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This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal.The methods treated in more detail include spectral representation and "frequency" of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of "wavelets" in connection with the "multi-scale" structure of data-sets.The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.
List of contents
Linear Spaces.- Linerar Analysis.- Spectral Methods and Applications.- Frequency-Domain Methods.- Data Compression.- Fourier Series.- Fourier Time-Frequency Methods.- Wavelet Transform and Filter Banks.- Compactly Supported Wavelets.- Wavelet Analysis.
Summary
This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal.
The methods treated in more detail include spectral representation and “frequency” of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of “wavelets” in connection with the “multi-scale” structure of data-sets.
The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.
Additional text
From the book reviews:
“The work under review is an elementary textbook on several contemporary topics in applied mathematics that should appeal to mathematics, science, and engineering students. It is written in a modular form that makes it suitable for a variety of courses or seminars in applied mathematics.” (Marcin M. Bownik, Mathematical Reviews, December, 2014)
Report
From the book reviews:
"The work under review is an elementary textbook on several contemporary topics in applied mathematics that should appeal to mathematics, science, and engineering students. It is written in a modular form that makes it suitable for a variety of courses or seminars in applied mathematics." (Marcin M. Bownik, Mathematical Reviews, December, 2014)
