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Index: Multivariable Calculus

I took this class in the summer of 2024. These notes are just for me to refresh the material and for anyone else looking to review multivariable calculus.

Why Multivariable Calculus?

Single-variable calculus deals with functions f:Rโ†’Rf: \mathbb{R} \to \mathbb{R}. But most real-world quantities depend on multiple variables:

  • Temperature depends on position (x,y,z)(x, y, z) and time tt
  • Electric fields are vector functions of position
  • Fluid flow involves velocity fields in 3D space

Multivariable calculus provides the tools to analyze these situations.

Articles

  1. Parametric Equations, Polar Coordinates
  2. Vectors
  3. Vector Functions and Space Curves
  4. Differential Calculus of Several Variables
  5. Integral Calculus of Several Variables
  6. Line Integrals
  7. Surface Integrals
  8. Vector Calculus Theorems