About the Book

This version of the world’s most successful and popular textbook for engineering mathematics -Advanced Engineering Mathematics by Prof. Erwin Kreyszig - brings to students this legendary textbook as per their latest (JNTU) syllabus. This version of the book fulfills the need for a book that not only effectively explains the concepts but also tests the grasping ability of the students. While retaining the basic ideology and vision of Kreyszig, the contents have been restructured for easy comprehension.

In a concise and easy-to-understand manner, this book exclusively promotes the numerical analysis of matrices and their transformations, vectors, ordinary and partial differential equations and nonlinear systems that form the crux of this discipline. These topics find application in proving various theorems, calculation of mathematical quantities, derivation of expressions and formulas.
Every chapter has easy to follow explanations of the theory and numerous step-by-step solved problems and examples. The questions have been hand-picked from the question papers of last five years and are suitable to the current pattern of questions asked.

How is this book different from original Kreyszig
Apart from the text from the original book, this book explains the following topics that are absent from Kreyszig’s text:
· Proof to Cayley-Hamilton Theorem and Inverse of Cayley-Hamilton Theorem provided as required by the current pattern of questions asked.
· The concept of Modal and Spectral Matrices introduced.
· The concepts of Positive, Negative, Definite, and Semi-definite Quadratic Forms as also Sylvester’s Law of Inertia introduced.
· Finite Fourier transforms and Inverse Fourier transforms added.
· Partial Differential Equations divided in two chapters.
An instructor CD is available that is designed to provide instructors with chapter-wise powerpoint presentations, and an image gallery.

About the Author

Dr. A. Ramakrishna Prasad is presently Head of the Department of Mathematics, Jawaharlal Nehru Technological University College of Engineering, Hyderabad and Chairman Board of Studies (Mathematics) of Jawaharlal Nehru Technological University, Hyderabad. Having a passion for teaching, he made a modest beginning as a teaching assistant in 1980 and has been serving the Jawaharlal Nehru Technological University in various capacities since then. He has a vast teaching experience of over two decades and has been teaching varied subjects such as Engineering Mathematics, Information Systems, Database Management Systems, etc., and continues to explore different domains in Sciences and Engineering. Besides vast experience in teaching, he is an able administrator and has held several key positions. He has published qualitative research papers in reputed journals. He is in the expert panel for many academic bodies like IGNOU and BROAU and has been actively involved in efficient organization of numerous seminars, workshops and orientation programs. Dr. Prasad is an M.Tech (1992) in Computer Science and Data Processing from one of the most prestigious premier institutions, IIT Kharagpur. Subsequently, in 1995, he obtained PhD in Mathematics from SK University, Anantapur. He is also a life member of ISTE, CSI, NHRDN, IETE and Neuro-Linguistic Program Practitioners Club Florida (USA).

Table of Contents:
Contents About the Author Preface Preface of the Ninth Edition 1 Linear Systems Learning Objectives • Introduction to Matrices • Systems of Linear Algebraic Equations • Rank of a Matrix • Consistent and Inconsistent Nonhomogeneous Linear Equations • Inverse of a Matrix • Reduction to Normal Form • Gauss Elimination Method Solved Problems Summary Review Questions and Problems 2 Eigenvalues and Eigenvectors Learning Objectives • 2.1 An Introduction to Eigenvalues and Eigenvectors • 2.2 Properties of Eigenvalues and Eigenvectors • 2.3 Cayley-Hamilton Theorem and Inverse of a Matrix • 2.4 Modal and Spectral Matrices • 2.5 Diagonalization and Powers of a Matrix • 2.6 Eigenvalue Problems Solved Problems Summary Review Questions and Problems 3 Linear Transformations 183 Learning Objectives • 3.1 Real Matrices • 3.2 Linear Transformations • 3.3 Orthogonal Transformations and Orthogonal Matrices • 3.4 Complex Matrices Solved Problems Summary Review Questions and Problems 4 Quadratic Forms Learning Objectives • 4.1 Introduction • 4.2 Types of Quadratic Forms • 4.3 Transformation of Quadratic Form • 4.4 Sylvester’s Law of Inertia Solved Problems Summary Review Questions and Problems 5 Fourier Series Learning Objectives • 5.1 An Introduction • 5.2 Periodic Functions • 5.3 Dirichlet’s Conditions • 5.4 Fourier Series in Arbitrary Interval • 5.5 Even and Odd Functions • 5.6 Half-Range Expansions Solved Problems Summary Review Questions and Problems 6 Partial Differential Equations Learning Objectives • 6.1 Basic Concepts • 6.2 Formation of PDE • 6.3 Solution of a PDE • 6.4 Solution of Nonlinear Partial Differential Equations Solved Problems Summary Review Questions and Problems 7 Solutions of Partial Differential Equations Learning Objectives • 7.1 Basic Concepts • 7.2 Modeling: Vibrating String, Wave Equation • 7.3 Solution by Separating Variables. Use of Fourier Series • 7.4 D’Alembert’s Solution of the Wave Equation • 7.5 Modeling: Membrane, Two-Dimensional Wave Equation • 7.6 Heat Equation: Solution by Fourier Series • 7.7 Laplacian in Polar Coordinates • 7.8 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential • 7.9 Solution of PDEs by Laplace Transforms Solved Problems Summary Review Questions and Problems 8 Fourier Integrals and Transforms Learning Objectives • 8.1 Fourier Integral Theorem • 8.2 Fourier Cosine Integral and Fourier Sine Integral • 8.3 Fourier Transform in Complex Form • 8.4 Fourier Cosine and Sine Transforms Solved Problems Appendix: Tables of Transforms Summary Review Questions and Problems Model Paper - I Model Paper - II Model Paper - III