• Chapter 8 – Solving Equations Numerically

     

    When students have completed this lesson they should be able to:

    • Use the sign-change rules to find approximate solutions by decimal search
    • Know how to use a chord approximation to improve the efficiency of decimal search
    • Use an iterative method to produce a sequence which converges to a root
    • Understand that the choice of iterative method affects whether a sequence converges or not, and know what determines its behavior
    • Appreciate that it is possible to modify and iterative method to speed up convergence
    • Appreciate that decisions about choice of method may depend on what sort of calculator or computer software you are using

     

    Chapter 9 – The Trapezium Rule

     

    When students have completed this lesson they should be able to:

    • Use the trapezium rule to estimate the value of a definite integral
    • Use a sketch, in some cases, to determine whether the trapezium rule approximation is an overestimate or an underestimate