Brown University
Mathematics Department
Nov 5, 2013
MA 1130 Functions of several variables
Homework n 8
This homework is due Monday November 11, 2013 at h 12:00.
Justify all your answers.
Exercise 1. Do exercise# 4, 5, 6, 7 at p. 219.
Exercise 2. [Optiona
Brown University
Mathematics Department
Oct 10, 2013
MA 1130 Functions of several variables
Homework n 5
This homework is due Tuesday October 22, 2013 at h 12:00.
Justify all your answers.
Exercise 1. Find the dierential df for f dened by f (r, ) =
Exerci
Brown University
Mathematics Department
Sep 30, 2013
MA 1130 Functions of several variables
Homework n 4
This homework is due Monday October 7, 2013 at h 12:00.
Justify all your answers.
Theorem 0.1. Let X be a metric space, Y be a topological space and l
Brown University
Mathematics Department
Sep 23, 2013
MA 1130 Functions of several variables
Homework n 3
This homework is due Monday September 30, 2013 at h 12:00.
Justify all your answers.
Exercise 1. Let B = cfw_(a, b] : < a < b < + cfw_. Show that B is
Brown University
Mathematics Department
Sep 09, 2013
MA 1130 Functions of several variables
Homework n 1
This homework is due Monday September 16, 2013 at h 12:00.
Exercise 1. Prove that, given set A, B, C , and a map f : A B , the following relations are
Brown University
Mathematics Department
Sep 16, 2013
MA 1130 Functions of several variables
Homework n 2
This homework is due Monday September 23, 2013 at h 12:00.
Exercise 1. Prove that the space of all bounded functions f : X Y (where (Y, d) is a comple
Brown University
Mathematics Department
Oct 24, 2013
MA 1130 Functions of several variables
Homework n 6
This homework is due Thursday October 31, 2013 at h 12:00.
Justify all your answers.
Exercise 1. Given > 0, consider the function f :
R2
R2
dened by f
Brown University
Mathematics Department
Oct 28, 2013
MA 1130 Functions of several variables
Homework n 7
This homework is due Monday November 4, 2013 at h 12:00.
Justify all your answers.
Exercise 1. [Optional] Prove the Jacobis formula dfA (H ) = tr(adj(
Brown University
Mathematics Department
Nov 26, 2013
MA 1130 Functions of several variables
Homework n 10
This homework is due Thursday December 5, 2013 at h 12:00.
Justify all your answers.
Let (X, A, ) be a measure space.
1. Show that the if f : R R is
Brown University
Mathematics Department
Nov 13, 2013
MA 1130 Functions of several variables
Homework n 9
This homework is due Thursday November 20, 2013 at h 12:00.
Justify all your answers.
Exercise 1. Let F be a closed subset of a metric space X . Dene
First Homework Assignment
Zijian Yao
October 15, 2013
Exercise 1:
Proof. (1). If x (A B ) C , then x A B, x C . If x A, then x A C ;
otherwise, x A x B x B C . So x (A C ) (B C ). This shows
/
(A B ) C (A C ) (B C ).
If x (AC )(B C ), then x AC or x B C .
Brown University
Mathematics Department
Dec 3, 2013
MA 1130 Functions of several variables
Homework n 11
This homework is due Thursday December 12, 2013 at h 12:00.
Justify all your answers.
Let (X, A, ) be a measure space.
1. Give an example, showing tha
Brown University
Mathematics Department
Sep 05, 2013
MA 1130 Functions of several variables
Homework no 0
This homework is due Monday September 9, 2013 at h 12:00.
Exercise 1. Answer the following questions:
(1) What college-level math classes have you al