This revised and updated edition has been specifically designed to comprehensively and expertly address the key skills and knowledge areas set out in the 2000 edition of the Mathematics Study Design. It emphasises relevant applications with clear examples and excellent exercises which specifically include questions and examples that foster effective and appropriate use of technology. Also included are excellent revision summaries and exercises, as well as analysis questions in every chapter to ensure that students are thoroughly prepared for examinations. Answers are provided for all exercises. Fully worked solutions to all applications and analysis questions are provided in Essential Further Mathematics Solutions Supplement (second edition).