4TTV410EX - Integration and differential equations (PI)

The pdf file contains a short course about numerical schemes to solve approximately differential equations.

The course offers a very clear introduction to these numerical schemes, but there are a few misprints:

• in the paragraph "Estimation of the error", the error is of order Δt, and not Δt^2
• in the paragraph "Backward Euler method", the text is not very clear. The idea is that the expressions (8) and (9) are equivalent in the sense that their Taylor expansions have the same accuracy if x is the solution of the differential equation.
• in the paragraphs "second order Runge Kutta" and "fourth order Runge Kutta",
  you can remove the  O(Δt^3) in the expression of x(n+1)