# Category Archives: Differential

## Finding Extrema of Multivariable Functions

1. Remember for a curve , we have maxima and minima occur whenever (1) What’s the multivariable analog to this notion? Advertisements

Posted in Calculus, Gradient, Optimization, Vector Calculus | Tagged | 1 Comment

## Differentiation Technique #1: Logarithmic Differentiation

1. We should recall the chain rule applied to gives us (1) where . So what? Well, if is some nightmarish function (e.g. ), then we have (2). Quite a quick way to compute nightmarish derivatives!

Posted in Calculus, Differential, Natural Logarithm | | 2 Comments

## Taylor Series Uses #1: Complicated Integrals

1. Can you compute ? Well, first we consider the antiderivative for …which doesn’t exist. What do we do? Cry. No, what I mean is, use Taylor series!

## Thinking “Infinitesimally”

1. SO I’d like to reiterate the intuitive picture one should have when working with calculus. We should think of a differential as a “really small” change in …well, it’s the “smallest” possible change! The reason I bring this up, … Continue reading

Posted in Calculus, Differential | Tagged | 2 Comments

## Taylor Polynomials

1. So last time we concluded discussing Taylor series with constructing a polynomial using the first terms in the Taylor series. This “Taylor polynomial” approximated our function, and we want to know how well does it approximate? We will derive … Continue reading