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