Syllabus for Math 414, Analysis I
Fall Semester, 2015
Instructor:
Office:
Office Hours:
Homepage:
Eric Weber
Email:
Carver Hall 454
Phone:
MWF 1:30-2:30pm, or by appointment
http://www.public.iastate.edu/∼esweber
esweber@iastate.edu
294-8151
Class Homepage: http://www.public.iastate.edu/∼esweber/Math414/ This page will contain a copy of this syllabus, a detailed calendar of the semester’s material, links to other
relevant information, and assignments when they are given. There is also a Blackboard
course that I will use for posting grades and information.
Course Description: MATH 414. Analysis I. (3-0) Cr. 3. F.S.SS. Prereq: Minimum of
C- in MATH 201. A careful development of calculus of functions of one real variable: real
number properties and topology, limits, continuity, differentiation, integration, series.
Learning Outcomes:
(1) Define the set of real numbers, and state its basic properties.
(2) Understand the Least Upper Bound Property and the Archimedean Property.
(3) Define sequences of real numbers, and understand bounded and convergence sequences.
(4) Understand the concept of limit superior and inferior.
(5) Know the statement of the Bolzano-Weierstrass theorem, and its consequences.
(6) Understand the concept of Cauchy sequences and the completeness of R
(7) Define series of real numbers, and identify when they converge or diverge.
(8) Understand the idea of a limit of a function; in particular, the ε-δ definition.
(9) Define continuous functions, and give relevant examples of continuous and discontinuous functions.
(10) State and understand the Extreme Value Theorem and the Intermediate Value Theorem.
(11) Define the derivative of a function, and understand the relevant derivate rules, i.e.
product, quotient, and chain.
(12) State and understand the Mean Value Theorem.
(13) Define the Riemann integral in terms of Darboux integrals.
(14) Understand the properties of integrals, including linearity of the integral.
(15) State and understand the Fundamental Theorem of Calculus.
Textbook: Basic Analysis: Introduction to Real Analysis by Jiřı́ Lebl, dated December 16,
2014. The textbook is freely available at http://www.jirka.org/ra/
Grading: Grade percentages break down as follows:
Assignment:
Percentage:
Midterm Exam 1 20%
Midterm Exam 2 20%
Final Exam
30%
Exercises
30%
Date:
Sept. 25
Oct. 30
Dec. 17
Daily
2
The following overall percentages will assure you of the associated letter grade: 90%: A;
80%: B; 70%: C; 60%: D. There may be a curve at the end of the semester. No individual
exams will be curved; do NOT ask!
Exams: The two midterm exams will be in class, and may also have a take home component.
They are not comprehensive. The final exam will be comprehensive.
Exercises: Exercises will be assigned during (most) each class period. Exercises assigned
will be due according to the following schedule: exercises assigned on Monday are due on
Friday of the same week; those assigned on Wednesday are due on Monday of the following
week; those assigned on Friday are due on Wednesday of the following week.
Each assignment is worth 2 points: 1 point for submitting on time and 1 point for correct
solution. If the first attempt is unsuccessful, you may attempt the assignment a second time;
the second attempt is due one week after the first attempt.
Timeline: We will cover most of the material of the first 5 chapters of the book, at a pace
of roughly one chapter per two and a half weeks. There may be additional material covered
outside of the textbook.
Academic Dishonesty: Academic dishonesty is very serious. Any case of cheating, plagiarism, etc, will be handled as described in the Student Disciplinary Regulations.
Disability Policy: Please address any special needs or special accommodations with me at
the beginning of the semester or as soon as you become aware of your needs. Those seeking
accommodations based on disabilities should obtain a Student Academic Accommodation
Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is
located on the main floor of the Student Services Building, Room 1076.
Copyright: Please note that all written and web materials for this course have an implied
copyright. In particular, you can photocopy or download for your own use, but you may not
reproduce them for others.