Vector spaces; inner product spaces; examples of n-space and the space of continuous functions. GramSchmidt process, QR-factorization of a matrix and least squares. Linear transformations, change of basis, similarity and diagonalization. Orthogonal diagonalization, quadratic forms. Applications in a variety of fields, numerical methods.

The course includes first order and second order linear differential equations with constant coefficients; curves, tangent vectors, arc length, integration in two and three dimensions, polar, cylindrical and spherical coordinates, line and surface integrals; Green's, divergence and Stoke's theorems.

Infinite series; plane curves and polar coordinates; vectors and three dimensional analytic geometry; partial derivatives will be explored.

Elementary Number Theory, Numeration Systems, Number Systems and Elementary Probability Theory are included in this course.

Systems of linear equations, vectors in n-space, vector equations of lines and planes, matrix algebra, inverses and invertibility, introduction to linear transformations, subspaces of n-space, determinants, introduction to eigenvalues and eigenvectors, the dot product and orthogonality, applications in a variety of fields.

Applications of integration to areas, volumes, work force and arc lengths are included in this course. Differentiation and integration of exponential, logarithmic and trigonometric functions; techniques of integration; indeterminate forms and improper integrals.

The course will include a review of analytic geometry; functions, limits, continuity; differentiation of elementary functions; applications to maxima, minima and rates; introduction to integration; Fundamental Theorem; numerical integration; and areas and other applications of the definite integral to areas.

This course explores set theory, counting methods, probability, rational expressions and equations, and functions (polynomial, exponential, logarithmic and sinusoidal).

This course explores polynomial, radical, rational, exponential and logarithmic functions, transformation and combinations of functions, trigonometry (including the unit circle, graphs, identities and equations), and permutations and combinations.

This course explores sequences and series, radical expressions and equations, quadratic equations and functions, linear and quadratic inequalities, linear-quadratic and quadratic-quadratic systems of equations, rational expressions and equations, absolute value functions, reciprocal functions, and trigonometry including the sine and cosine laws.