| Title Details: | |
|
Analysis |
|
| Other Titles: |
Real Functions of one Variable |
| Authors: |
Papadimitrakis, Michail |
| Reviewer: |
Sarantopoulos, Ioannis |
| Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > REAL FUNCTIONS |
| Keywords: |
Limit
Continuity Integral Derivative Sequence Metric space Series |
| Description: | |
| Abstract: |
The classical content of Infinitesimal Calculus (mainly of functions of one variable) with an empasis on the rigorous foundations and on the theoretical proofs of theorems. The supremum property. Existence of roots. Rigorous definition of powers with rational and irrational exponents and of logarithms. Sequences (monotonic, Cauchy, the Bolzano-Weierstrass theorem, limsup-liminf). Limits of functions (monotonicity, Cauchy criterion). Continuity of functions and the basic theorems. Continuity of the inverse function. Uniform continuity. Derivative and the basic theorems. Monotonicity. Convexity. Indeterminate forms. Taylor’s theorems. Integral. Methods of Darboux and of Riemann. Properties of the integral. Relation between derivative and integral. Calculation of integrals. Series of numbers. Criteria of convergence. Sequences of functions. Uniform convergence. The theorem of Weierstrass. Series of functions. Uniform convergence. Criteria of convergence. Power series. Trigonometric functions. Metric spaces. Completeness. Compactness. Connectedness. Generalised integrals. Criteria of convergence. Integrals with parameter. Axiomatic foundation. Dedekind cuts.
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| Type: |
Undergraduate textbook |
| Creation Date: | 2015 |
| Item Details: | |
| ISBN |
978-960-603-403-9 |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| DOI | http://dx.doi.org/10.57713/kallipos-739 |
| Handle | http://hdl.handle.net/11419/2890 |
| Bibliographic Reference: | Papadimitrakis, M. (2015). Analysis [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-739 |
| Language: |
Greek |
| Consists of: |
1. The real numbers 2. Sequences and limits of sequences 3. Limits of functions 4. Continuous functions 5. Derivatives of functions 6. Riemann integrals 7. Relation between derivative and integral 8. Series of numbers 9. Sequences of functions 10. Series of functions 11. Metric spaces 12. Generalised integrals 13. Axiomatic foundations 14. Hints and solutions of exercises |
| Number of pages |
898 |
| Publication Origin: |
Kallipos, Open Academic Editions |
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