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E-book
Author Tang, K. T., 1936-

Title Mathematical methods for engineers and scientists. 1, Complex analysis and linear algebra / Kwong-Tin Tang
Edition 2nd ed
Published Cham : Springer, 2022

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Description 1 online resource (498 p.)
Contents Intro -- Preface to Second Edition -- Preface to the First Edition -- Contents -- Part I Complex Analysis -- 1 Complex Numbers -- 1.1 Our Number System -- 1.1.1 Addition and Multiplication of Integers -- 1.1.2 Inverse Operations -- 1.1.3 Negative Numbers -- 1.1.4 Fractional Numbers -- 1.1.5 Irrational Numbers -- 1.1.6 Imaginary Numbers -- 1.2 Logarithm -- 1.2.1 Napier's Idea of Logarithm -- 1.2.2 Briggs' Common Logarithm -- 1.3 A Peculiar Number Called e -- 1.3.1 The Unique Property of e -- 1.3.2 The Natural Logarithm -- 1.3.3 Approximate Value of e
1.4 The Exponential Function as an Infinite Series -- 1.4.1 Compound Interest -- 1.4.2 The Limiting Process Representing e -- 1.4.3 The Exponential Function ex -- 1.5 Unification of Algebra and Geometry -- 1.5.1 The Remarkable Euler Formula -- 1.5.2 The Complex Plane -- 1.6 Polar Form of Complex Numbers -- 1.6.1 Powers and Roots of Complex Numbers -- 1.6.2 Trigonometry and Complex Numbers -- 1.6.3 Geometry and Complex Numbers -- 1.7 Elementary Functions of Complex Variable -- 1.7.1 Exponential and Trigonometric Functions of z -- 1.7.2 Hyperbolic Functions of z
1.7.3 Logarithm and General Power of z -- 1.7.4 Inverse Trigonomeric and Hyperbolic Functions -- 2 Complex Functions -- 2.1 Analytic Functions -- 2.1.1 Complex Function as Mapping Operation -- 2.1.2 Differentiation of a Complex Function -- 2.1.3 Cauchy-Riemann Conditions -- 2.1.4 Cauchy-Riemann Equations in Polar Coordinates -- 2.1.5 Analytic Function as a Function of z Alone -- 2.1.6 Analytic Function and Laplace's Equation -- 2.2 Complex Integration -- 2.2.1 Line Integral of a Complex Function -- 2.2.2 Parametric Form of Complex Line Integral -- 2.3 Cauchy's Integral Theorem
2.3.1 Green's Lemma -- 2.3.2 Cauchy-Goursat Theorem -- 2.3.3 Fundamental Theorem of Calculus -- 2.4 Consequences of Cauchy's Theorem -- 2.4.1 Principle of Deformation of Contours -- 2.4.2 The Cauchy Integral Formula -- 2.4.3 Derivatives of Analytic Function -- 3 Complex Series and Theory of Residues -- 3.1 A Basic Geometric Series -- 3.2 Taylor Series -- 3.2.1 The Complex Taylor Series -- 3.2.2 Convergence of Taylor Series -- 3.2.3 Analytic Continuation -- 3.2.4 Uniqueness of Taylor Series -- 3.3 Laurent Series -- 3.3.1 Uniqueness of Laurent Series -- 3.4 Theory of Residues
3.4.1 Zeros and Poles -- 3.4.2 Definition of the Residue -- 3.4.3 Methods of Finding Residues -- 3.4.4 Cauchy's Residue Theorem -- 3.4.5 Second Residue Theorem -- 3.5 Evaluation of Real Integrals with Residues -- 3.5.1 Integrals of Trigonometric Functions -- 3.5.2 Improper Integrals I: Closing the Contour with a Semicircle at Infinity -- 3.5.3 Fourier Integral and Jordan's Lemma -- 3.5.4 Improper Integrals II: Closing the Contour with Rectangular and Pie-Shaped Contour -- 3.5.5 Integration Along a Branch Cut -- 3.5.6 Principal Value and Indented Path Integrals -- 4 Conformal Mapping
Summary Part 1 of this popular graduate-level textbook focuses on mathematical methods involving complex analysis, determinants, and matrices, including updated and additional material covering conformal mapping. The second edition comes with extensive updates and additions, making them a more complete reference for graduate science and engineering students while imparting comfort and confidence in using advanced mathematical tools in both upper-level undergraduate and beginning graduate courses. This set of student-centered textbooks presents topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transformations, and ordinary and partial differential equations in a discursive style that is clear, engaging, and easy to follow. Replete with pedagogical insights from an author with more than 30 years of experience in teaching applied mathematics, this indispensable set of books features numerous clearly stated and completely worked out examples together with carefully selected problems and answers that enhance students' understanding and analytical skills
Notes 4.1 Examples of Problems Solved by Conformal Mappings
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed November 3, 2022)
Subject Mathematical physics.
Engineering mathematics.
Mathematical models.
Engineering mathematics
Mathematical models
Mathematical physics
Form Electronic book
ISBN 9783031056789
3031056787
Other Titles Complex analysis and linear algebra