Multivariable calculus and vector analysis

The multivariable calculus readings have moved

I have revamped the multivariable calculus readings and moved them to a new web site called Math Insight. The above links will take you directly to pages on that web sites. Or you can find links to selected pages below.

Highlighted multivariable Math Insight pages

Below are links to selected Math Insight pages on multivariable calculus.

• Pages about the derivatives of multivariable calculus
  • partial derivatives
  • multivariable differentiability
  • the multivariable chain rule
  • the directional derivative and the gradient
• Pages about the integrals of multivariable calculus
  • double integrals
  • triple integrals
  • change of variables in double integrals
  • change of variables in triple integrals
  • line integrals of scalar functions (sometimes called path integrals)
  • line integrals of vector fields
  • surface integrals of scalar functions
  • surface integrals of vector fields (sometimes called flux integrals)
• Pages about curves and surfaces
  • parametrized curves and parametrized curve derivatives
  • arc length (also called path length)
  • parametrized surfaces
  • surface area
• Pages about vector fields
  • divergence of a vector field
  • curl of a vector field
• Pages about the fundamental theorems of vector calculus
  • Green's theorem
  • conservative vector fields (also called path-independent vector fields)
  • the gradient theorem for line integrals (also called the fundamental theorem of calculus for line integrals)
  • Stokes' theorem
  • the divergence theorem (also called Gauss' theorem)

Highlighted vector algebra Math Insight pages

Below are links to selected Math Insight pages on vector algebra.

• Pages about vectors and their products
  • multi-dimensional vectors
  • the cross product
  • spherical coordinates
• Pages about lines and planes
  • line parametrization
  • forming planes
  • equation for line or plane
  • distance from pont to plane
  • parametrization of a plane
• Pages about visualization
  • level sets, i.e., level curves and level surfaces
  • graphing surfaces
  • cross sections of surfaces