Multivariable Calculus_2 Application of Multivariable Derivatives

Math is quite abstract but it has immense usage in our life. Multivariable calculus essentially helps solve complicated problems in practice such as simple needs to measure an irregular area, volume by approximating.

To do a good job of approximating, first, introduce the concept of local linearilization by first dirivative for simple x, y function.

Lf(x0,y0) = a f(x0, y0) partial derivative with respect to x (x-x0) + bf(x0 ,y0) partial derivative with respect to y(y-y0) + constant(f(x0,y0). This complex algebra form can be compactly expressed in vector language below:

Analogously, this simple linear form is inadequate to treat convoluted surface/volume, so quadratic form is necessary, where higher level of derivatives are included.

Again, we try to express it in a succinct way that tens of hundreds of potential variables can be exhibited with the help of Hessian matrix and matrix multiplication rule:

Hessian Matrix

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.