MATH 1025 3.0 M  W 2002 APPLIED LINEAR ALGEBRA

 SYLLABUS (the syllabus is subject to changes announced in class) Polar, Cylindrical and -Polar Coordinate System Spherical Coordinates -Polar Coordinate Equations and their Graphs -Cylindrical Coordinate System -Spherical Coordinate System Complex Numbers -Complex Numbers in Standard Form -Operations on Complex Numbers in Standard Form -Polar Form of a Complex Number -Finding Powers and Roots of Complex Numbers Systems of Linear Equations -Gaussian Elimination -Matrices and Matrix Operations -Inverses; Rules of Matrix Arithmetic -Elementary Matrices and Method for Finding A-1 -Further Results on Systems of Equations and Invertibility -Diagonal, Triangular, and Symmetric Matrices Determinants -Evaluating Determinants by Row Reduction -Properties of the Determinant Function -Cofactor Expansion; Cramer's Rule Vectors in 2-space and 3-space -Introduction to Vectors (Geometric) -Norm of a Vector; Vector Arithmetic -Dot Product; Projections -Cross Product -Lines and Planes in 3-space Euclidean Vectors Spaces -Euclidean n-Space -Linear Transformations from Rn to Rm -Properties of Linear Transformations from Rn to Rm General Vector Spaces -Real Vector Spaces -Subspaces -Linear Independence -Basis and Dimension -Row Space, Column Space, Nullspace -Rank and Nulllity Inner Product Spaces -Orthonormal Bases -Gram-Schmidt Process; QR-Decomposition Eigenvalues, Eigenvectors -Eigenvalues and Eigenvectors -Diagonalization -Orthogonal Diagonalization