This book has been primarily written according to the latest syllabus of professional mathematics for third semester students of the polytechnics. Emphasis has been laid on making the concepts clear. Presentation is very simple and in logical manner. Simple and lucid language has been used while writing the text. Lots of pain and concentration on the part of the author has gone into solving the examples in the best possible way. There are large number of solved examples added in different chapters. The examples are graded from simple to difficult. While providing solutions to the problems care has been taken not to miss even minor steps so that the students can follow the subject easily. Tabular explanation of specific topics have been included in the solutions of the problems. The book is very user-friendly. The students should be able to grasp the matter even without the help of a teacher.