The second edition differs from the first in three respects. First, the format is different. Wide margins are now provided so that readers can pencil in small individual notes and comments which may be of assistance to them later on. Second, each chapter has been provided with extra exercises. Generally these are of the more routine variety and have been incorporated hefore the assignment. All the exercises are supplied with answers which are located at the end of the book. Third, some marginal diagrams and ref- erences have heen included to help illuminate the material and occasionally to indicate where a topic fits into the overall scheme. It is hoped that students will find in the new edition plenty to sustain the development of their mathematical knowledge and skills. The author thanks all those who have contrihuted to the production of this book. eWE Preface to the first edition Students reading for degrees and diplomas in Engineering and Applied Science arrive with a wide variety of mathematical backgrounds. Neverthe- less by the end of the first year of study all of them must have achieved a minimum standard in mathematics and also have acquired sufficient skill to enable them to cope with the more advanced mathematical topics in the second year. Experience has shown that many students are unable to cope with the traditional mathematics textbooks because they find them remote and the concepts difficult to handle.