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  • Vector Calculus
  • Geometry of Euclidean Space and real-valued functions
  • Differentiation
  • Vector-Valued Functions
  • Double integrals
  • Integrals over paths and surfaces

Vector Calculus

Author:
Juan Carlos Ponce Campuzano
Topic:
Calculus
Geometrical approach to Vector Calculus
Vector Calculus

Table of Contents

  • Geometry of Euclidean Space and real-valued functions

    • Addition of vectors
    • Scalar multiplication
    • Vector product
    • Plotting 3D surfaces
    • Parametric surfaces
    • Klein bottle
    • Distance: Point to Plane
  • Differentiation

    • Partial derivatives and Tangent plane
    • Directional derivatives and Gradient
  • Vector-Valued Functions

    • Vector fields in 2D
    • Vector field 3D
    • Dynamic Frenet-Serret frame
    • Vector Fields
    • Divergence and Curl calculator
  • Double integrals

    • Double integral over a rectangle
  • Integrals over paths and surfaces

    • Path integral for planar curves
    • Area of fence Example 1
    • Line integral: Work
    • Line integrals: Arc length & Area of fence
    • Surface integral of a vector field over a surface
    • Line integrals of vector fields: Work & Circulation
    • Line integrals of vector fields: Flux
    • Line integral for planar curves
Next
Addition of vectors

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