This book is based on the experience and the lecture notes of the authors while teaching Mathematics courses for more than four decades. This comprehensive textbook covers the material for one semester core course in mathematics for Engineering students. The emphasis is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. Graded sets of examples (in text) and problems (in exercises) are used to explain each theoretical concept and application of these concepts in problem solving. Answers for every problem and hints for difficult problems are provided. This text offers a logical and lucid presentation of both theory and techniques for problem solving to motivate the students in the study and application of mathematics to solve Engineering problems.