Titlebook: Higher Mathematics for Physics and Engineering; Tsuneyoshi Nakayama,Hiroyuki Shima Textbook 2010 Springer-Verlag Berlin Heidelberg 2010 An

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Wavelet Transformationical mold with a finite-length and fast-decaying oscillating waveform, which is used to divide a given function into different scale components. Wavelet transforms have certain advantages over conventional Fourier transforms, as they can reveal the nature of a function in the time and frequency doma

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tical topology for knot theory.- Exposition of mathematical .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 contemporar

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Textbook 2010signed 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 con

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Hilbert Spaces covered in this volume are AQ1 based on Hilbert spaces. In particular, L. spaces and l. spaces (Sect. 4.3), which are specific classes of Hilbert spaces, are crucial for the formulation of the theories of orthonormal polynomials, Lebesgue integrals, Fourier analyses, and others, as we discuss in subsequent chapters.

Seminar

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Complex Functions that are highly relevant and useful in mathematical physics. However, before moving on to the principal discussion, we deal with the underlying concepts of analytic functions (Sect. 7.1.2) and the geometric meaning of analyticity (Sect. 7.1.5).

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Conformal Mappingons with inconvenient geometries. In this chapter we show that a problem can be drastically simplified by choosing an appropriate mapping, which allows us to evaluate the solution using elementary calculus.

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Fourier Seriesseries (Sect. 11.2.1) and the conditions that are necessary for the series to be uniformly convergent (Sect. 11.3.1). Better understanding of convergence properties clarifies the reasons for the utility and the limit of validity of Fourier series expansion in mathematical physics.