Advanced Engineering Mathematics
This text/reference covers essential areas of engineering mathematics involving single, multiple, and complex variations. Taken as a whole, this book provides a succinct, carefully organized guide for mastering engineering mathematics.
Unlike typical textbooks, Advanced Engineering Mathematics begins with a thorough exploration of complex variables because they provide powerful techniques for understanding topics, such as Fourier, Laplace and z-transforms, introduced later in the text. The book contains a wealth of examples, both classic problems used to illustrate concepts, and interesting real-life examples from scientific literature.
Ideal for a two-semester course on advanced engineering mathematics, Advanced Engineering Mathematics is concise and well-organized, unlike the long, detailed texts used to teach this subject. Since almost every engineer and many scientists need the skills covered in this book for their daily work, Advanced Engineering Mathematics also makes an excellent reference for practicing engineers and scientists.
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The Fourier Transform
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amplitude analytic Bessel functions boundary conditions closed contour complex number compute contour integral convergence convolution cosine ct/L delta function denotes derivative difference equations eigenfunction eigenvalues eigenvectors equals zero evaluate Example expansion Figure find the inverse finite fluid formula Fourier series Fourier transform frequency function f(t half-range harmonic heat equation illustrates infinite number interval Laplace transform Laplace's equation Legendre Let us find Let us solve line integral linear matrix method numerical solution ordinary differential equations orthogonality oscillations partial differential equation particular solution plane polynomials positive radius residue theorem rewrite right side Section separation of variables shifting theorem simple poles sine singularities solve the wave step function string Sturm-Liouville problem Substituting Taking the Laplace temperature tion transfer function vector field velocity vibrations wave equation yields yn(x z-transform