How many lives could have been so much better if we all had teachers like Professor Strang? You are a gift to humanity, sir, and thank you so very much.
The way he connected the linear approximation of e^.01 to the power series representation of e^x was brilliant! Its something that's so obvious but very easy to overlook.
awsome! wish I had discovered prof. Strang some 20 plus yrs ago! as my daughter says: "there is no bad studen, there are bad teachers", my greatest congrats to Gilbert Strang, who masters how to engage the students! He spells out for every body what the better students recite on their own.
For a student, the key to learning is motivation the key to which is pleasure from learning. Professor Strang shows us the pleasure of learning every second. From that we've got motivation which keeps us going on learning.
This is the most brilliantly simplified lecture I've seen on math so far, and it perfectly retains all the necessary information in an easy to understand way.
Newton's method is one of the most beautiful root-finding algorithms out there. It is a pity it doesnt always converge to the value because it depends on the function and the first guess you take.
It just occurred to me a degree from a place like MIT simply means that you may have better grades because your instructors we're better and learning was facilitated by genius. Doing well in a less impressive school may actually be more impressive if it is only less impressive not because of the expectations of learning by because of the facilitations of learning. Doing well in a less impressive school shows a great improvement of self efficacy or that you don't have money.
The Newton /Raphson method is a great way to solve nonlinear equations. Once again DR. Strang thank you for a solid input into Newton/Raphson and the Linear Approximation method.
+9BoStOnGeOrGe It is Hagoromo chalk. No wrong theorem can be proven with that chalk. Unfortunately, the company that makes the chalk is going out of business. (Cf. www.independent.co.uk/life-style/gadgets-and-tech/news/hagoromo-chalk-why-the-demise-of-a-japanese-company-is-a-blow-to-mathematics-10326313.html)
A really good teacher, check out his linear algebra videros on OCW. They are amazing, I've even picked up his textbook "Introduction to Linear Algebra" It's amazing especially alongside his lectures.
so, am I correct - linear approximation, all you are really doing is taking a point and multiplying by the slope of a known point. That seems pretty straightforward. And the slope for a curve is the derivative. But ya..you are just taking a short line and multiplying by slope. Doesn't seem very difficult
+Luis Lomeli Probably because some people just want to know all the details. I mean, of course some people might want a more basic approach when learning things, but me for instance, I want to know lots of itty bitty details about it so i can have a concrete idea about it.
+Luis Lomeli Probably because some people just want to know all the details. I mean, of course some people might want a more basic approach when learning things, but me for instance, I want to know lots of itty bitty details about it so i can have a concrete idea about it.
Yeah I find the geometric look at this to be a lot more intuitive, he started off looking at it from the algebraic standpoint and I had to concentrate to follow.
unless ur a genius urself the tutelage of a genius will be fruitless. i think the idea is u r of hi intellect u get into MIT , where u r exposed to a genius level of difficulty. So if u pass, ur a genius
