Introduction -- 2 To begin with: PGD for Poisson problems -- 2.1 Introduction -- 2.2 The Poisson problem -- 2.3 Matrix structure of the problem -- 2.4 Matlab code for the Poisson problem -- 3 Parametric problems -- 3.1 A particularly challenging problem: a moving load as a parameter -- 3.2 The problem under the PGD formalism -- 3.2.1 Computation of S(s) assuming R(x) is known -- 3.2.2 Computation of R(x) assuming S(s) is known -- 3.3 Matrix structure of the problem -- 3.4 Matlab code for the influence line problem -- 4 PGD for non-linear problems -- 4.1 Hyperelasticity -- 4.2 Matrix structure of the problem -- 4.2.1 Matrix form of the term T2 -- 4.2.2 Matrix form of the term T4 -- 4.2.3 Matrix form of the term T6 -- 4.2.4 Matrix form for the term T8 -- 4.2.5 Matrix form of the term T9 -- 4.2.6 Matrix form of the term T10 -- 4.2.7 Final comments -- 4.3 Matlab code -- 5 PGD for dynamical problems -- 5.1 Taking initial conditions as parameters -- 5.2 Developing the weak form of the problem -- 5.3 Matrix form of the problem -- 5.3.1 Time integration of the equations of motion -- 5.3.2 Computing a reduced-order basis for the field of initial conditions -- 5.3.3 Projection of the equations onto a reduced, parametric basis -- 5.4 Matlab code -- References -- Index. .