Math Insight

Pages similar to: The formula for the cross product

• 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.
• The formula for the dot product in terms of vector components
  Derivation of the component formula for the dot product, starting with its geometric definition based on projection of vectors.
• The dot product
  Introduction to the dot product with a focus on its basic geometric properties.
• The scalar triple product
  Definition of the scalar triple product and derivation of its formula. Include interactive graphic to illustrate its properties.
• Cross product examples
  Examples of calculating the cross product.
• Dot product examples
  Examples of calculating the dot product of two- and three-dimensional vectors.
• Vectors in two- and three-dimensional Cartesian coordinates
  A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space.
• The relationship between determinants and area or volume
  The properties of the cross product and the scalar triple product give links between determinants and area or volume.
• An introduction to vectors
  A introduction to the concept of a vector as an object with magnitude and direction.
• Scalar triple product example
  Example showing how to calculate the scalar triple product.
• Multiplying matrices and vectors
  How to multiply matrices with vectors and other matrices.
• Determinants and linear transformations
  A description of how a determinant describes the geometric properties of a linear transformation.
• Developing an initial model to describe bacteria growth
  By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria.
• Exploring the derivative of the exponential function
  A guided tour into the reasons that the derivative of the exponential function with base e is the function itself.
• Matrices and determinants for multivariable calculus
  Brief description of matrices and determinants, at the level needed for multivariable calculus.
• The idea of the chain rule
  An illustration of the basic concept of the chain rule using interactive graphics to diagram the relevant points on the graphs and the corresponding slopes.
• Spruce budworm outbreak model
  A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years.
• A discrete SIR infectious disease model
  
• The definition of differentiability in higher dimensions
  The definition of differentiability for multivariable functions. Informal derivation designed to give intuition behind the condition for a function to be differentiable.
• Introduction to the multivariable chain rule
  Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example.

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