Advanced Mathematical Analysis: Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications: 12 - Rilegato

Beals, R.

Rilegato

ISBN 10: 0387900659 ISBN 13: 9780387900650

Casa editrice: Springer-Verlag GmbH, 1973

Riassunto

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi­ neering" from what might be called "advanced mathematical analysis for mathematicians."

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Contenuti

One Basis concepts.- §1. Sets and functions.- §2. Real and complex numbers.- §3. Sequences of real and complex numbers.- §4. Series.- §5. Metric spaces.- §6. Compact sets.- §7. Vector spaces.- Two Continuous functions.- §1. Continuity, uniform continuity, and compactness.- §2. Integration of complex-valued functions.- §3. Differentiation of complex-valued functions.- §4. Sequences and series of functions.- §5. Differential equations and the exponential function.- §6. Trigonometric functions and the logarithm.- §7. Functions of two variables.- §8. Some infinitely differentiable functions.- Three Periodic functions and periodic distributions.- §1. Continuous periodic functions.- §2. Smooth periodic functions.- §3. Translation, convolution, and approximation.- §4. The Weierstrass approximation theorems.- §5. Periodic distributions.- §6. Determining the periodic distributions.- §7. Convolution of distributions.- §8. Summary of operations on periodic distributions.- Four Hilbert spaces and Fourier series.- §1. An inner product in ?, and the space ?2.- §2. Hilbert space.- §3. Hilbert spaces of sequences.- §4. Orthonormal bases.- §5. Orthogonal expansions.- §6. Fourier series.- Five Applications of Fourier series.- §1. Fourier series of smooth periodic functions and periodic distributions.- §2. Fourier series, convolutions, and approximation.- §3. The heat equation: distribution solutions.- §4. The heat equation: classical solutions; derivation.- §5. The wave equation.- §6. Laplace’s equation and the Dirichlet problem.- Six Complex analysis.- §1. Complex differentiation.- §2. Complex integration.- §3. The Cauchy integral formula.- §4. The local behavior of a holomorphic function.- §5. Isolated singularities.- §6. Rational functions; Laurent expansions; residues.- §7. Holomorphic functions in the unit disc.- Seven The Laplace transform.- §1. Introduction.- §2. The space ?.- §3. The space ??.- §4. Characterization of distributions of type ??.- §5. Laplace transforms of functions.- §6. Laplace transforms of distributions.- §7. Differential equations.- Notes and bibliography.- Notation index.

Product Description

Book by Beals R

Dettagli dell'edizione

• Editore: Springer-Verlag GmbH
• Data di pubblicazione: 1973
• Lingua: Inglese
• ISBN 10: 0387900659
• ISBN 13: 9780387900650
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 248
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania