Download Document

College of Science (Female Branch) – Departmentof Mathematics
Semester 2 2012/2013
REAL ANALYSIS (Math 231)
Coordinator and instructor: MARIAM ABDULLAH ALHARBY.
Email:[email protected]
Textbook:
An Introduction to Analysis ,4th edition, William R. Wade
Description: In this course we will study series and sequences of real numbers, sequences and series of functions, uniform
convergence of sequences , power series, limits, continuity, derivatives, closed and open sets, continuous real- valued function,
chain rule and Taylor’s Theorem.
Grading Policy:
1. Major Exam 1: 20%
2. Major Exam 2: 20%
3. Final Exam:
50%
4. Course Work: 10%
(Comprehensive exam)
: consist of: Quizzes, Homework/Attendanc
Exam Questions: The questions of the common exams are based on the examples, homework problems, recitation
problems and the exercises of the textbook.
Attendance:
Full class attendance is required.
 5 hours unexcused absences – 1st warning
 8 hours unexcused absences – 2nd warning
 A DN grade will be issued to any student who accumulates 12 hours unexcused absences.
Academic Integrity:
All Hail University policies regarding ethics apply to this course.
Semester 2 2012/2013
SYLLABUS MATH 231 (Real Analysis)
Date
Week
Contents
1
Feb 2- 6
Introduction Real number system and its basic properties ,ordered
relations, solving equations and inequalities
2
Feb 9- 13
Definition of fields and its examples, ordered field axioms and some
results
3
Feb 16- 20
Fundamental Theorem of Absolute Value, solution of absolute
equation and inequalities
Completeness axioms
Supremum, and related axioms
4
Feb 23- 27
Infimum and related examples,exercises
Limits of functions and sequences, Limit Theorems exercises
5
March 2-6
Squeeze theorem
Examples
Comparision theorem
Major 1 Exam (20%) ( Exam Date will be announced later)
6
March 9-13
Balzano- Weirestrass Theorem
Related remarks
7
March 16-20
Cauchy’s sequences
Remark and definition
Theorem(Cauchy’s)
Midterm Vacation
8
March 30-Apr 3
Functions on R.Two sided limits , remarks, examples
One sided and two sided limits at infinity
9
Apr 6-10
Uniform continuity and related exercises
examples
10
Apr 13-17
Differentiability on R
Major 2 Exam (20%) ( Exam Date will be announced later)
11
12
13
14
Apr 20-24
Differentiabilty theorems
Apr 27-May 1
May 4-8
Taylor’s theorem, l’hospital’s rule
Infinite series of real numbers, Absolute convergence
May 11-15
Infinite series of functions ,Uniform Convergence , Power Series
Final Exam will be comprehensive (50%) ( Exam Date will be announced later)
Grading Policy
Major Exam I
(20%)
Major Exam II
(20%)
Final Exam
(50%)
Class WORK
(10%)
(Quizzes, Homework, Attendance)
Note :
Attendance Warnings:
Unexcused Absences .
5 Hours Absences - 1st Warning
8 Hours Absences - 2nd Warning
DN - 12 Hours