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.
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