MA 243 Lecture Notes - Lecture 2: Quadric, Partial Derivative, Multivariable Calculus
Document Summary
We continue our study of the geometry of three-dimensional space, formally known as. As we shall discover, many of the concepts and techniques encountered earlier in calculus have extensions in higher dimensions. Any point p in three-dimensional space can be located with three coordinates (x,y,z). A set of these points forms a graph or surface that could describe the landscape of a mountain range, perhaps encountered by a wandering goat. The set of all points that satisfy the equation f(x,y,z) = k forms a graph or surface in the space . The distance formula produces the equation of a common surface, the sphere: a set of points p(x,y,z) a constant distance a from the origin: Observe that this sphere also has the form r a r = *r* = a . Another basic surface is the plane given by the linear equation.
