Topics in MAT 104 include techniques and applications of integration including area, length, and volume and an introduction to differential equations. The course also introduces complex numbers and polar coordinates, analysis of convergence of infinite series and improper integrals, and approximation using Taylor's theorem with remainder. It emphasizes the development of mature problem-solving skills through problems that require sophisticated pattern recognition and the ability to apply and adapt multiple techniques to solve a single problem.

This course will teach some of the fundamental concepts needed to succeed in the calculus sequence, and develop students' mathematical writing and presentation skills. It is comprised of lectures, precepts, and writing workshops. Written work will be assigned weekly, and a final project will be due at the end of the summer.

Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes's theorem.

Companion course to MAT201. Matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvectors and their applications to quadratic forms and dynamical systems.

Summer research project designed in conjunction with the student's advisor and an industrial, private or government sponsor that provides practical experience relevant to the student's research area. Start no earlier than June 1. A final written report is required.