Vectors in three dimensions. The dot and vector products. Lines and planes. Surfaces. Vector-valued functions and space curves. Limits, derivatives and integrals. Motion. Curvature. Tangential and normal components of acceleration. Functions of several variables. Limits and continuity. Partial derivatives. Chain rules. Directional derivatives. Tangent planes and normal lines. Extrema of functions of several variables. Lagrange multipliers. Double integrals. Area and volume. Double integrals in polar coordinates. Triple integrals. Cylindrical and spherical coordinates.

This is a foundation course for many majors ( Mathematics, Sciences and Engineering ). It focuses on real numbers, functions, limits, continuity, derivatives, integrals and their applications. At the end of the course, students will be able to strengthen their knowledge on fundamental algebra and basic principles of differential and integral calculus, find limits of functions, calculate the rates of change, apply techniques of differentiations to find derivatives of functions, find the extrema of functions using the first and second derivetive tests, sketch the graphs of polynomial and rational functions, and find antiderivatives.

The course contents are real vector spaces, linear dependence, bases, linear transformations, matrix Calculus, determinants and ranks, eigenvalues and Eigenvectors, Gaussian-Jordan elimination and system of Homogeneous equations.