Let’s Revise High Dimensional Calculus

Finally, let’s get on to brush-up the last set of mathematical concepts before we dive into the world of implementation of these tools, so called Machine Learning or a more glamorous term “Artificial Intelligence”.

FUNCTIONS(1D):
Firstly, we all know what functions.They are basically transformation of a variable to another variable.You give one value as input to a function and it spits out another value depending upon a relation between them.
F(x) = y , where x is input and y is output and F() is a relation between these two.

FUNCTIONS(3-D):

VECTOR FIELDS :

FUNCTIONS AS TRANSFORMATIONS:

“Transformations give better understanding of the dimensional changes”.

PARTIAL DERIVATIVES:

GRADIENT OPERATOR:

DIRECTIONAL DERIVATIVE:

CURVATURES AND DIVERGENCE:

LAPLACIAN AND HARMONIC FUNCTIONS:

LOCAL LINEARITY AND QUADRATIC APPROXIMATION

FINDING POINTS OF MAXIMA AND MINIMA

This finishes the crash course tour of the concepts of Multivariate Calculus, I have touched upon the important topics here, though one of the most important topic which i did not cover was that of multivariate chain rule , which is the heart of back propagation algorithm in neural network. I will get to that topic when i derive the networks for you.

Rest i have given out good amount of info for you to dig in more and expand your horizons.

Stay tuned :)

Homo Bayesian