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Mathematics

Calculus: The Fundamental Theorem

Calculus is the mathematical study of continuous change. The fundamental theorem of calculus links the concept of differentiating a function with the concept of integrating a function:

$$\int_{a}^{b} f(x) dx = F(b) - F(a)$$


Linear Algebra: Eigenvalues

In linear algebra, an eigenvector is a non-zero vector that changes at most by a scalar factor when a linear transformation is applied to it. The corresponding eigenvalue is the factor by which it is scaled:

$$A \mathbf{v} = \lambda \mathbf{v}$$