BRAC University
Spring Semester 2015
Course No: MAT 221, Section: 01
Course Title: Real Analysis
Course Contents:
Real number system: Completeness of real numbers, supremum and infimum principles and their consequences,
Dedekind's theorems, Bolzano-Weierstrass theorem. Sequences of Real Numbers: Infinite sequence,
Convergent sequences, Monotone sequences, subsequences, Cauchy sequence, Cauchy criteria for
convergence of sequences. Infinite Series: Concept of sum and convergence, series of positive terms,
alternating series, absolute and conditional convergence, test for convergence, Convergence of
sequences and series of functions. Continuity and Limits: Properties of continuous functions, Extreme
Value Theorem and Intermediate Value Theorem, Uniform continuity concepts, Limits, Heine-Borel
theorem. Integration: Necessary and sufficient conditions for integrability, Darboux Sums and
Riemann Sums, Improper integral and their tests for convergence.
Reference Book
1. Principle of Mathematical Analysis: W. Rudin.
2. Real Analysis (3rd edition): H.L. Royden.
3. Mathematical Analysis: Tom .M. Apostol.
4. Real Analysis: A. Malik.
5. Elements of Real Analysis:Shanti Narayan and M.D. Raisinghania
Instructor Information
Name: Ms. Mehnaz Karim
Background: B.S. (Hons) in Mathematics, University of Toronto, Canada; M. S. in Applied
Statistics and Operational Research, RMIT University, Australia.
Office: UB 15th Floor
E-mail: mehnazkarim@bracu.ac.bd
Course procedure:
Course activities will include lectures and discussion of examples, homework, assignments, quizzes, a
midterm and a comprehensive final examination. Homework and assignments will be given during the
classes. The completion of these assignments before the deadline is absolutely essential for the
mastering of this material. Four quizzes will be taken and best three will be counted out of them.
There will be no make up quizzes.
Attendance:
Attending class is an important component to do well in this course. Mathematics is a subject, which
builds on concepts covered each day in class. Hence, it is important to be regular in attending class so
that one does not fall behind. If it is necessary to miss class due to personal, family emergencies, etc.,
one should inform me beforehand. Moreover, 5% of the total marks is allocated for attendance. If one
does not attend at least 70% of the total classes, s/he will not be allowed to take the final exam.
Marks Distribution
Attendance
Quiz (best 3 out of
4)
Midterm
Final Exam
Total
5
25
20
50
100
Attendance
90% and above
85% - 89%
80% - 84%
75% - 79%
70% - 74%
Less than 70%
Marks
5
4
3
2
1
0
Class Routine & Consultation Schedule
Day
Class
Sunday
Tuesday
Tues/Wednesday
Time
11.00-12.20 pm
11.00-12.20 pm
Room
Consultation Schedule
Time
Office
2-3.30
UB 2, 15th Floor
Lecture Delivery Plan
Lec. No.
Topics
Real Numbers, Completeness of real numbers.
Supremum, infimum principles and their consequences.
Dedekinds theorems.
Bolzano- weierstrass theorem.
Sequences of Real Numbers , Infinite sequence,
Convergent sequences, Review of the previous lectures.
Monotone sequences , Subsequences.
Cauchy sequence, Cauchy criteria for convergence of sequences.
9
10
Infinite Series, Concept of sum and convergence.
series of positive terms, alternating series.
11
absolute and conditional convergence, test for convergence.
12
13
Review of the previous lectures.
Midterm examination (tentative)
14
convergence of sequences and series of functions.
15
Continuity and Limits, Properties of continuous functions.
16
Review of the previous lectures.
17
Extreme value theorem and Intermediate Value theorem.
18
Uniform continuity concepts.
19
Review of the previous lectures.
20
Limits, Heine- Borel theorem.
21
Review of the previous lectures.
22
Integration: Necessary and Sufficient conditions for inerrability
23
Darboux sums and Riemann sums.
24
Improper integral and their tests for convergence.
25
Review of the previous lectures.
Quiz # 01
Quiz # 02
Quiz # 03
Quiz # 04
There will be changes in lecture plans, if necessary, according to the progress of the students.
You will find other supporting documents at \\tsr\Fall\MNS\MZK\MAT221
There will be no makeup midterm as well, unless any student submits application through the
corresponding chair of the department at least 7 days before the midterms scheduled date.
No students will be allowed to sit for final exam if he/she misses 30% of the total classes.
