Math 420 (Introduction to OneVariable Calculus)
Fall 2013
Instructor:
Reza Pakzad
Email: pakzad AtSign pitt Dot edu
Lectures: MW 4:00PM4:15PM at Thack 627
Office hours (subject to change):
TTh 11:0011:50AM, or by appointment, held at Thackeray Hall 610.
Recitation: W 6:30PM7:20PM at Allen 106,
Instructor: Nan Jiang
Textbook: Jiri Lebl: Basic Analysis.
Custom Pitt edition.
Prerequisites: The course concerns the "theoretical" OneVariable Calculus.
Prerequisite is Math 413: Introduction to Theoretical Mathematics. If you do not feel comfortable
with the prerequisite material, please contact the instructor in the beginning of the course.
Syllabus:

The BolzanoWeierstrass Theorem; Cauchy sequences; Cauchy completeness
of the real numbers.

Realvalued functions on an interval: limits and continuity.

Intermediate Value Theorem; MaxMin Theorem.

Uniform continuity; continuous functions on a closed and bounded
interval are uniformly continuous.

Differentiable functions.

Interior Extremum Theorem, Rolle's Theorem, Mean Value Theorem.

Taylor's Theorem and Taylor Series.

The Riemann Integral on a closed and bounded interval.
Increasing functions are Riemannintegrable. Continuous functions are
Riemannintegrable.

The Fundamental Theorem of Calculus.

Definition and examples of pointwise and uniformly convergent sequences
of functions.

Continuity of uniform limits of continuous functions.

Interchange of uniform limits and integration.

Interchange of limits with differentiation.

The Mtest for uniform convergence of series.

Application to power series.
Grading: Exam grading is curved. Your final grade depends
on your performance on the final exam as well as on your total grade
calculated as follows:
Homework (30%), Class midterms (30%), final (40%).
Important notices about homeworks and exams:
Attending classes and recitations and working on the homework exercises are absolutely recommended
for success in the exams. Clarity and tidiness of presentation, completeness and correctness are necessary
to obtain full grade. In particular untidy presentations of correct proofs will be severely
penalized.
You may work with other students or use library resources, but each student must
write up his or her solutions independently. Copying solutions from other students
will be considered cheating, and handled accordingly. The lowest homework
score will be dropped.
There will be no make up midterm exams. If you miss the midterm exam for
a *documented* medical reason, your grade on it will be the prorated grade
of your final exam.
Homework:
Weakly assignments will appear here.
Homeworks are due every Wednesday at the beginning of class.
Midterm exams: The dates are: Monday Oct. 7 , 2011;
Monday Nov. 11 , 2011; during class.
Final Exam: The final exam will be held on Saturday Dec. 14,
10:0011:50 am at Thackeray Hall 627 . Here is a
guideline.