Course Description
algebraic properties of R, roots, supremum and infimum, open and closed sets, nested intervals and cluster points, sequences, subsequences, convergence and divergence, Cauchy criterion , completeness of R, limits of functions and some extensions of the limit concept. Notion of continuity, uniform continuity, Lipchitz function.
Course Objectives & Outcomes
Objectives:
- Understand the topological and algebraic properties of the space real numbers, especially the completeness and ordering property.
- Equip students with necessary knowledge and skills to deal with analysis problems involving notions like sequences and continuity.
Outcomes:
Upon successful completion of this course, the student will be able to:
- Recall the basic properties of real numbers.
- Check the convergence or divergence of sequences, and compute their limits.
- Discuss the existence of the limit for the function
- Discuss the continuity, uniform continuity, Lipchitz function
- Students will be expected to write some proofs and understand the logical steps
References
1. Bartle R.G., Sherbert D.R. (2011) Introduction to Real Analysis, 4th edition, John Wiley & sons, ISBN-13: 978-0471433316, ISBN-10: 0471433314.
2. Gaughan E. D.(2009) Introduction to Analysis, 3rd edition, Publishing company, ISBN-13: 978-0821847879, ISBN-10: 0821847872.
2. Al-Gwaiz M.A., Elsanousi S.A.(2007) Elements of real analysis, Chapman &Hall /CRC, ISBN-13: 9781584886617, ISBN-10: 1584886617.
3. Lara A.(2014) How to Think About Analysis, Oxford University Press, ISBN-13: 978-0198723530, ISBN-10: 0198723539.
Course ID: MATH 403
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 4 | 4 | 4 | MATH 203 |
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