The lecture deals with the numerical treatment of differential equations which arise from different mechanical and thermodynamical problems. Contents are:

• deduction of differential equations based on the principles of mechanics and thermodynamics and their classification
• the Finite Difference Method
• the method of weighted residuals: method of subdomains, collocation method, least squares method, and Galerkin's method
• the Finite Element Method
• different time integration schemes, convergence and stability