481 ريض- التحليل الحقيقي 2-Real Analysis

 

Course Description:

- Riemann  and Improper Integrals.
- Numerical Series.
- Sequences and Series of  Functions.
- Lebesgue Measure.
- Lebesgue Integral.

Objectives:

The main purpose for this course is to introduce:

1. The Riemann integral
2.  The improper integrals
3. Numerical series, sequences and series  of functions.
4. Lebesgue integral. 

After studying this course, the student will able to:

1. Computing some Riemann integral and determine the convergence of improper integrals.
2. Determine the convergence of numerical series and series of functions
3. Compare Riemann and Lebesgue integral.
4. Develop fundamental theorems of convergence of integrals. (Monotone convergence theorem and Dominate convergence theorem).

 List Required Textbooks
 

1. Dr. M. Gwaiz and S. Alsanosi, Elements of real analysis, 1425H.
2. Measure and Integral: An Introduction to Real Analysis, R.L.  Wheeden & A. Zygmund.
3. Introduction to Real Analysis;  R.G. Bartle and D.R. Schebert.