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I.M Sigal (1)

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I.M Sigal

INTRODUCTION TO REAL ANALYSIS (MAT337HS) I. M. SIGAL, TAS BEN RIFKIND AND ANDREW STEWART Any feedback on lectures, tests and grading will be greatly appreciated! Place and time: M 4 5 pm, W 2 4 pm in UC A101 Course description: The goal of this course is to explain key concepts of Real Analysis with the view at applications. The course is about the same level as MAT357, but while MAT357 deals mainly with theory, the present course aims at developing interesting applications. Syllabus: * Review: Sequences, series, functions (limits and continuity, dierentiation and integration) * Vector and normed spaces * Convergence * Spaces of functions * Orthonormal sets and Fourier series * Compactness * Calculus of vector functions * Contraction mapping principle * Ordinary dierential equations: Existence and uniqueness of solutions * Optimization Textbook: [DD] Kenneth R. Davidson and Allan P. Donsig, Real Analysis and Applications, Springer, 2010. Tests Quizzes, midterm test, nal test. Quizzes and midterm and nal exams will be on the material covered in the lectures. All the problems for the quizzes and midterm exam most of the problems for the nal test will be modications of the problems from the homework. The problems in quizzes and exams will involve proofs. Quizzes will last 25 min each. We will have six quizzes: Jan 17 (changed to 19), 31, Feb 7, and Feb 28, March 14, 28 (changed to March 7, 21, April 4). Midterm: February 16. Marking scheme Breakup of the grade: Quizzes midterm nal test 35%35%30% . Homework problems and supplementary material The list of topics covered, homework problems and material which is not found on the book (supplementary material) will be posted on each Thursday on the webpage http:www.math.utoronto.casigalRealAnalNotes.pdf Tutorials: Before or after each quiz, during the class time, the TA will have a tutorial on the last week problems. (This will take place on all quiz days.) On Mondays without quizzes, I will review problems on Wednesdays, preceding quizzes. Please, raise problems you have diculty with. Oce hours: TA will hold oce hours every week. On Fridays before a quiz TA will hold two oce hours from 11-1. On other Fridays there will be one oce hour from 11-12. If these times do not work for you, you can email TA Date: April 1, 2011. 1
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