Further series
Section overview:
The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
Summary questions:
Topic assessment 1 (with solutions) - Method of differences
Topic assessment 2 (with solutions) - Maclaurin series
Extra resources:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
In particular, 'The Essence of Calculus' video series is dotted throughout the relevant topic pages in A-level Maths and Further Maths, or you can find the full playlist here. These videos demonstrate a deeper cut of some of the most important ideas within A-level, so they are well worth a watch!
Topic videos:
- The method of differences
- Introduction to Maclaurin series: polynomial approximations
- The general Maclaurin series [Given in formulae booklet]
- Maclaurin series of standard functions [Initial results given in formulae booklet]
- Maclaurin series of composite functions
Another nice introductory video to Taylor series:
Extra fun! The Essence of Calculus - Taylor series:
Applications of Taylor series:
Infinite fun!