TY  - GEN
AU  - Little,Charles H.C.
AU  - Teo,Kee L.
AU  - Brunt,Bruce van
TI  - Real analysis via sequences and series
T2  - Undergraduate texts in mathematics
SN  - 9781493926503
U1  - 515.8 23
PY  - 2015///
CY  - New York
PB  - Springer
KW  - Mathematical analysis.
KW  - Functions of real variables.
KW  - Sequences (Mathematics)
N1  - Includes bibliographical references and index;  1. Introduction --
 2. Sequences --
 3. Series --
 4. Limits of Functions --
 5. Continuity --
 6. Differentiability --
 7. The Riemann Integral --
 8. Taylor Polynomials and Taylor Series --
 9. The Fixed Point Problem --
 10. Sequences of Functions --
 Bibliography --
 Index
N2  - This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating℗ℓ definitions, results, and proofs. Simple examples℗ℓ are provided to℗ℓ illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallisℓ́ℓs formula and Stirlingℓ́ℓs formula, proofs of the irrationality of ℓℓ and e, and a treatment of Newtonℓ́ℓs method as a special instance of finding fixed points of iterated functions.
ER  -