The present book is based on lectures given by the author to students of various colleges studying mathematics. In designing this course, the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore, in most cases we did not give rigorous formal proofs of the theorem. The rigorousness of a proof often fails to be fruitful and therefore it is usually ignored in practical applications. The book can be of use to readers of various professions dealing with applications of mathematics in their current work. The subject matter is presented in a very systematic and logical manner. It contains material which you will find of great use, not only in the technical courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. In writing, the book the actual mathematical background of working engineers is taken for granted. The author has injected in this book his experience and expertise of teaching.