1. Simpson's rule is three-diagonal 2. For the standard linear basis is the smallest possible functions, the degrees of freedom (dofs) 3. The 2nd law of Thermodynamics states that is made smaller the entropy of an isolated macroscopic system 4. The Finite element method is an orthogonal basis for L^2(0,2*pi) 5. Forming a projection into a subspace of is unique functions 6. Trapezoidal rule is constant 7. Linear hat-functions and exact is equal to the required integration implies that the number of degrees of freedoms mass-matrix (dofs) 8. A finer computational mesh generally, is non-decreasing but not always, implies that the error 9. The Legendre polynomials is dependent on the regularity of the target function 10. Generally, whatever basis is used, is not the same thing a mass-matrix 11. The Laws of Thermodynamics imply that is mathematically equivalent the energy in a closed system to the Lagrange interpolant, but is numerically preferred 12. The Finite difference method is diagonal 13. For a well-posed problem, the solution is a matter of defining suitable basis functions and forcing the residual to be orthogonal against all such basis functions 14. The family of trigonometric functions sin(m*x) is exact for quadratic and cos(n*x), for m = 1,2,3,... and n = 0,1,2,3... polynomials 15. Standard linear hat-functions plus the is an orthogonal polynomial trapezoidal rule implies that the mass-matrix basis for L^2(-1,1) 16. The dimensionality of a discrete is obtained by integrating function space a linear interpolant 17. Orthogonal basis functions implies that is always symmetric the mass-matrix 18. Beware that order of convergence and is diagonal accuracy 19. When measured in the L^2-norm, the error is a kind of "PDE-solver in the projected result through interpolation" 20. The error in an interpolant is just the function's nodal-values 21. The Newton interpolating polynomial is a projection-based PDE-solving numerical method