The Marsden and Tromba notation system
The notation from Vector Calculus, Fifth Edition by Jerrold Marsden and Anthony Tromba. Currently, this is the same as the default notation system.
The following Math Insight pages allow one to specifically select the Marsden and Tromba 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