# Category Archives: Calculus

## Introduction to Double Integration

1. Consider . What is the volume of the region (1) The first thing we do: consider the rectangle and form a partition of into segments and into segments. This gives us a mesh of rectangles as specified by the … Continue reading

## Lagrange Multipliers

1. So, last time we considered finding extrema for some function , but what if we constrain our focus to some surface ? For example, the unit circle would have (1) How do we find extrema for on the unit … Continue reading

## 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?

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1. Suppose we have a scalar function of several variables (1) Let be some unit vector. How does change in the direction? We can consider this quantity as a function (2) What does this look like?

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## Chain Rule for Partial Derivatives

1. Problem. Consider a function where we parametrize (1) If , how does change? We will need to use partial derivatives and Taylor expansion…