Surfaces.

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Presentation transcript:

Surfaces

Constructing Functions of Several Variables The temperature at points in the xy-plane is proportional to the square of the distance of the point to the origin. Write the temperature as a function of x and y.

Constructing Functions of Several Variables The ideal gas law states that the pressure of a gas is proportional to its temperature and inversely proportional to its volume. Write a function that represents the pressure of a gas in terms of its temperature and volume.

Graphs of Functions of Several Variables z y x

Examples

Quadratic Surfaces

Ellipsoid

Sketching Surfaces A trace of a surface is the intersections of a surface with a plane. A sequence of traces for a surface form a wire mesh that represents the surface.

Ellipsoid

Elliptic Cone

Hyperboloid of Two Sheets

Hyperboloid of One Sheet

Elliptic Cylinder

Hyperbolic Cylinder

Parabolic Cylinder

Hyperbolic Paraboloid

Elliptic Paraboloid

Identify and Sketch the Surfaces