the Geometry is kind of a prerequisite as well, since that course is an important foundation for Trigonometry, which deals a lot with triangles and the unit circle.
Great stuff! But I have to disagree with your approach here and would appreciate it if you would respond if you see my message. It seems to me that the most logical ordering of transformations is to follow "order of operations". For the first equation, that ordering would be: right 3 to adjust the x value to input to the absolute value function, multiply the output from the absolute value function by 1/2, reflect the output over the x--axis, and finally, increase the magnitude of the f(x) output value by 2 (the +2) at the end. My reasoning for this is that the graph is calculated in this order, so this is guaranteed to produce the correct answer, and is easy to remember as a process because it just follows the order of operations that we all learned in 6th grade. EDIT - Another comment. For f(x) = 3/(x-2) + 1, you talk about the "inside of the function". I would suggest a different terminology and a slightly different way of looking at this. These "inside" elements that you speak of are really functions within the function. For example, the division operation is a function, sqrt is a function, an exponent is a function. When looked at that way, it becomes clear that modifications to x, e.g. x-2 in this case, are analogous and can be treated the same way as when you invoke f(x) with x-2. It is these inner functions that dictate the overall shape of the graph, hence marking the beginning of the graph transformation exercise. EDIT - on 2*sqrt(1-x) + 3, again, I must disagree with your graphing method. While it works and may make the drawing of the graph easier, it's also somewhat illogical, at least to me. Again, if you follow the order of operations and do the y-axis reflection first, the +1 inside the sq root function does exactly what you'd expect -- shifts to the left - after! the y-axis reflection. No need to remember a special case. It works like call other horizontal shifts. EDIT - By the way, I'd like to thank you so much for your videos. I'm finding them a bit beating a dead horse, but it seems to work. I understand domain and range for the first time, and I am understanding graph transformation for the first time. And I took calc 1 and 2 in high school a long time ago, but never really understood some of these key base concepts, which compromised my ability to get into any more advanced math after that. I'm well past school age, but I am taking all of your courses in a quest to learn AI programming. Haha, a big endeavor, but one with your amazing math help, I am hopeful to achieve. To all you folks of H.S. or college age, I encourage you -- don't skimp on the basics -- you cannot build a houlse without a foundation and you cannot move forward in math without a foundation either.
Hello, I agree with your comments. Based on the order of the operations, the graphs of the transformed functions seemed to be incorrect. Shifting up or down to be done at the very end after the brackets and the operations inside the brackets are taken care of. But for the last example i.e. 2*sqrt(1-x) + 3, his output is still correct for the exact reason you mentioned. But for the other two transformations, I don't agree with his answers. However, I might be wrong as well. If someone more knowledgeable tries this on their own and replies, that would be great. Having said that, the contributions of Prof. Leonard is awesome. He is teaching us a lot of things which we learnt but didn't really grasp. He is a shining light and hopefully he makes more videos in the near future, at least general videos if not in math.
@@shorndrack Totally agree about Prof Leonard. He's awesome. I've now finished his precalc and his calc 1 course. I think he actually does get around to explaining things in the manner I suggested in a later video somewhere. Thanks for your comment.
@@rickhoro Glad to hear and thanks for the reply. Good luck with Calculus 2 and 3. I did his Calculus I five years ago and it helped me do a research project in Advanced Macroeconomics. Now I am going back to the foundations and start over.
What is causing trouble for me are the tables. If you could better explain that to me bc that is where I am having trouble. You have in the first example a table for the parent function, but when you go to the key points for the transformed equation the multiplication gets confusing.
