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BL
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| Record Number
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843706
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| Main Entry
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D'Angelo, John P.
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| Title & Author
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Linear and complex analysis for applications /\ John P. D'Angelo.
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| Edition Statement
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1st
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| Publication Statement
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Boca Raton :: CRC Press,, 2017.
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| Series Statement
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Advances in applied mathematics
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| Page. NO
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1 online resource
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| ISBN
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131511884X
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: 1498756115
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: 1498756166
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: 1498756174
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: 9781315118840
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: 9781498756112
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: 9781498756167
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: 9781498756174
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1498756107
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9781498756105
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1: Linear algebra; 1. Introduction to linear equations; 2. Vectors and linear equations; 3. Matrices and row operations; 4. Equivalence relations; 5. Vector spaces; 6. Dimension; 7. Eigenvalues and eigenvectors; 8. Bases and the matrix of a linear map; 9. Determinants; 10. Diagonalization and generalized eigenspaces; 11. Characteristic and minimal polynomials; 12. Similarity; 13. Additional remarks on ODE; Chapter 2: Complex numbers; 1. Basic definitions; 2. Limits; 3. The exponential function and trig.
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1. Least squares2. The wave equation; 3. Legendre polynomials; 4. Probability; 5. Quantum mechanics; 6. The Dirichlet problem and conformal mapping; 7. Root finding; 8. Linear time-invariant systems; Chapter 8: Appendix: The language of mathematics; 1. Sets and functions; 2. Variables, constants, and parameters; References; Index.
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4. Subsets of C5. Complex logarithms; 6. Linear fractional transformations; 7. Linear fractional transformations and matrices; 8. The Riemann sphere; Chapter 3: Vector analysis; 1. Euclidean geometry; 2. Differentiable functions; 3. Line integrals and work; 4. Surface integrals and flux; 5. The divergence theorem; 6. The classical Stokes' theorem; 7. A quick look at Maxwell's equations; 8. Differential forms; 9. Inverse and implicit functions; Chapter 4: Complex analysis; 1. Open subsets of C; 2. Complex differentiation; 3. Complex integration; 4. The Cauchy theory.
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5. Polynomials and power series6. Singularities; 7. Residues; 8. More residue computations; Chapter 5: Transform methods; 1. Laplace transforms; 2. Generating functions and the Z-transform; 3. Fourier series; 4. Fourier transforms on R; Chapter 6: Hilbert spaces; 1. Inner products and norms; 2. Orthonormal expansion; 3. Linear transformations; 4. Adjoints; 5. Hermitian and unitary operators; 6. L2 spaces; 7. Sturm-Liouville equations; 8. The Green's function; 9. Additional techniques; 10. Spectral theory; 11. Orthonormal expansions in eigenvectors; Chapter 7: Examples and applications.
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| Abstract
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"Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author's teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work, to unify many distinct and seemingly isolated topics, to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems. The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises"--The publisher.
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| Subject
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Mathematical analysis.
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| Subject
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Mathematical analysis.
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| Subject
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MATHEMATICS-- Algebra-- Intermediate.
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| Dewey Classification
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515
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| LC Classification
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QA331.7 .D3564 2017
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