Math 21a, Fall 2007

Exhibit page Math 21a 07, Multivariable Calculus

Scary: discontinuous f continuous on each line

Course head: Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

The function
f(x,y) = xis discontinuous at (0,0) but on each line through the origin, the function is continuous. |

The contour map of f. Level curves of different values meet at the origin. | The graph of f shows the mountain rist, y=x^{2} on which the limit is 1/2 |
On every line through the origin, f is continuous: the limit is 0. |

Questions and comments to knill@math.harvard.edu

Math21b | Math 21a | Fall 2007 |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University