Mathematical Foundations · Differential Calculus

Applications of the Derivative · Differential Calculus

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Treatise on Mathematical Analysis

Overview

Topics covered

  • Introduction
  • Applications of the Derivative: Theory, Rigor and Modeling
  • Instantaneous Change and the Derivative as a Dynamic Limit
  • Curve Geometry: Tangent and Normal Lines
  • 2.1 The Tangent Line
  • 2.2 The Normal Line

Related concepts

Main connections

  • Calculus & differentiation
  • Mathematical optimization & gradients
  • Supervised machine learning
  • Epidemiological measures & risk ratios
  • Causal inference & potential outcomes

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

ΔyΔx=f(x0+h)−f(x0)h
View LaTeX source\frac{\Delta y}{\Delta x} = \frac{f(x_0 + h) - f(x_0)}{h}