School of Science - Department of Mathematics

0301213Real Analysis I

• Course Description :The completeness property of R. The Archimedean principle in R. Limit of a sequence. Convergent sequences. Monotone and bounded sequences. Cauchy sequences. Subsequences and limit points. Liminf and limsup of sequences of real numbers. Open sets, closed sets, bounded sets and compact sets in R. Limits of real valued functions. Definition of limits by neighbourhoods. Definition of limits by sequences. Continuous functions on R. Sequence definition and neighbourhood definition of continuity. Boundedness of continuous functions on compact intervals. The extreme value theorem. The intermediate value theorem. Uniformly continuous functions. The sequential criterion for uniform continuity. The derivative of functions. Rolles Theorem. Mean value theorem. Taylor Theorem with remainder. L' Hospital's rule. The Riemann Stieitjes Integral. Fundamental Theorem of Calculus.
• Pre Request : 0301211
• Credit Hour :3
• Department : Mathematics
• Program :
• Course Level :Bachelor
• Course Outline :

  0301213 Syllabus.pdf