| 000 | 04589cam a22004817i 4500 | ||
|---|---|---|---|
| 999 |
_c196622 _d196622 |
||
| 020 | _a9781461496373 | ||
| 040 | _cCUS | ||
| 082 | 0 | 4 |
_a515 _bPON/R |
| 100 | 1 | _aPons, Matthew A. | |
| 245 | 1 | 0 |
_aReal analysis for the undergraduate: with an invitation to functional analysis / _cMatthew A. Pons |
| 260 |
_aLondon: _bSpringer, _c2014. |
||
| 300 |
_axviii, 409 p. _billustrations ; _c24 cm |
||
| 504 | _aIncludes bibliographical references and index. | ||
| 505 | 0 | _aThe real numbers -- Preliminaries -- Complete ordered fields -- The real number system -- Set structures in R -- Normed linear spaces -- Sequences in R -- Sequences and convergence -- Properties of convergent sequences -- Completeness in R revisited -- Set structures in R via sequences -- Complete spaces -- Numerical series -- Series of real numbers -- Basic convergence tests -- Absolute and conditional convergence -- Sequence spaces -- Continuity -- Sequences and the limit of a function -- Continuity -- The intermediate value theorem -- Continuity on a set and uniform continuity -- Bounded linear operators -- The derivative -- The definition of the derivative -- Properties of the derivative -- Value theorems for the derivative -- Consequences of the value theorems -- Taylor polynomials -- Eigenvalues and the invariant subspace problem -- Sequences and series of functions -- Sequences of functions -- Series of functions -- Power series -- A continuous nowhere differentiable function -- Spaces of continuous functions -- The Riemann integral -- The Riemann integral -- Properties of the Riemann integral -- The Fundamental Theorem of Calculus -- The exponential function -- Spaces of continuous functions revisited -- Lebesgue measure on R -- Length and measure -- Outer measure on R -- Lebesgue measure on R -- A nonmeasurable set -- General measure theory -- Lebesgue integration -- Measurable functions -- The Lebesgue integral -- Limits and the Lebesgue integral -- The Lp spaces. | |
| 650 | 0 | _aMathematical analysis. | |
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aFunctional analysis. | |
| 650 | 7 | _aFunctional analysis. | |
| 650 | 7 | _aMathematical analysis. | |
| 650 | 7 | _aMathematics. | |
| 856 | 4 | 2 | _uhttps://www.loc.gov/catdir/enhancements/fy1702/2013956133-b.html |
| 856 | 4 | 2 | _uhttps://www.loc.gov/catdir/enhancements/fy1702/2013956133-d.html |
| 856 | 4 | 1 | _uhttps://www.loc.gov/catdir/enhancements/fy1702/2013956133-t.html |
| 942 | _cWB16 | ||