LaGuardia Community College
City University of New York
Department of Mathematics, Engineering, and Computer Sciences
MAT 212: Linear Algebra and Vector Analysis for Engineers
Prerequisite: MAT 203. Credits/Contact hours: 3 hours.
Instructional Objectives:
This course serves as an extension of the traditional calculus sequence and contains additional
topics relevant to students majoring in engineering. Topics include matrix algebra, systems of
linear equations and Gaussian elimination method, determinant of a matrix, eigenvalues and
eigenvectors, parametric curves and surfaces, arc length, line and surface integrals, fundamental
theorem for line integrals, curl and divergence, Green's theorem, Stokes' theorem and Divergence
theorem. Major applications will be developed.
Performance Objectives:
During this course, the students will acquire the ability:
•To represent systems of linear equations as matrix equations and to obtain solutions by matrix
methods such as Gaussian elimination.
•To recognize algebraic properties of matrices and to perform matrix operations such as addition
and multiplication.
•To find inverse of matrix where possible.
•To compute the determinant of square matrices using various methods.
•To determine spanning sets, bases and the corresponding dimension, and coordinate systems for
such spaces.
•To determine linear independence or dependence of sets of vectors.
•To find eigenvalues and eigenvectors for 2 × 2 and 3 × 3 matrices.
•To use eigenvector methods to solve a system of first-order ordinary differential equations.
•To find arc lengths, areas of surfaces, and volumes of solids.
•To describe parametrized surfaces, surface areas.
•To compute line integrals, recognize and apply the fundamental theorem for line integrals.
