عنوان

Linear and complex analysis for applications /

(Number (ISBN

131511884X

(Number (ISBN

1498756115

(Number (ISBN

1498756166

(Number (ISBN

1498756174

(Number (ISBN

9781315118840

(Number (ISBN

9781498756112

(Number (ISBN

9781498756167

(Number (ISBN

9781498756174

Erroneous ISBN

1498756107

Erroneous ISBN

9781498756105

Title Proper

Linear and complex analysis for applications /

General Material Designation

[Book]

First Statement of Responsibility

John P. D'Angelo.

Edition Statement

1st

Place of Publication, Distribution, etc.

Boca Raton :

Name of Publisher, Distributor, etc.

CRC Press,

Date of Publication, Distribution, etc.

2017.

Specific Material Designation and Extent of Item

1 online resource

Series Title

Advances in applied mathematics

Text of Note

Includes bibliographical references and index.

Text of Note

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.

Text of Note

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.

Text of Note

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.

Text of Note

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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8

8

8

Text of Note

"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.

Source for Acquisition/Subscription Address

Ingram Content Group

Stock Number

9781498756167

International Standard Book Number

9781498756105

Mathematical analysis.

Mathematical analysis.

MATHEMATICS-- Algebra-- Intermediate.

MAT-- 002040

Number

Edition

Class number

D'Angelo, John P.

Date of Transaction

20200822170843.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y