Intermediate Mathematics (EQT 241/3)

This third edition of Advanced Engineering Mathematics has been completely updated and revised to reflect changes in undergraduate engineering education based on the widespread use of computers. Written specifically for engineering students, it introduces mathematical methods essential to solving real-world problems. Written in a clear, accessible style, the third edition incorporates three software packages--Maple®, Excel®, and MATLAB®--in problems and examples throughout the text. Topics covered include series methods, Laplace transforms, matrix theory and applications, vector analysis, Fourier series and transforms, partial differential equations, numerical methods using finite differences, complex variables, and wavelets. Advanced Engineering Mathematics, Third Edition, is ideal for upper-level undergraduate or first-year graduate courses in advanced engineering mathematics, engineering analysis, or applied mathematics.

Engineers require a solid knowledge of the relationship between engineering applications and underlying mathematical theory. However, most books do not present sufficient theory, or they do not fully explain its importance and relevance in understanding those applications. Advanced Engineering Mathematics with Modeling Applications employs a balanced approach to address this informational void, providing a solid comprehension of mathematical theory that will enhance understanding of applications - and vice versa. With a focus on modeling, this book illustrates why mathematical methods work, when they apply, and what their limitations are.Designed specifically for use in graduate-level courses, this book: Emphasizes mathematical modeling, dimensional analysis, scaling, and their application to macroscale and nanoscale problems Explores eigenvalue problems for discrete and continuous systems and many applications Develops and applies approximate methods, such as Rayleigh-Ritz and finite element methods Presents applications that use contemporary research in areas such as nanotechnology Apply the Same Theory to Vastly Different Physical Problems Presenting mathematical theory at an understandable level, this text explores topics from real and functional analysis, such as vector spaces, inner products, norms, and linear operators, to formulate mathematical models of engineering problems for both discrete and continuous systems. The author presents theorems and proofs, but without the full detail found in mathematical books, so that development of the theory does not obscure its application to engineering problems. He applies principles and theorems of linear algebra to derive solutions, including proofs of theorems when they are instructive.Tying mathematical theory to applications, this book provides engineering students with a strong foundation in mathematical terminology and methods.

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are: - Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis. This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.