Monthly Archives: July 2012

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

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Notes on Mathematical Writing

1. I’m going to be posting my double integral notes, but I’d like to discuss my strategy when writing “more rigorous” mathematics. Modern mathematics consists of definitions, theorems, and proofs…so I’ll discuss the idiosyncrasies of each. (I’ll probably revise this … Continue reading

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Meta: Higgs Boson

So, they discovered the Higgs Boson the other day. I think I will ultimately get to discussing the Standard Model in mathematical detail. It would be awesome to discuss the classical Standard Model, then the quantum Standard Model. I have … Continue reading

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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

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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?

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

Directional Derivative, Gradient

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?

Posted in Directional Derivative, Gradient, Vector Calculus | Tagged | 1 Comment

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…

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