Wavy Surface Approximation

Vincent Vu
November 8, 2021
George Mason University MATH 401: Mathematics through 3D Printing

This print represents a Taylor series approximation of a multivariable function. In single variable calculus, a Taylor series can be used to approximate a function about a point using derivatives. Higher accuracy is achieved by taking more and more derivatives, and for many functions this means that they can be represented using an infinite series of derivatives. When extended to multivariable functions, the same process is applied except extra terms are involved due to each function having partial derivatives with respect to multiple variables rather than a single variable. The function I used for my approximations was f(x,y) = sin(x^2 + y).

The linear approximation given by the first partial derivatives yields a tangent plane. I did my approximations about the point f(0.5,0.5) as the approximation about f(0,0), or the origin, yielded a tangent plane that was only dependent on the va