Dear students (especially JC 2s),
When we study the various topics in H2 Mathematics, it is
useful and practical to find a unifying link between them, to
achieve effective and efficient learning.
In this short article, I will mention the role of
substitutions in H2 Mathematics through a few examples below.
We use substitutions in inequalities, when we wish to
deduce the solution of a new inequality based on a
previously solved one.
We use substitutions in integration, so that a complex
expression may become easier to integrate.
We use substitutions in solving some differential
equations, when the original DE looks daunting.
We use substitutions when finding the areas of curves
defined parametrically.
We use substitutions to understand the behaviour of
curves that have undergone transformations, e.g. the relationship
between the graphs of y = f(x) and y = f(ax).
We use substitutions in series expansions, e.g. we may
obtain the series expansion of ln (1 - 2x) from the standard
series expansion of ln (1 + x).
I would welcome more additions from fellow forumers,
to enrich this article further.
It is my hope that this will help students master a
number of topics at the same time when they revise :)
Thanks!
Cheers,
Wen Shih