• 5 Pages hw9
    Hw9

    School: Concordia Chicago

  • 3 Pages reals
    Reals

    School: Concordia Chicago

    ANALYSIS In the first part of this course we studied the topology of the continuum, without reference to any algebra. We now rectify this omission. 1. The Real Numbers We define the real numbers axiomatically. In contrast to the situation with the c

  • 1 Page final
    Final

    School: Concordia Chicago

    (1) Let and be smooth functions on an interval (a, b) on so that is equal to zero on the boundary of (a, b) and (x) = 0 on [a, b]. Show that for all N > 0 there exists a constant CN such that b | a (x) sin (x) dx| CN -N . (2) Given a vector s

  • 3 Pages sh17
    Sh17

    School: Concordia Chicago

    Sheet 17: Trigonometric Functions Liz Beazley April 17, 2007 Just like we dened log and exp using integrals on the last sheet, it is possible to build the trig functions in this way. Ponder each of the following denitions carefully, always searching

  • 1 Page homework2
    Homework2

    School: Concordia Chicago

    MATH 16300 SECTION 50, HOMEWORK 1 DUE DATE TUESDAY APRIL 17 (1) Show that the function f : R R+ given by f (x) = x2 , is not uniformly continuous on R. (2) Let a > 0 and f (x) = x if x [a, a] Q, 0 if x [a, a] \ Q. Find supP L(P, f ) and inf P U

  • 79 Pages homework5
    Homework5

    School: Concordia Chicago

    MATH 16300 SECTION 50, HOMEWORK 10 DUE DATE THURSDAY MAY 10 (1) Assume that f is i C ([a, b]). Show that if all derivatives f (n) are uniformly bounded on [a, b], then f n (a) f (x) = (x a)n . n! n=0 (2) Assume that f C (I), for some open inter

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