Math Insight

Pages similar to: The linear function

• Matrices and linear transformations
  A description of how every matrix can be associated with a linear transformation.
• Function notation
  A description of how we denote functions.
• Linear transformations
  Definition of a linear transformation of Euclidean spaces.
• 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.
• Subtleties of differentiability in higher dimensions
  A description of some of the tricky ways where a function of multiple variables can fail to be differentiable. Example two variable functions are illustrated with interactive graphics.
• The derivative matrix
  The derivative matrix is presented as a natural generalization of the single variable derivative to multivariable functions.
• Surfaces as graphs of functions
  Illustration of how the graph of a scalar-valued function of two variables is a surface.
• 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.
• Domain of functions
  How to determine the domain of a function.
• How linear transformations map parallelograms and parallelepipeds
  Why linear transformations map parallelograms onto parallelograms and parallelepipeds onto parallelepipeds.
• The function machine
  The function machine metaphor helps explain the definition and properties of a function.
• Function examples
  Basic examples of functions illustrating the definition of a function.
• Function machine parameters
  Illustrating function parameters as dials that influence the behavior of a function machine.
• Function machine composition
  Composing two functions simply means connecting together their respective function machines.
• The function machine inverse
  The inverse of a function is represented by running its function machine backwards.
• Function composition examples
  Examples of composing functions to form a new combined function.
• Inverse function examples
  Examples of forming an inverse function that does undoes the action of another function.
• The exponential function
  Overview of the exponential function and a few of its properties.
• Calculating the derivative of a linear function using the derivative formula
  Exploring how the limit definition of the derivative gives the slope of a linear function.

Back to: The linear function