Introduction to limits and derivatives as preparation for further courses in calculus. Fundamental functions (polynomials, rational functions, exponential, logarithmic, trigonometric) and their graphs will be also reviewed. Other topics include tangent and normal lines, linearization, computing area and rates of change. The emphasis will be on learning to think independently and creatively in the mathematical setting.

First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus.

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.

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.