Philip Hirschhorn

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.

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.

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.