Educational guide 2023_24 School of Chemical Engineering

Contents

Topic	Sub-topic
First order ordinary differential equations.	Analysis of critical points. Derivatives field. Numerical methods to solve odes: Euler, Runge-Kutta, predictor-corrector and multistep methods. Stiff type problems. Implicit Euler's method. MATLAB "ode suite" solvers
Systems of first order ordinary differential equations.	Solution of homogeneous linear ode systems with constant coefficients. Non-homogeneous systems: method of variation of constants. Solution by Laplace transform. Stability analysis of planar autonomous systems. Linear stability criterion for non-linear systems. Solving with MATLAB
Second and higher order ordinary differential equations	Analytical solution. Initial value problems: numerical solution of the equivalent system of odes. Boundary problems: shooting method, MATLAB solvers and finite difference method.
Laplace transform	Definition, properties. Inverse Laplace transform. Application to the resolution of initial value problems of linear differential equations.
Partial differential equations.	Introduction and types of partial differential equations. Separation of variables. Example: linear diffusion problems. Stationary and non-stationary problems. Diffusion, convection, evolution and propagation terms. Finite difference solution. Solving with MATLAB.