With Applications to Differential Equations and Fourier Analysis
Buch, Englisch, 201 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1080 g
ISBN: 978-0-8176-4329-4
Verlag: Birkhäuser Boston
This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ample examples and brief explanations---with very few proofs and little axiomatic machinery---are used to highlight all the major results of real analysis, from the basics of sequences and series to the more advanced concepts of Taylor and Fourier series, Baire Category, and the Weierstrass Approximation Theorem. Replete with realistic, meaningful applications to differential equations, boundary value problems, and Fourier analysis, this unique work is a practical, hands-on manual of real analysis that is ideal for physicists, engineers, economists, and others who wish to use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Valuable as a comprehensive reference, a study guide for students, or a quick review, "A Handbook of Real Variables" will benefit a wide audience.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
Basics.- Sets.- Operations on Sets.- Functions.- Operations on Functions.- Number Systems.- Countable and Uncountable Sets.- Sequences.- to Sequences.- Limsup and Liminf.- Some Special Sequences.- Series.- to Series.- Elementary Convergence Tests.- Advanced Convergence Tests.- Some Particular Series.- Operations on Series.- The Topology of the Real Line.- Open and Closed Sets.- Other Distinguished Points.- Bounded Sets.- Compact Sets.- The Cantor Set.- Connected and Disconnected Sets.- Perfect Sets.- Limits and the Continuity of Functions.- Definitions and Basic Properties.- Continuous Functions.- Topological Properties and Continuity.- Classifying Discontinuities and Monotonicity.- The Derivative.- The Concept of Derivative.- The Mean Value Theorem and Applications.- Further Results on the Theory of Differentiation.- The Integral.- The Concept of Integral.- Properties of the Riemann Integral.- Further Results on the Riemann Integral.- Advanced Results on Integration Theory.- Sequences and Series of Functions.- Partial Sums and Pointwise Convergence.- More on Uniform Convergence.- Series of Functions.- The Weierstrass Approximation Theorem.- Some Special Functions.- Power Series.- More on Power Series: Convergence Issues.- The Exponential and Trigonometric Functions.- Logarithms and Powers of Real Numbers.- The Gamma Function and Stirling’s Formula.- An Introduction to Fourier Series.- Advanced Topics.- Metric Spaces.- Topology in a Metric Space.- The Baire Category Theorem.- The Ascoli-Arzela Theorem.- Differential Equations.- Picard’s Existence and Uniqueness Theorem.- The Method of Characteristics.- Power Series Methods.- Fourier Analytic Methods.- Glossary of Terms from Real Variable Theory.- List of Notation.- Guide to the Literature.
