The Stewart notation system
The notation from Calculus, Sixth Edition by James Stewart.
The following Math Insight pages allow one to specifically select the Stewart notation system. On these pages, a box to select the notation system appears at the right.
- Calculating the formula for circulation per unit area
- How to determine if a vector field is conservative
- Finding a potential function for conservative vector fields
- Finding a potential function for three-dimensional conservative vector fields
- An introduction to conservative vector fields
- A conservative vector field has no circulation
- The definition of curl from line integrals
- The idea behind the divergence theorem
- The fundamental theorems of vector calculus
- The gradient theorem for line integrals
- A simple example of using the gradient theorem
- Green's theorem examples
- Using Green's theorem to find area
- The idea behind Green's theorem
- Green's theorem with multiple boundary components
- Other ways of writing Green's theorem
- When Green's theorem applies
- The integrals of multivariable calculus
- Length, area, and volume factors
- Line integrals as circulation
- Line integrals are independent of parametrization
- Examples of scalar line integrals
- Introduction to a line integral of a scalar-valued function
- Alternate notation for vector line integrals
- Vector line integral examples
- Introduction to a line integral of a vector field
- The arc length of a parametrized curve
- Parametrized curve arc length examples
- Derivatives of parameterized curves
- Parametrized curve and derivative as location and velocity
- An introduction to parametrized curves
- Orienting curves
- Tangent lines to parametrized curves
- Tangent line to parametrized curve examples
- Surface area of parametrized surfaces
- Calculation of the surface area of a parametrized surface
- Parametrized surface area example
- Parametrized surface examples
- An introduction to parametrized surfaces
- Normal vector of parametrized surfaces
- Orienting surfaces
- A path-dependent vector field with zero curl
- Stokes' theorem examples
- The idea behind Stokes' theorem
- Scalar surface integral examples
- Introduction to a surface integral of a scalar-valued function
- Vector surface integral examples
- Introduction to a surface integral of a vector field
- Triple integral change of variable examples
- Introduction to changing variables in triple integrals
- Triple integral change of variables story
- Volume calculation for changing variables in triple integrals
- Triple integral examples
- Introduction to triple integrals
- The shadow method for determining triple integral bounds