Advanced Engineering Mathematics

The fourth edition of this very successful 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 the book are illustrative examples and exercises that explain each theoretical concept. NEW TO THE FOURTH EDITION: Chapters on: \* Condition number of a matrix and Singular Value Decomposition (Chapter 3) \* Application of Z-transforms to find the sum of series (Chapter 17) \* Cubic splines, B-splines, Romberg integration, Gauss quadrature rules and Two- point boundary value problems Front Cover Title Page Preface Contents 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 Solutions of Differential Equations 7. Legendre Polynomials, Chebyshev 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 16. Partial Differential Equations 17. Z Transformation 18. Numerical Methods 19. Theory of Probability 20. Mathematical Statistics - Test of Significance Appendix 1. Tests for Convergence Appendix 2. Canonical form of Variable Coefficient Second Order Partial Differential Equations Appendix 3. Orthogonal Curvilinear Coordinate Systems Some Reference Textbooks Index Back Cover