Pages similar to: The relationship between determinants and area or volume
- Matrices and determinants for multivariable calculus
Brief description of matrices and determinants, at the level needed for multivariable calculus. - The cross product
Introduction to the cross product with a focus on its basic properties. Includes an interactive graphic to illustrate these properties of the cross product. - Cross product examples
Examples of calculating the cross product. - The formula for the cross product
Derivation of the formula to calculate the cross product of two vectors. - The scalar triple product
Definition of the scalar triple product and derivation of its formula. Include interactive graphic to illustrate its properties. - Scalar triple product example
Example showing how to calculate the scalar triple product. - Determinants and linear transformations
A description of how a determinant describes the geometric properties of a linear transformation. - Geometric properties of the determinant
Explanation of some of the basic geometric properties of the determinant. - Introduction to changing variables in triple integrals
Introduction to the concepts behind a change of variables in triple integrals. - Volume calculation for changing variables in triple integrals
A derivation of how a mapping that changes variables in triple integrals transforms volume.