The following chapters are taken from:
Mixture Theories for Biological Tissues
(textbook in preparation)
by Gerard Ateshian, PhD
Department of Biomedical Engineering
Columbia University
I. INTRODUCTIO
3/29/16
Experimental Methods
Tendon and Ligament
The primary func:on of tendons and ligaments is to
transmit tensile forces; therefore, mechanical tes:ng
typically consists of uniaxial tensile te
7. VISCOELASTIC SOLIDS FUNGS QUASILINEAR THEORY
Viscoelastic solids and fluids
We have already recalled that a material has a viscoelastic behaviour if its response to external
actions is time depende
Partnering Engineering & the Clinic
to Improve Treatment of Young
Adult Hip Disorders
Michael D. Harris, PhD
Program in Physical Therapy
Department of Orthopaedic Surgery
In conjunction with Universit
Topology I Midterm 2
November 9, 2016
Name:
There are four questions, each worth twenty-five points, so you should pace yourself at around
1215 minutes per question, since they vary in difficulty and
Topology I Midterm 1
October 5, 2016
Name:
There are five questions, each worth twenty points, so you should pace yourself at around
1012 minutes per question, since they vary in difficulty and youll
Topology I Midterm 1
October 5, 2016
Name:
There are five questions, each worth twenty points, so you should pace yourself at around
1012 minutes per question, since they vary in difficulty and youll
Topology I Midterm 2
November 9, 2016
Name:
There are four questions, each worth twenty-five points, so you should pace yourself at around
1215 minutes per question, since they vary in difficulty and
Topology I Final Exam
December 21, 2016
Name:
There are ten questions, each worth ten points, so you should pace yourself at around 1012
minutes per question, since they vary in difficulty and youll
Topology I Final Exam
December 21, 2016
Name:
There are ten questions, each worth ten points, so you should pace yourself at around 1012
minutes per question, since they vary in difficulty and youll
Mathematics 4171, Fall 2012
Assignment 6, due 11 October
Problem 1: Consider the space
(an )n= such that
n=
2 (R)
which consists of all two-sided, real-valued sequences
1/2
(an )
2
2
|an |
=
< .
n=
1.
Final Exam Solutions
Problem 1:
Solution.
1. Observe that since f and g are continuous into R, the function F given by F (x) =
f (x) g (x) is continuous into R. cfw_0 is closed in R, so by continuity
Math 4171, Fall 2013
Homework 1
0. To do but not to hand in:
i) Which of the following are true when is inserted in the blank space? Which are
true when is inserted?
a)
b)
c)
d)
e)
g _g, g
g _g, g
g_
Math 417, Fall 2009
Final Exam Solutions
All your solutions should be written in the test booklet. No references (text, notes, etc.) are
allowed during the exam.
Throughout the exam:
, 8 and all their
Math 4171, Fall 2013 Exam II
Solutions
Take Home: distributed in class Thursday November 7 and due in class Tuesday, November 12.
Write your solutions on 8 " " paper, with a new sheet for each problem
Math 4171
Exam I, Fall 2013
Name_
Write all your answers on the test booklet. No consultation, notes, texts, or electronic devices of
any kind are allowed.
are the sets of natural numbers, rationals,
Math 4171, Fall 2013
Homework 2
0. To do but not to hand in:
i. True or false? Explain.
a) if E is infinite and F is countable, then E F
b) if E is infinite and F is countable, then E F
a) False: for
Math 4171, Fall 2013
Homework 3 Solutions
0. To do but not to hand in:
i) (Part of Exercise E55) Prove or disprove:
a) i- #!
b) if # 7
2i! , then 7i! -
a) is true since # i! b) is true since # 7
2i!
#
Math 4171, Fall 2013
Homework 7
The following problems are to hand in.
Due in class on Tuesday, November 19
Please write up solutions neatly and staple pages together. If you tear pages out of a spira
Math 4171, Fall 2013
Homework 6 Solutions
The following problems are to hand in.
Due in class on Tuesday, November 5
Please write up solutions neatly and staple pages together. If you tear pages out o
Math 4171, Fall 2013
Homework 5
0. To do but not to hand in:
a) Prove or give a counterexample:
i) For any B in a space \ g B is equal to the intersection of all
open sets containing B.
False: The sim
Math 4171, Fall 2013
Homework 4 Solutions
0. To do but not to hand in:
i) (parts of Exercise E10) Let \ . be a pseudometric space. Prove or disprove each
statement.
F% B is never a closed set.
This is
Math 4171, Fall 2013
Homework 8, Solutions
Please write up solutions neatly and staple pages together. If you tear pages out of a spiral
notebook, please remove any ragged edges.
1. (Exercise E15) Sup
Mathematics 4171, Fall 2012
Midterm Exam
Due 30 Oct 2012 by beginning of class
Directions: During this exam, you are allowed to use your class notes, homework assignments from class, and the textbook.
Mathematics 4171, Fall 2012
Midterm Exam Solutions
Problem 1: This problem was mostly already done via homework problems or during
lecture with some very minor modications. I included it because I thi