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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