Advanced Calculus: Lecture 1 part 1: normed linear spaces

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Here I give a very brief overview of linear algebra, for my students, I hope the first homework helps complete the review. Then I discuss normed linear spaces, metric spaces and inner product spaces. Again, the first homework will flesh out the discussion begun here. Finally, we define open sets and limits on a NLS and explore the norm-indendence of topology in the plane.

James Cook Math

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Just remember this man started by adding 1+1

osvaldovaldovinos

Calculus that starts with a prayer? Fascinating dichotomy

chatter

Thank you for posting these! It is not that common on youtube to find full blown courses on more advanced topics such as these. Coming from engineering background, studying traditional Calc III and Vector Calculus at my school a lot of these topics were missing. Now going into ML and dealing with high dimensional vector calculus really showed gaps in my knowledge, excited to fill them in here!

alek

Ooh my god I took this course 7 years ago, I absolutely have no idea how I passed this 😂 I tried to remmeber anything from this lecture and
literally “ nothing at all”
Looks like I was smart back then, not anymore after getting married😅

I better run and watch something else😊

مدريمين-لج

I already learnt something at the beginning of the video, usually say ur prayers before a test but i spose before a lesson aswell

Kelvin-ww

I just wondered how advanced maths look. Im not even in university but im watching this. Not understanding a thing, but still interesting!

gooo

I've taken your class before. I remember you talking about your brother-in-law, (I think) Digital Dave.

m

I did this to look cool at school and now I know it

Keanelikesprotein

Calculus is an.important tool and it's totally awesome.

haroldfoutz

Hi professor. What is the difference between your two courses called advanced calculus and which one do I need to take in order to be able to take your differential geometry course? Thanks

matthiasandersen

sir can you please suggest me books for this course

اسلامكمال-خذ

Even before watching video I like to ask what advanced calculus precisely means. There are several contexts calling Advanced Calculus. But this video lecture deals with functional analysis normed banach or inner product Hilbert spaces calculus of them?.. Or it studies calculus of spaces over R^n. Or calculus over functions of several variables which involve jacobians etc. Or the concepts of analysis like infinite products dealt in book by 'Advanced Calculus by Gibson. I am seriously confused because the term used in modern is not one branch.

premkumar-soff

I’m here because I can’t sleep and I need something so boring

_PeterGabriel

Is there a specific textbook that you follow in this course? Or can you recommend texts covering the topics in this course?

__donez__

What book do you use for this class? The website says it uses differential geometry but I think the school website might have mixed that up with the wrong course.

tanyafitchett