Math 320-1: Final Exam Practice
Northwestern University, Fall 2014
1. Give an example of each of the following. Justify your answer.
(a) A nonconstant and nonnegative integrable function on [0, 1] with integral zero.
(b) A nonintegrable function f on [3,
Math 320-1: Homework 1
Northwestern University, Fall 2014
1. Wade, 1.2.7bd. Let x R.
(b) Prove that |x| 1 implies |x2 + 2x 3| 4|x 1|.
(d) Prove that 1 < x < 0 implies |x3 2x + 1| < 1.26|x 1|.
2. Wade, 1.3.3. Prove that if a < b are real numbers, then ther
Math 320-1: Final Exam Practice Solutions
Northwestern University, Fall 2014
1. Give an example of each of the following. Justify your answer.
(a) A nonconstant and nonnegative integrable function on [0, 1] with integral zero.
(b) A nonintegrable function
Math 320-1: Midterm 2 Practice Solutions
Northwestern University, Fall 2014
1. Give an example of each of the following. Justify your answer.
(a) A function on (1, 2) which is continuous but not uniformly continuous.
(b) A function which sends Cauchy sequ
Math 320-1: Midterm 2 Practice
Northwestern University, Fall 2014
1. Give an example of each of the following. Justify your answer.
(a) A function on (1, 2) which is continuous but not uniformly continuous.
(b) A function which sends Cauchy sequences to C
Math 320-1: Lecture Notes
Northwestern University, Fall 2013
Written by Santiago Caez
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These are lecture notes for Math 320-1, the rst quarter of Real Analysis, taught at Northwestern University in the fall of 2013. The book used was the 4th edition of A
Math 320-1: Homework 2
Northwestern University, Fall 2014
1. Wade, 2.1.0bcd. Decide which of the following statements are true and which are false. Prove
the true ones and provide a counterexample for the false ones.
(b) If xn does not converge, then xn /