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Alternate notation for vector line integrals
An alternative notation for the line integral of a vector field is introduced.
Surfaces as graphs of functions
Illustration of how the graph of a scalar-valued function of two variables is a surface.
Domain of functions
How to determine the domain of a function.
The function machine
The function machine metaphor helps explain the definition and properties of a function.
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.
The linear function
Overview of the linear function of one variable and a few of its properties.
How composing two functions forms a new combined function.