Course Content

Complex Numbers and Representations. Powers and Roots. Function of Complex Variables. Cauchy-Reimann Equation. Complex Integration. Line Integral. Cauchy’s Integral. Matrices. Matrix Algebra. Linear System of Equations. Rank of a Matrix. Determinants. Cramer’s Rule. Inverse of a Matrix. Vector Spaces. Inner Product. Eigenvalues and Eigenvectors. Symmetric and Orthogonal Matrices. Eigenbases. Diagonalization. Quadratic Forms. Gram-Schmidt Orthogonalization. Differential Equations. Ordinary Differential Equations (ODEs). Separable ODEs. Exact ODEs. Linear ODEs. Second-Order Linear ODEs. Homogeneous Linear ODEs with Constant Coefficients. Euler–Cauchy Equations. Modeling Engineering Problems with ODEs. Higher Order Linear ODEs. Systems of ODEs. Wronskian. Function of Matrices. Constant-Coefficient Systems. Critical Points and Stability.

•  Do the mathematical operations on complex numbers
•  Take the derivative and integral of functions of complex variables
•  Do operations on matrices and determinants
•  Determine the eigenvalues and eigenvectors of matrices
•  Solve the linear system of equations using matrices.
•  Analyze the linear, separable, and exact ordinary differential equations
•  Solve second order ordinary differential equations.
•  Find the solutions to the systems of ordinary differential equations