Math 420 (Introduction to OneVariable Calculus)
Fall 2011
Instructor:
Reza Pakzad
Email: pakzad AtSign pitt Dot edu
Lectures: MWF 1:00PM1:50PM at Thack 627
Office hours:
MW 3:00PM3:50PM, or by appointment, held at Thackeray Hall 610.
Recitation: Tu 1:00PM1:50PM at Thack 627,
Instructor: Nicholas Hurl
Textbook: Bartle and Sherbert, Introduction to Real Analysis,
Third Edition, Wiley. The course covers chapters 4 through 10.
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:
Quizes (10%), Homework (20%), Class midterms (30%), final (40%).
Important notices about homeworks, quizzes and 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.
Quizzes will be given in class, usually on Wednesdays, but without previous warning.
They can cover the topics covered during the same day class. The lowest quiz score will
be dropped. There will be no makeup quizzes. If you miss a quiz, that will be
the one that's 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 during your recitation.
Midterm exams: The dates are: Wednesday Oct. 5 , 2011;
Wednesday Nov. 16 , 2011; during class.
Final Exam: The time, date and place of the final exam
will be posted here soon.