Mathematics II
Deep Understanding: 85 hours
This course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigenvalues and eigenvectors, and singular value decomposition of a matrix.
Familiarize with concepts and techniques of linear algebra,Solve systems of linear equations using the Gauss-Jordan method,Understand vector spaces and subspaces,Compute eigenvalues and eigenvectors of a matrix,Understand diagonalization of a matrix, linear programming, and basic algebraic structures such as Group, Ring, and Field
Course Contents
System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence
Introduction to linear transformations, The matrix of a linear transformation, Linear models in business, science, and engineering
Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Partitioned matrices, Matrix factorization, The Leontief input-output model, Subspace of Rn, Dimension and rank
Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems
Dimension of vector space and Rank, Change of basis, Applications to difference equations, Applications to Markov Chains
Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to differential equations
Inner product, Length, and Orthogonality, Orthogonal sets, Orthogonal projections, The Gram-Schmidt process, Least squares problems, Application to linear models, Inner product spaces, Applications of inner product spaces