Author | Krantz, Steven G. author |
---|---|
Title | A Handbook of Real Variables [electronic resource] : With Applications to Differential Equations and Fourier Analysis / by Steven G. Krantz |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8128-9 |
Descript | XIII, 201 p. online resource |
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 Stirlingโs 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 -- Picardโs 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