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.

Concisely and clearly written, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics in condensed matter physics and statistical mechanics. The first part outlines different fractal structures observed in condensed matter. The main part of the book is dedicated to the dynamical behaviour of fractal structures, including anomalous and percolating systems. The concept of multifractals is illustrated for the metal-insulator quantum phase transition. The authors emphasize the unified description of these different dynamic problems, thus making the book accessible to readers who are new to the field.

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.

Concisely and clearly written, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics in condensed matter physics and statistical mechanics. The first part outlines different fractal structures observed in condensed matter. The main part of the book is dedicated to the dynamical behaviour of fractal structures, including anomalous and percolating systems. The concept of multifractals is illustrated for the metal-insulator quantum phase transition. The authors emphasize the unified description of these different dynamic problems, thus making the book accessible to readers who are new to the field.