This textbook on engineering mathematics is designed as a self-study text for students of all engineering branches for the second level core course in mathematics. Besides the students, it is an useful reference for scientists and practicing engineers. The demands of current technology calls for solving difficult mathematical problems, some of which require an understanding of advanced mathematical concepts. So this book is designed in a manner that serves both as a textual, as well as a job oriented book, to fulfill the modern requirements. The text takes the reader from ordinary differential equations to more sophisticated mathematics - fourier analysis, vector and tensor analysis, complex variables, partial differential equations, and random processes. The emphasis is on the use of mathematical tools and techniques. Table of Contents 1. Ordinary Differential Equations. 2. Special Functions. 3. Matrix Methods and Linear Vector Spaces. 4. Vector Analysis. 5. Tensor Analysis. 6. Complex Variables. 7. Complex Integration, Laurent Series, and Residues. 8. Fourier Series, Eigenvalue Problems, and Green's Function. 9. Fourier and Related Transforms. 10. Laplace, Hankel, and Mellin Transforms. 11. Calculus of Variations. 12. Partial Differential Equations. 13. Probability and Random Variables. 14. Random Processes. 15. Applications.