This comprehensive, well organized and easy to read book presents concepts in a unified framework to establish a similarity in the methods of solutions and analysis of such diverse systems as algebraic equations, ordinary differential equations and partial differential equations. The distin-guishing feature of the book is the clear focus on analytical methods of solving equations. The text explains how the methods meant to elucidate linear problems can be extended to analyse nonlinear problems. The book also discusses in detail modern concepts like bifurcation theory and chaos.To attract engineering students to applied mathematics, the author explains the concepts in a clear, concise and straightforward manner, with the help of examples and analysis. The significance of analytical methods and concepts for the engineer/scientist interested in numerical applications is clearly brought out.Intended as a textbook for the postgraduate students in engineering, the book could also be of great help to the research students. About The Author: PUSHPAVANAM S. Ph.D. (Florida) Associate Professor, Department of Chemical Engineering, Indian Institute of Technology Madras. Earlier, he taught at Indian Institute of Technology Kanpur. A recipient of the prestigious Fullbright Fellowship, Dr. Pushpavanam pursues research in areas such as applied mathematics, mathematical modelling, chemical engineering and multiphase flow. Table Of Contents Preface. Models in Chemical Engineering. Vector and Vector Spaces. Matrices, Operators and Transformations. Applications to Chemical Engineering Systems. Partial Differential Equations. Sturm-Louiville Theory. Separation of Variables and Fourier Transforms. Green's Function. Uniqueness Conditions for Linear and Nonlinear Systems. Steady State Characteristics of Nonlinear Dynamical Systems. Linear Stability and Limit Cycles. Secondary Bifurcations and Chaos. Index