Applied Numerical Analysis

1 - Introduction Preliminary background; Formulation of ordinary and partial differential equations; Singular solution and complete primitive; Initial and boundary value problems; Graphical representation; References 2 - Ordinary differential equations Introduction; Some preliminaries of finite difference; Numerical differentiations; Numerical integrations; Numerical solution of ODE; Second- and higher-order equations; Finite difference methods; Application to practical problems; References 3 - Partial differential equations Introduction; Finite difference methods; the finite element method; The boundary element method; References 4 - Nonlinear differential equations and stability Introduction; Solutions of trajectories; The phase plane and the linear system; Stability of almost linear systems; Liapounov's second method; Periodic solutions and limit cycles; Some practical problems; References 5 - The calculus of variations Introduction; Systems of Euler-Lagrange equations; The extrema of integrals under constraints; Sturm-Liouville problems; Principles of variations; Hamilton's principles; Hamilton's equations; Some practical problems; References 6 - Applications Introduction; Stability of subsystems; Oceanwaves; Nonlinear wave-wave interactions; Seismic response of dams; Green's function method for waves; References