Joe Lauer
Lecturer in Mathematics
My research interests lie in geometric evolution equations and geometric analysis. This is an active area where problems allow one to use a wide variety of techniques from analysis, PDE theory, differential geometry and topology. Often it is the combination of several of these tools which proves the most fruitful. More specifically, I focus on smoothness questions in mean curvature flow, curve shortening flow and Ricci Flow, three geometric PDEs that have found applications in many fields.
Outside of my work in the Math Department I am also an Assistant Coach with Wellesley Cross Country and Track and Field.
Education
- B.Math., University of Waterloo
- M.Sc., McGill University
- Ph.D., Yale University
Current and upcoming courses
Calculus II
MATH116
The course begins with applications and techniques of integration. It probes notions of limit and convergence and adds techniques for finding limits. Half of the course covers infinite sequences and series, where the basic question is, What meaning can we attach to a sum with infinitely many terms and why might we care? The course can help students improve their ability to reason abstractly and also teaches important computational techniques. Topics include integration techniques, l'Hôpital's rule, improper integrals, geometric and other applications of integration, infinite series, power series, and Taylor series. MATH 116 is the appropriate first course for many students who have had AB calculus in high school.
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Multivariable Calculus
MATH205
Most real-world systems that one may want to model, whether in the natural or in the social sciences, have many interdependent parameters. To apply calculus to these systems, we need to extend the ideas and techniques of single-variable Calculus to functions of more than one variable. Topics include vectors, matrices, determinants, polar, cylindrical, and spherical coordinates, curves, partial derivatives, gradients and directional derivatives, Lagrange multipliers, multiple integrals, vector calculus: line integrals, surface integrals, divergence, curl, Green's Theorem, Divergence Theorem, and Stokes’ Theorem.