Math 3001, Analysis 1
Semester 2, 2015-16
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer
Course Syllabus: For course syllabus, complete with list of university policies, click here!
LaTeX: Here is a link to information about the mathematical typewriting software LaTeX. This site has links to download sites, including
here .
Course Information:
This course is meant to familiarize the student with the rigorous theory behind the study of functions of a single real variable, and goes over the proofs of some of the
major results used in calculus. Topics to be covered include:
the topology and order structure of the real line; sequences of real numbers and limits of sequences; functions of a real variable:
limits of functions at a point, continuous functions and their properties -- Intermediate Value Theorem , uniform continuity;
the derivative of a function at a point and differentiability, the Mean Value Theorem, and
Taylor's Theorem; the Riemann integral and its properties, and the Fundamental Theorem of Calculus; and if time permits,
a brief overview of series of real numbers and power series expansions.
Prerequisite:
Math 2001 or the equivalent, or instructor consent.
Course Text:
We will use the text "Analysis, With an Introduction to Proof", S.R. Lay, Pearson - Prentice Hall, 2014,
5th edition. After a quick review of Chapters 1 and 2, we will cover most of Chapters 3--7, and part of Chapter 8.
Assessment:
Lecture Hours and Venue:
MWF 10 a.m.-10:00 a.m. ECCR 118.
Office Hours:
MWF 11 a.m. - 12 noon, and by appointment.
Extra slides:
Homework:
- Assignment 1: Due Wednesday, January 20: read Sections 3.1 and 3.2; do problems 3.1.3, 3.1.4, 3.1.7, 3.1.16,
3.1.20, 3.2.3 (a) (e) (j), 3.2.4, 3.2.6 all parts, 3.2.7, 3.2.8, 3.2.9.
- Some solutions to HW 1.
- Assignment 2: Due Friday, January 29: read sections 3.3 and 3.4, do problems 3.3.3 (a), (d), (f), (h), (i), (k), (n),
3.3.7 (a), 3.3.8, 3.3.12 (a), (b), 3.4.3 (a), (c), (e), 3.4.4 (a), (c), (e), 3.4.5, 3.4.8, 3.4.14. For extra credit do 3.3.7 (b).
- Some solutions to HW 2.
- Assignment 3, due Friday, February 5: Review Section 3.4, begin reading Section 3.5, do problems 3.4.6 (a), (c), (e), 3.4.9 (a), 3.4.10,
3.4.16 (a), 3.4.20, 3.4.22 (a), (c), 3.4.24 (a), (d).
- Some solutions to HW 3.
- Assignment 4, due Friday, February 12: Review Section 3.5, begin reading Section 4.1, do problems 3.5.1, 3.5.3 (a), (c), (part (e) for extra credit), 3.5.5, 3.5.6,
4.1.2, 4.1.6 (a), (c), (d), (e), 4.1.7 (a), (c), (d), 4.1.9 (a), (b).
- Some solutions to HW 4.
- Assignment 5, due Friday, February 26, Complete reading 4.1, read Sections 4.1.4.2, 4.3; do problems 4.2.1, 4.2.5 (a),(b),(e),(g),(j),(k),
4.2.15 (b),(c), 4.2.16, 4.3.1, 4.3.3 (a),(d), 4.3.7, 4.3.10 (a). Extra credit problem: 4.3.9.
- Some solutions to HW 5.
- Assignment 6, due Friday, March 4: read Sections 4.4 and 5.1, do problems 4.4.3 (all), 4.4.4 (all), 4.4.7 (all), 4.4.11, 4.4.13;
5.1.3 (a), (c), (d), (e), (h), 5.1.4, 5.1.9, 5.1.14, 5.1.16, 5.1.18.
- Some solutions to HW 6.
- Assignment 7, due Friday, March 11: read Sections 5.2 and 5.3 through p. 217, do problems 5.2.3, 5.2.4, 5.2.8. 5.2.10, 5.2.12, 5.2.13, 5.2.14, 5.2.17, 5.2.18, 5.3.4, 5.3.6.
- Some solutions to HW 7.
- Assignment 8, due Friday, March 18: read the rest of Sections 5.3 and Section 5.4, read 6.1 pp. 237-238, do problems 5.3.7, 5.3.8, 5.3.9, 5.3.12, 5.4.4 (all parts), 5.4.5, 5.4.6, 5.4.7, 5.4.11. 6.1.3 (a), (b).
- Some solutions to HW 8.
- Assignment 9, due Friday, April 8: read the rest of Section 6.1 and Section 6.2, do problems 6.1.5, 6.1.8, 6.1.11, 6.1.12, 6.1.13, 6.1.15,
6.2.1, 6.2.3, 6.2.5 (a),(b),(f), 6.2.11, 6.2.13, 6.2.15, 6.2.17, 6.2.18.
- Some solutions to HW 9.
- Assignment 10, due Friday, April 15: Read Secion 7.1, and begin reading Section 7.2: do 7.1.4, 7.1.5, 7.1.8. 7.1.11, 7.1.12,
7.1.13, 7.1.15, 7.1.16, 7.1.17, 7.2.2, 7.2.5.
- Some solutions to HW 10.
- Assignment 11, due Friday, April 22: Read the rest of section 7.2 and Section 7.3; do problems 7.2.6, 7.2.8, 7.2.9, 7.2.11, 7.2.15,
7.2.17, 7.3.5 (c), (d), 7.3.11, 7.3.12, 7.3.14, 7.3.15.
- Some solutions to HW 11.
- Assignment 12, due Friday, April 29: Do Questions 3 part (i), 4 part (i), 5 part (i), and 6 part (ii) of the sample final from Spring 2012 online.
- Solutions to the Spring 2012 sample final exam.
Some Important Names associated with Analysis :
Various other matters :
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religious obligations, honor code, student classroom and course-related behavior,
and discrimination and harassment issues, see the university pages on these matters at:
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www.colorado.edu/disabilityservices.
Missed Exams:
If you know that you are going to miss an exam or cannot take the final
exam at the scheduled time, please notify me at least two weeks
in advance. If you miss a midterm exam for any acceptable reason (e.g.
religious obligation, documented illness), you will be given an average score
based on your performance in the other midterm and final exam.
If you miss all midterm exams for
acceptable reasons, your course grade will be based entirely on your final
exam score. If you miss the final exam and have not rescheduled it in
advance, you will score zero on the final.
Religious Obligations:
Campus policy regarding religious observances requires that faculty
make every effort to reasonably and fairly deal with all students who,
because of religious obligations, have conflicts with scheduled exams,
assignments or required attendance. In this class, you should notify me of any conflict at least two weeks in advance.
See full details at
www.colorado.edu/policies/observance-religious-holidays-and-absences-classes-andor-exams.
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Students and faculty each have responsibility for maintaining an
appropriate
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treat all students with understanding, dignity and respect, to guide classroom
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All students of the University of Colorado at Boulder are responsible for
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Violations of this policy may include: cheating, plagiarism, aid of academic
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The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning,
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Last modified January 6, 2016.