Advanced Engineering Mathematics

This book, based on the experience and notes of the authors while teaching mathematics courses to engineering students for more than three decades, emphasizes the fundamental and theoretical concepts. The key features of this book are Illustrative examples and exercises explain each theoretical concept, 682 Solved Examples and 2984 Problems, Answers and hints for problems given to motivate students for self-learning, Logical and lucid presentation of both the theory and problem solving techniques. Table Of Contents: Preface to the Third Edition / Preface to the Second Edition / Functions of a Real Variable / Functions of Several Real Variables / Matrices and Eigenvalue Problems / Ordinary Differential Equations of First Order / Linear Differential Equations / Series Solution of Differential Equations / Legendre Polynomials, Chebyshev Polynomials, Bessel Functions and Sturm-Liouville Problem / Laplace Transformation / Fourier Series, Fourier Integrals and Fourier Transforms / Functions of a Complex Variable: Analytic Functions / Integration of Complex functions / Power Series, Taylor and Laurent Series / Zerosz Singularities and Residues / Bilinear Transformations and Conformal Mapping / Vector Differential and Integral Calculus / Partial Differential Equations / Z Transformation / Numerical Methods / Theory of Probability / Mathematical Statistics ? Tests of Significance / Appendix / Some Reference Textbooks / Index. Audience Applied Mathematicians & Engineering Students Special Features: New to the Third Edition Chapters on:?Numerical Methods?Theory of Probability?Mathematical Statistics ? Tests of Significance 1. Functions of a Real Variable 2. Functions of Several Real Variables 3. Matrices and Eigenvalue Problems 4. Ordinary Differential Equations of First Order 5. Linear Differential Equations 6. Series Solution of Differential Equations 7. Legendre Polynomials, Bessel Functions and Sturm-Liouville Problem 8. Laplace Transformation 9. Fourier Series, Fourier Integrals and Fourier Transforms 10. Functions of a Complex Variable: Analytic Functions 11. Integration of Complex functions 12. Power Series, Taylor and Laurent Series 13. Zeros, Singularities and Residues 14. Bilinear Transformations and Conformal Mapping 15. Vector Differential and Integral Calculus. This work is based on the experience and notes of the authors while teaching mathematics courses to engineering students at the Indian Institute of Technology, New Delhi. It covers syllabi of two core courses in Mathematics for Engineering students.