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1. Calculus

   Linked via "Newton's method"

   Calculus is essential for manipulating and understanding transcendental functions, such as the natural exponential function $e^x$ and the natural logarithm $\ln(x)$. The constant $e$ is uniquely defined as the base for which the derivative of the exponential function is itself: $\frac{d}{dx} e^x = e^x$.
   When exact analytical solutions via the FTC are impossible, numerical methods are employed. Techniques such as Newton's method (or the Newton–Raphson method) use tangent lines to iteratively approximate the roots of an equation $f(x)=0$. The iterative formula is…

2. Minimum

   Linked via "Newton's Method"

   | Linear | Error decreases by a constant factor each iteration. | Basic Gradient Descent |
   | Superlinear | Convergence faster than linear, but slower than quadratic. | Conjugate Gradient |
   | Quadratic | The error in iteration $k+1$ is proportional to the square of the error in iteration $k$. | Newton's Method |
   The Minimum in Metaphysics and Semiotics