Course Information

Course Name	Turkish	Reel Analiz I
	English	Real Analysis I
Course Code	MAT 288E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	3	4	4	-	-
Course Language		English
Course Coordinator		İbrahim Kırat
Course Objectives		1. To teach the student the techniques and methods of Mathematical Analysis and to allow the student to develop a certain level of proficiency in these methods. 2. To teach students to use the basic concepts they learned in Calculus classes in a mathematically rigourous way.
Course Description		Real numbers. Normed vector spaces. Finite dimensional real vector spaces. Young’s, Hölder’s and Minkowski’s inequalities. Metric spaces. Sequences in metric spaces. Convergence and boundedness. Cauchy sequences and completeness. Topology of Metric spaces: open and closed sets. Compactness. Heine-Borel Theorem. Real valued continuous functions on metric spaces and their metric structure. Continuity and uniform continuity. Lipschitz continuity. Derivatives. Normed spaces C^k[a,b], \ell^p and L^p and their duals. Hilbert spaces. Sequences and series of real valued functions on metric spaces. The Stone-Weierstrass Theorem. Pointwise and uniform convergence. Cauchy criterion for uniform convergence. The Arzelà–Ascoli Theorem. Weierstrass M-test.
Course Outcomes		A student who completed this course successfully is expected to I. Know the proofs of limit theorems on metric spaces and use these theorems in calculations correctly, II. Know the proofs of theorems on bounded, monotone, continuous and uniformly continuous functions and use these theorems, III. Determine pointwise convergence or uniform convergence in sequences and series of functions.
Pre-requisite(s)
Required Facilities
Other
Textbook		W.R. Parzynski & P.W. Zipse, Introduction to Mathematical Analysis, McGraw-Hill, International (Textbook) Edition, 1987. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976 J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, Macmillan, 1993.
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