Athenastudying - Blog Posts
What does FTC say?
It says that if a person takes the derivative of a function and then integrates it over a region on the number line say [a, b] then this is the same as evaluating the function on its endpoints.
What does the Green's Theorem say?
Green's Theorem is the fundamental theorem of calculus in 2 dimensions.Instead of taking the derivative of a single variable function we take the curl of a 2 variable function.Instead of integrating this over a number line we integrate it on the xy plane.Instead of evaluating the function at the two endpoints a and b and taking the difference, we take the line integral of the function and integrate it around the curve in a counterclockwise direction.
What does the stokes' theorem say?
Stokes' theorem is the fundamental theorem of calculus in 3 dimensions. Instead of taking the derivative of a single variable function, we take the three-dimensional curl. Instead of integrating this over a number line, we integrate it on the surface (To evaluate the surface integral one has to dot the vector field with unit normal vectors). Instead of evaluating the function at the two endpoints a and b and taking the difference, we take the line integral of the function and integrate it around the curve on a surface in a counterclockwise direction just like in Green's Theorem.
🐻5th July - Do you have any special plans or activities for this summer?🐻
I plan on learning some cooking.The other day I experimented with some paneer recipes I found on Instagram and I have been making soya noodles a lot lately as well.They have become my comfort food 🐿I have attached an image I took of my noodles this afternoon.
🐰6th July - What do you usually do during the summer? Is anything different this year?🐰
For me summer means a lot of cycling.My dad and me wake up early in the morning and just ride our bikes till we are tired.There is a nice sun rise spot where we can have tea and enjoy the sunrise..This time we couldn't do it a lot because of covid but we did try to drink tea while enjoying the sunrise on our terrace but oh boy I do miss cycling.
🐼3rd July and 4th July of Summer Studying Challenge 2021🐼
Do you have a lot of work this summer?
The work is not a lot but I do need to be disciplined to get it all done.
What is the most important task that you need to complete this summer ?
I have to complete my mathematics assignments.These include Vector Calculus, Integral Calculus, Real Analysis, Linear algebra and Group theory.It might look like it's a lot but it is not.I have been struggling with Group theory assignment 3.It has been such a nightmare lol.I did speak to my maths professor about this and he said he will help me out.So a bit relived for that.