Real Analysis 2

Course Description

Differentiability of real functions, Mean-value theorem, L’hopital’s rule, Taylor theorem, Riemann integral, Cauchy Criteria for integrability, Fundamental theorems of calculus, Sequence of functions, Pointwise and uniform convergence of sequences and series of functions, and the interchange between sum and limit ,derivative, Integral operations in series.

Course Objectives & Outcomes
Objectives:

• Provide students with necessary knowledge and skills to enable them analysis problems involving notions like continuity, differentiability of real functions of one variable.
•  Train students to deal with interchange between sum and limit, derivative, integral operations in series.

Outcomes:
Upon successful completion of this course, the student will be able to:

•  Discuss differentiability and Riemann integrability of a function.
•  Describe Intermediate , Mean-value theorem, L’hopital’s rule ,Taylor formulas, Fundamental theorems of calculus
• Distinguish between the pointwise and uniform convergence of sequences (series) of functions. 
• Write some proofs and interpret the logical steps

References
1. R.G. Bartle, D.R. Sherbert, Introduction to Real Analysis, 4th edition, John Wiley & sons 2011. ISBN 978-0-471-43331-6 .ISBN10:0471433314
2. E. D. Gaughan, Introduction to Analysis, 3rd edition, Publishing Company, 1998. ISBN-13: 978-0821847879- ISBN-10: 082184787.
3. M.A.Al-Gwaiz and S.A. Elsanousi, Elements of real analysi , Chapman &Hall /CRC, 2007, ISBN 978-1-58488661-7.
4. Edward, D. Gaughan,1998, Introduction to Analysis, 3rd edition, Publishing company.ISBN-13: 978-0821847879- ISBN-10: 082184787

Course ID: MATH 502