Course Description :
Vector, matrix, linear space, linear independent, linearly dependence, basis, span, sweep operation, basic matrix, matrix and subspace, linear equation system, the following linear equation system, non-homogeneous system of linear equations, inverse matrix, LU decomposition of the matrix, general inverse matrix, determinant, Definition of the determinant, nature of the determinant, cofactor matrix, area and volume, inner product and orthogonality, axioms and nature of the inner product, vector projection of least-squares method, general inverse matrix and linear equation system, subspace and orthogonality, orthogonalization of Gram-Schmidt, QR decomposition, orthogonal complement, Eigenvalues, Eigenvectors, diagonalization, real symmetric matrix, triangle of the matrix, quadratic form, 1st order linear differential equation system, Input-Output Analysis, transition probability matrix, Differential Equations, induction of differential equations, 1st order linear differential equation, homogeneous linear differential equation of higher order, Laplace transform and its applications, Laplace transform of basic function, fundamental law of Laplace transform, initial value problems of ordinary differential equations, function space and Fourier series, function space, Orthogonalization, Fourier series.
