A Brief Introduction to Infinitesimal Calculus

Lecture 3: Local Linearity

Explicit Graphs

z = f[x, y] & dz = ∂f/∂x dx + ∂f/∂y dy

Implicit Graphs

Implicit Tangents

The Implicit Function Theorem

Parametric Graphs

Curves

The  X '[t] ≠0 Condition

Coordinate Systems in 2D

Surfaces in 3D

Coordinate Systems in 3D

Vector Fields

2D

3D

Surface Flux

Stokes' Theorem & deRahm Cohomology

Differential Equations

A Theorem in the F & M Deiner Style

Created by Mathematica  (July 2, 2004)