Going back a few years, I took a precalculus course at a community college 1n 1968. I had taken high school algebra 1 &2 about ten years prior to that. I took this as a summer course and was in way over my head. I studied 5 hours just about everyday and just squeezed by. I needed some of your courses to prepare me.
Man! It must've been the public school teachers that could not pique my interest so many years ago, but I've always been deficient in higher mathematics. I've always been able to solve the basic 4, and simple algebra in my head, but never cared for the more complex operations. You have changed that dramatically. I attribute that to the method of explanation, i guess. GREAT JOB! I am 55. Have been making good money doing electronic work for the last 28 years. Your explanations and logical diagrams will help me from going completely brain dead in my old age. I'll be putting it in front of my kids, who are 6 and 10, as well. A medium like this was not available in my day. Many Thanks!
I've had and am drowning in life set backs...Holidays are always an add on. But, lately...I'm being reminded stronger than ever to get back to water management and get back on your website for lessons. (@ synchronicities and timing) So, I better get back in the boat at sea, and steer hope. One day, I hope to literally own every lesson you offer and in every format you offer. (One) of the biggest anxiety producers for me about teachers is their expecting that I should know more than I do. In comparison, you teach from a place of their not knowing, without any belittling, and yet with a challenging level and respect.
Another outstanding lesson with clear explanations and the usage of the language is accessible to learners/students. Very satisfied with the learning where Bloom's Taxonomy is always applied to the lesson. Thank you ) Wishing you and all your learners a Merry Christmas & a Happy New Year filled with health, wealth, happiness and joy! Thank you for being with us. You are a great teacher
@@MathAndScience thanks in advance . Also , a bit more of integral calculus , just saw only one tutorial for the introductory part , I'm an Engineering student and my course is actually based on calculus 1 and 2 . Please do me a favour .
That's a refresher for things I've forgotten from years ago. The process I get pretty well, l but what would make it clearer is if I had an example of a real world problem that requires imaginary numbers to solve. (That was the problem even in high school...we learned the processes but not what to use them for)
-25 is essentially -5 repeated 5 times and the reason we can't write down it's square root that easily due to it's negative sign.That's where comes the importance of imaginary value i. As we are unable to represent 5 × (-5) = -25 in it's roots,we can represent it in another form. We know √25 = +/-5, So we can take √25 = 5i,where 5 is a real no.& i is an imaginary no,we call both of them together a complex no. That also means 5i × 5i = -25 We know 5 × 5 = 25,so if we want to get the whole product - 25,the product or value of i² should be -1 & i should be √-1. Then only we can write,5i × 5i [5(√-1)×5(√-1)]= 25 i² = 25(-1) = - 25 So,√-25 = 5i
When you get to looking at electric power, you'll find that this "imaginary" i is one of the things that keeps the lights on. Very warm, and maybe oscillating rather than fuzzy.
It is an older recording that I am re-releasing. Believe it or not, I cleaned up the picture and sound. Newer lessons have much better equipment as this was over a decade ago! Still, you should be able to hear and see everything. Thanks and take care! Jason
![Exponential Functions, Exponential Graphs, Growth & Decay - [2]](http://i.ytimg.com/vi/OvN7prRcYL8/mqdefault.jpg)
![Exponential Functions, Exponential Graphs, Growth & Decay - [2]](/img/tr.png)
I don't think I can put into words how much gratitude and for a lack of a better term love I have for this man.
Awww thank you!
Going back a few years, I took a precalculus course at a community college 1n 1968. I had taken high school algebra 1 &2 about ten years prior to that. I took this as a summer course and was in way over my head. I studied 5 hours just about everyday and just squeezed by. I needed some of your courses to prepare me.
Man! It must've been the public school teachers that could not pique my interest so many years ago, but I've always been deficient in higher mathematics. I've always been able to solve the basic 4, and simple algebra in my head, but never cared for the more complex operations. You have changed that dramatically. I attribute that to the method of explanation, i guess. GREAT JOB! I am 55. Have been making good money doing electronic work for the last 28 years. Your explanations and logical diagrams will help me from going completely brain dead in my old age.
I'll be putting it in front of my kids, who are 6 and 10, as well. A medium like this was not available in my day. Many Thanks!
Thanks!
No problem! Thank you so much!
omg thank you so much ! I was watching your videos a few weeks ago for sat algebra and now precalc for clep exams !! Wish you all the best !!
Thank you for this superb tutorial. Very clear and enjoyable.
If only you were online 30 years ago! THANK GOD YOU ARE NOW!
I've had and am drowning in life set backs...Holidays are always an add on. But, lately...I'm being reminded stronger than ever to get back to water management and get back on your website for lessons. (@ synchronicities and timing) So, I better get back in the boat at sea, and steer hope. One day, I hope to literally own every lesson you offer and in every format you offer. (One) of the biggest anxiety producers for me about teachers is their expecting that I should know more than I do. In comparison, you teach from a place of their not knowing, without any belittling, and yet with a challenging level and respect.
Nice 👍
I remember imaginary numbers... 5i or any containing "i"
Thank you. Merry Christmas 🎄⛄.GOD bless you.
Merry Xmas!🌲
Merry Christmas and a Very Happy New Year! )
Thank you v much Sir. You really done a mazing job. .Great job.
I've been waiting for this. Thanks
First time I've ever heard that imaginary numbers can be plotted on an axis. Cool!
Me too mTe.
Me imaginary 3i
SO helpful! Thank you so much, finaly I understood what imaginary and complex numbers are
I hope this video helps me pay my bills (complex numbers) with the money in my bank account (imaginary numbers).
lol
Another outstanding lesson with clear explanations and the usage of the language is accessible to learners/students. Very satisfied with the learning where Bloom's Taxonomy is always applied to the lesson. Thank you )
Wishing you and all your learners a Merry Christmas & a Happy New Year filled with health, wealth, happiness and joy! Thank you for being with us. You are a great teacher
Thanks 🙏🙏🙏👍👍👍
(4+5i) = 9i(x+3x-3i)
THANK YOU SIR...!!!
(√- 25=5^5 (x+5x-5i)
Wow thanks sir nice tutorial 🎉, 💯 I just love your session . Would you please give more examples on the chain Rule in calculus to work on self
Sure I will
@@MathAndScience thanks in advance .
Also , a bit more of integral calculus , just saw only one tutorial for the introductory part , I'm an Engineering student and my course is actually based on calculus 1 and 2 . Please do me a favour .
That's a refresher for things I've forgotten from years ago. The process I get pretty well, l but what would make it clearer is if I had an example of a real world problem that requires imaginary numbers to solve. (That was the problem even in high school...we learned the processes but not what to use them for)
-25 is essentially -5 repeated 5 times and the reason we can't write down it's square root that easily due to it's negative sign.That's where comes the importance of imaginary value i. As we are unable to represent 5 × (-5) = -25 in it's roots,we can represent it in another form.
We know √25 = +/-5,
So we can take √25 = 5i,where 5 is a real no.& i is an imaginary no,we call both of them together a complex no.
That also means 5i × 5i = -25
We know 5 × 5 = 25,so if we want to get the whole product - 25,the product or value of i² should be -1 & i should be √-1.
Then only we can write,5i × 5i [5(√-1)×5(√-1)]= 25 i² = 25(-1) = - 25
So,√-25 = 5i
Would you show us practical applications of complex numbers? (would 'compound number' be a better term?)
25i (x+5x,-5i)
1/3+2i=,1/6i { (x+1x-6i)
Great lectures but I wish it covered the complete module
,(3+2i)= 5i (x+1x-5i)
(a+bi)(a-bi)=a^2+b^2 is always a real number. That why complex conjugate works.
√5 (x+1x-5).
"Something that was sort of made up". This doesn't instill warm and fuzzy feelings.
When you get to looking at electric power, you'll find that this "imaginary" i is one of the things that keeps the lights on. Very warm, and maybe oscillating rather than fuzzy.
Ayooooo 🎉❤ got it! Was a intresting session 🪭 hope to see 🙈 u next time tadda ✋
√25{{x+5x-5)
Is this an old recording? Sound quality is not as good as your usual videos.
It is an older recording that I am re-releasing. Believe it or not, I cleaned up the picture and sound. Newer lessons have much better equipment as this was over a decade ago! Still, you should be able to hear and see everything. Thanks and take care! Jason
@@MathAndScience Thanks for your reply. Yes, you can see and hear but I much prefer the newer videos. Love the range of content!
@@brenmclean makes total sense. Thank you!
Harp who this man
Wait a minute is it just me or does he look like a teenager here? Not tryna be offensive tho you Just look younger here
Yeah... ?🤔
10i/3= (x+2x-5i) (x+3x-3i)