Math 414: Analysis I
Exam 3 Topics
1. Cluster Points/Limits of Functions (See in book: 3.1.1(c), 3.1.2-3.1.5, 3.1.8-3.1.10,
HW 8 #1#8)
2. Continuous Functions (See in book: 3.2.13.2.6, 3.2.93.2.12, HW 9 #7)
3. Intermediate Value Theorem/ Location of Roots
Math 414: Analysis I
Homework 6
Due: March 7, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 2.4.4, 2.4.5
Turn in the following problems.
1. Exercise 2.3
Math 414: Analysis I
Practice Exam 2
Spring 2014
Name:
*Please be aware that this practice test is longer than the test you will see on March 14,
2014. Also, this test does not cover every possible topic that you are responsible for on
the exam. For a com
Math 414: Analysis I
Homework 5
Due: February 28th, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 2.2.1-2.2.8, 2.3.1-2.3.3, 2.3.5(a), 2.3.8
Turn in the
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Math 414: Analysis I
Exam 1 Topics
1. Sets involving Unions and Intersections, Set Minus Operation, and DeMorgans
Laws (See in book: 0.3.1, 0.3.6, 0.3.8, HW 1 #1)
2. Functions (Injections, Bijections, Surjections, Composition of Two Functions), Direct Ima
Math 414: Analysis I
Exam 1 (80 points)
Spring 2014
Name:
*No notes or electronic devices. You must show all your work to receive full credit.
When justifying your answers, use only those techniques that we learned in class.
1. Suppose that f : X R is a f
Math 414: Analysis I Exam 2 (80 points) Spring 2014
Name: \ b1
*No notes or electronic devices. You must ShOW all your work to receive full credit.
When justifying your answers, use only those techniques that we learned in class.
1. (5) Let (an) be a
Math 414: Analysis I
Practice Exam 1
Spring 2014
Name:
*Please be aware that this practice test is longer than the test you will see on February
17, 2014. Also, this test does not cover every possible topic that you are responsible for
on the exam. For a
Math 414: Analysis I
Homework 4
Due: February 19th, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 2.1.1-2.1.5, 2.1.9-2.1.11, 2.1.13, 2.1.14, 2.1.17, 2.1
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Math 414: Analysis I
Exam 2 Topics
1. Sequences (including what it means for a sequence to be bounded/unbounded),
Denition of lim(xn ) (See in book: 2.1.12.1.7, , HW 4: #3#4)
2. Monotone Sequences, Monotone Convergence Theorem (See in book: 2.1.92.1.12,
H
Math 414: Analysis I
Homework 7
Due: March 28, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: (See Exam 2 Topics for Practice Problems.) Material for Exa
Math 414: Analysis I
Practice Exam 3
Spring 2014
Name:
*Please be aware that this practice test is longer than the test you will see on April 23,
2014. Also, this test does not cover every possible topic that you are responsible for on
the exam. For a com
Math 414: Analysis I
Homework 10
Due: April 18, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 3.4.3, 3.4.4, 3.4.7, 4.1.2, 4.1.5, 4.1.6, 4.1.9, 4.1.11
Tu
Math 414: Analysis I
Homework 9
Due: April 14, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 3.2.13.2.3, 3.2.9, 3.2.12, 3.3.1, 3.3.2, 3.3.10
Turn in the
Math 414: Analysis I
Homework 8
Due: April 4, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 3.1.1-3.1.5, 3.1.8 , 3.1.10
Turn in the following problems.
Math 414: Analysis I
Exam 2 (80 points)
Spring 2014
Name:
*No notes or electronic devices. You must show all your work to receive full credit.
When justifying your answers, use only those techniques that we learned in class.
1. (5) Let (an ) be a sequence
Math 414: Analysis I
Homework 3
Due: February 10th, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 1.3.1, 1.3.2, 1.3.3, 1.3.4
Turn in the following probl
Math 414: Analysis I
Homework 2
Due: February 3rd, 2014
Name:
The following problems are for additional practice and are not to be turned in: (All
problems come from Basic Analysis, Lebl )
Exercises: 1.1.1, 1.1.3, 1.1.4, 1.1.5, 1.2.1, 1.2.2, 1.2.5, 1.2.8,
1
Lecture 4 : Continuity and limits
Intuitively, we think of a function f : R R as continuous if it has a continuous curve. The term
continuous curve means that the graph of f can be drawn without jumps, i.e., the graph can be
drawn with a continuous moti
Math 345
Equinumerous Intervals
The goal of these notes is to answer questions 5-9 in section 15 of the textbook. Rather than answer each one
individually, we will show that any non-degenerate interval in R is equinumerous to any other non-degenerate
inte
Real Analysis, H.L Royden and P.M. Fitzpatrick Errata/Comments on Fourth Edition
Last Edited on 2013 04 05 Dedication Page: Change to I dedicate this book to John Slavins, H.L. Royden, and
my wife, Teresita Lega.(Mr. Slavins and Mr. Royden were inadverten