NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Mathematical Analysis
Course code:MtP 313 MA
Unit Coordinator
Dr. Wadhah S. Jassim
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 3
Soran University
Faculty of Science
Department of Mathematics
Course Book
Mathematical Analysis
Third Year Pure Mathematics
Academic Year 2012 - 2013
Five Hours Per Week
Lecturer: Dr. Wadhah S. Jassim
Assistant Professor in Mathematics - Algebra
e- mail: wadhahjassim@yahoo.co.uk
M: o7702584067
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Soran University
Faculty of Science
Department of Mathematics
Course Book
Mathematical Analysis
Third Year Pure Mathematics
Academic Year 2012 - 2013
Five Hours Per Week
Lecturer: Dr. Wadhah S. Jassim
Assistant Professor in Mathematics - Algebra
e- mail: wadhahjassim@yahoo.co.uk
M: o7702584067
Office hours: Saturday – Tuesday
9am – 3 Pm
Classes :
Sunday : 8.30 am– 11.30 pm
11.30 am – 12.30 pm
Tuesday : 8.30 am – 10.30pm
10.30 am – 12.30 pm
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Course Objective
The course provide a mathematically rigorous introduction to mathematical Analysis. The only prerequisite is an elementary calculus sequence. I have followed the principle that the material should be as clear and as intuitive as possible. A major aim of this course is to teach students to understand mathematical proofs as well as to formulate and write them.
Methods of teaching
Different methods of teaching will be used to reach the goal of this course, such as the attention given to motivating the ideas under discussion, work sheet will be designed to let the chance for practicing on several aspects of the course in the class room.
Grading
The students are required to do two closed book exam at each term . The midterm exam has 15 marks, the attendance, class room activities and quizzes count 5 marks . Therefore the total mark for the first term is 20 marks and similarly for the second term. Therefore midterms exams count 40 marks and the final exam has 60 marks. Hence the grade will be best up on the following criteria :
Midterm exams : 30%
Class room participation and assignments : 10 %
Final exam : 60 %.
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Marking System
The grades for each piece of assessed work are as follows:
90 – 100 % excellent
80 – 89 % very good
70 – 79 % good
60 – 69 % moderate pass
50 – 59 % pass
49 < % fail
Course Programmed
Week 1 : The Real number system:
Sets, Properties of the Real numbers as an ordered Field.
Method of construction of Real Numbers.
Week 2: Complete ordered Field. Bounded sets and unbounded
sets. The Completeness Axiom. Archimedean property
of Real numbers.
Week 3: Sequences of real numbers, Convergent sequences.
Week 4: Range of a sequences, bounded sequences.
week 5: First Exam .
Week 6 : Diverges sequences, Algebra of sequences
Week 7: Monotone increasing an monotone decreasing and Cauchy
sequences,
Week 8: Subsequences, Upper limit and Lower Limit of sequences.
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Week 9 : Second Exam
Week 10: Metric spaces, definition, examples and some basic notion in
Real numbers . Some Topological concepts of metric
spaces, such as open sphere, open sets,
Week 11: Mid term holyday
Week 12: closed sphere and closed sets. Sequences , subsequences of
metric spaces and nested intervals.
Week 13: Bolzano – weierstrass Theorem, Convergence in
metric spaces . Complete metric space
Week 14: Limits and Continuity in the metric spaces. Limits of
the function. Limits and continuity at a point.
Week 15 : Third exam.
Week 16 : Compact metric spaces
Week 17: Hein Borel Theorem.
Week 18: Sequences and series of functions.
Week 19 : Fourth Exam.
Week 20: Riemann integral. Partition, Riemann upper sum and Riemann
Lower sum. Lower and upper integral,
Week 21: continuity and Integration
Week 22: Theorems of integral functions.
Week 23: Fundamental Theorem of Calculus of definite and
indefinite integral. Differentiation and properties of
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differentiation. Rolle's Theorem and mean value
Theorem.
Week 24: Stieltjes integration and Riemann stieltjes integration.
Week 25: Elementary measure Theory.
Week 26: Lebesuge integration.
Week 27 and 28: Final exam. :
References
1) An introduction to analysis .
By Kirk wood.
2) Analysis.
By K. Parkash and M. Goyal.
3) Real analysis.
By N. P. Bali.
4) Real Variables.
By C. W. Burrill and J. R. Kmidsen.
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