# topic/math/calculus

Calculus and Optimization

Calculus studies local change; optimization uses local change to choose better parameters. The useful mental model is: derivatives describe sensitivity, Taylor expansions…

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Chain Rule (Multivariable)

If , the chain rule gives:

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# topic/math/calculus

Gradient

The gradient of a scalar function is the vector of all partial derivatives:

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# topic/math/calculus

Hessian Matrix

The Hessian of a scalar function is the matrix of second partial derivatives:

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# topic/math/calculus

Jacobian Matrix

The Jacobian of a vector-valued function is the matrix of all partial derivatives:

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# topic/math/calculus

Taylor Expansion

Taylor expansion approximates a function near a point using its derivatives:

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# topic/math/calculus