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
  • Slope field
  • 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