SOLUTIONS

BUILTIN MATHEMATICA SYMBOL
ContourPlot[f, {x, x_{min}, x_{max}}, {y, y_{min}, y_{max}}]
generates a contour plot of f as a function of x and y.
ContourPlot[f==g, {x, x_{min}, x_{max}}, {y, y_{min}, y_{max}}]
plots contour lines for which .
ContourPlot[{f_{1}==g_{1}, f_{2}==g_{2}, ...}, {x, x_{min}, x_{max}}, {y, y_{min}, y_{max}}]
plots several contour lines.
Details and OptionsDetails and Options
 ContourPlot by default generates colorized grayscale output, in which larger values are shown lighter.
 At positions where f does not evaluate to a real number, holes are left so that the background to the contour plot shows through.
 ContourPlot treats the variables x and y as local, effectively using Block.
 ContourPlot has attribute HoldAll, and evaluates the and only after assigning specific numerical values to x and y.
 In some cases it may be more efficient to use Evaluate to evaluate the and symbolically before specific numerical values are assigned to x and y.
 The plot is left blank in any regions where f evaluates to None.
 ContourPlot has the same options as Graphics, with the following additions and changes:

AspectRatio 1 ratio of height to width BoundaryStyle None how to draw RegionFunction boundaries BoxRatios Automatic effective 3D boundingbox ratios ClippingStyle None how to draw values clipped by PlotRange ColorFunction Automatic how to color regions between contour lines ColorFunctionScaling True whether to scale the argument to ColorFunction ContourLabels Automatic how to label contour levels Contours Automatic how many or what contours to use ContourShading Automatic how to shade regions between contours ContourStyle Automatic the style for contour lines EvaluationMonitor None expression to evaluate at every function evaluation Exclusions Automatic curves to exclude ExclusionsStyle None what to draw at excluded curves Frame True whether to put a frame around the plot FrameTicks Automatic frame tick marks LightingAngle None effective angle of the simulated light source MaxRecursion Automatic the maximum number of recursive subdivisions allowed Mesh None how many mesh lines in each direction to draw MeshFunctions {} how to determine the placement of mesh lines MeshStyle Automatic the style for mesh lines Method Automatic the method to use for refining contours PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends for contour regions PlotPoints Automatic the initial number of sample points in each direction PlotRange {Full,Full,Automatic} the range of f or other values to include PlotRangeClipping True whether to clip at the plot range PlotRangePadding Automatic how much to pad the range of values RegionFunction (True&) how to determine whether a point should be included WorkingPrecision MachinePrecision the precision used in internal computations  Typical settings for PlotLegends include:

None no legend Automatic automatically determine legend Placed[lspec,...] specify placement for legend  With the default setting ContourShading>Automatic, shading is used for ContourPlot[f, ...] but not for ContourPlot[f==g, ...].
 ContourPlot[{f_{1}==g_{1}, f_{2}==g_{2}, ...}, ...] superimposes the contour lines associated with all of the equalities .
 In determining how to color regions between contour levels, ContourPlot looks first at any explicit setting given for ContourShading, then at the setting for ColorFunction.
 ContourPlot initially evaluates f at a grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to generate smooth contours.
 You should realize that since it uses only a finite number of sample points, it is possible for ContourPlot to miss features of your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
 With some settings for PerformanceGoal, other specific option settings may be overridden.
 The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, f.
 ColorFunction is supplied with a single argument, given by default by the average of the scaled values of f for each pair of successive contour levels.
 With the default settings Exclusions>Automatic and ExclusionsStyle>None, ContourPlot breaks continuity in its sampling at any discontinuity curve it detects. The discontinuity is immediately visible only if it jumps out of a particular contour level.
 With a setting other than LightingAngle>None, ContourPlot includes simulated lighting based on height values determined by BoxRatios.
 ContourPlot returns Graphics[GraphicsComplex[data]].
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