Bulletnotestudies - Blog Posts
Day 1
Assignment: Classwork of Vector Calculus
[11.32 am]I have ODE lab viva soon and I am terrified but hopefully, it will be over soon. I have given myself the task of completing 20 problems of vector calculus.
***
[3.20 pm] I did start but there has been a dip in my motivation.So I guess I will just take a nice bath, cook some snacks for myself and my parents and then sit and study again.
***
[9.45 pm] I am done for the day.Today I did some problems on vector calculus.I don't know why but I felt tired in the evening and just could not sit and solve stuff so I did not force myself.There is some kind of peace in calculating the angle between two very complex surfaces don't you think? Only if I had more energy to go through it.But now I remember also loving the concept of directional derivative.It is not done yet so gotta continue tomorrow.
222 days left to go..
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.
