Hooman Fatoorehchi Assistant Professor School of Chemical Engineering University of Tehran, Tehran, Iran Formulas in this page are typed in $\LaTeX$. Advanced Engineering Mathematics Syllabus for Advanced Engineering Mathematics (AEM-2020-1) 1- Applied linear algebra (withe emphasis on chemical engineering applications) 2- Analytical solution of functional equations including ODEs and PDEs (mostly linear cases) 3- Numerical solution of (nonlinear) ODEs and PDEs (using the FDM, the NSFDM, the Galerkin method, the Sinc collocation method, FEM, etc.) + Error analysis 4- Introduction to optimization 5- Mathematical libraries and software packages (MATLAB/simulink & Python) 6- Extras (orthogonal polynomial solutions of DEs)