Xerxesshock2 said:Homework Statement
Express the quantity ∂2/∂x2+∂2/∂y2 in polar coordinates.
Homework Equations
x=ρcosφ
y=ρsinφ
ρ=sqrt(x2+y2)
The Attempt at a Solution
This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot figure out exactly how to set it up. I don't know what function to differentiate for x and y... Any guidance would be appreciated. Thank you!
Polar coordinates are a mathematical system used to locate points in a plane. They are represented by a distance from the origin (called the radius) and an angle from a reference line (called the polar axis).
To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), you can use the equations r = √(x² + y²) and θ = tan⁻¹(y/x). This means that the radius is the square root of the sum of the squared x and y coordinates, and the angle is the inverse tangent of the y coordinate divided by the x coordinate.
Polar coordinates are useful for describing circular or symmetric patterns, as well as for simplifying calculations involving complex numbers. They can also be more intuitive and easier to visualize in certain situations.
To convert from polar coordinates (r,θ) to Cartesian coordinates (x,y), you can use the equations x = r cos(θ) and y = r sin(θ). This means that the x coordinate is the radius multiplied by the cosine of the angle, and the y coordinate is the radius multiplied by the sine of the angle.
Polar coordinates are a two-dimensional system used to locate points in a plane, while spherical coordinates are a three-dimensional system used to locate points in space. In spherical coordinates, an extra coordinate (called the azimuth) is added to represent the angle in the xy plane, and the angle from the z-axis (called the polar angle) is used instead of the radius.