Titlebook: Mathematical Methods for Engineers and Scientists 1; Complex Analysis and Kwong-Tin Tang Textbook 2022Latest edition The Editor(s) (if appl

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Complex NumbersThe most compact equation in all of mathematics is surely.

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Complex Series and Theory of ResiduesSeries expansions are ubiquitous in science and engineering. In the theory of complex functions, series expansions play a crucial role because they are the basis for deriving and using the theory of residues, which provide a powerful method for calculating both complex contour integrals and some difficult integrals of real variable.

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Matrix AlgebraMatrices were introduced by British mathematician Arthur Cayley (1821–1895). The method of matrix algebra has extended far beyond mathematics into almost all disciplines of learning.

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Eigenvalue Problems of MatricesGiven a square matrix ., to determine the scalars . and the non-zero column matrix . which simultaneously satisfy the equation.

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https://doi.org/10.1007/978-3-031-05678-9Advanced Engineering Mathematics; Graduate-Level Calculus; Differential Equations; Conformal Mapping; Gr

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Determinantsrobably already possess the knowledge of evaluating second- and third-order determinants. After a systematic review, we introduce the formal definition of a .th-order determinant through the Levi-Civita symbol. All properties of determinants can be derived from this definition.

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Mathematical Methods for Engineers and Scientists 1Complex Analysis and