Linear Algebra & Analytical Geometry
Linear Equations. Gaussian Elimination And Matrices. Gauss-Jordan Method. Making Gaussian Elimination Work. Row Echelon Form And Rank. The Reduced Row Echelon Form. Consistency Of Linear Systems. Homogeneous Systems. Nonhomogeneous Systems. Linearity. Matrix Multiplication. Matrix Inversion. Inverses Of Sums and Sensitivity. Elementary Matrices And Equivalence. The LU Factorization. Vector Spaces. Spaces And Subspaces. Four Fundamental Subspaces. Linear Independence. Basis And Dimension. Classical Least Squares. Linear Transformations. Change Of Basis And Similarity. Invariant Subspaces. Vector Norms And InnerProducts. Orthogonal Vectors.
Gram-Schmidt Procedure. Eigenvalues And Eigenvectors. Elementary Properties of Eigen systems. Diagonalization by Similarity Transformations. Functions Of Diagonalizable Matrices. Normal Matrices. Positive Definite Matrices. Non-Diagonalizable Matrices And Jordan Form. Inclination and Slope of a Line. Division of a Line Segment. Relations & Functions; Equation of a Graph. Lines & First-Degree Equations. Other Forms of First-Degree Equations. Directed Distance from a Line to a Point; Families of Lines. Circles. Parabolas. Ellipses. Hyperbolas. Simplification by Translation. Rotation of Axes. Rotations & Translations. Polynomials. Rational Functions. Irrational Equations. The Polar Coordinate System. Graphs of Polar Coordinate Equations. Parametric Equations. Space Coordinates. Surface of Revolution and Quadric Surfaces. Cylindrical & Spherical Coordinates. Operations on Vectors