Instructor: Piotr Hajlasz
Office Hours: Monday 2:05-3:00 pm, 4:00-5:00 pm and by appointment.
Office: 420 Thackeray Hall
Email: hajlasz@pitt.edu
Textbook: I will not use any particular textbook, but I will post my notes online. You can find here some hand written notes that I used in the past for the course, but I will be writing a new set of notes (in LaTeX) that will cover whole material of the course. For the paractice problems use the book Berkeley Problems in Mathemtics and study problems from the past preliminary exams.
Advanced Calculus I (pages 1-296)
Advanced Calculus I (supplementary materials)
Reccomended books:
1. Berkeley Problems in Mathemtics, Third Edition, by P. N. De Souza and J.-N. Silva
This is an excellent collection of problems for the course. Problems have full solutions. Chapters 1,2,4 cover much of the material needed for the Preliminary Exam in Analysis. Other chapters contain excelelnt problems for other graduate courses like Linear Algebra, Algebra, Analysis II and Ordinary Differential Equations. This book is a must for any Ph.D. student.
2. Elementary Classical Analysis , Second Edition, by J. E. Marsden and M. J. Hoffman
3. Principles of Mathematical Analysis, by W. Rudin
4. Mathematical Analysis, Second Edition, by T. M. Apostol
5. Real Mathematical Analysis by Ch. Ch. Pugh.
Course Grade: Homework (30%) + Two midterm exams (20% + 20 %) + Final exam (30%)
Homework: Posted weakly on the course webpage to be returned to Behnam Esmayli. The problems must be typed in LaTeX. Late homework will not be accepted.
Course content Logic and set theory. Axiom and construction of real numbers. Supremum, infimum, limits and seties, upper and lower limits. Continuity and differentiability of functions. Riemann integral. Metric spaces, contraction principle with applications, Arzela Ascoli theorem, Stone-Weierstrass theorem.
HW#1 (LaTeX file) September 13, recitations HW#1 (pdf file)
HW#2 (LaTeX file) September 20, recitations HW#2 (pdf file)
HW#3 (LaTeX file) October 9, recitations HW#3 (pdf file)
HW#4 (LaTeX file) October 23, recitations HW#4 (pdf file)
HW#5 (LaTeX file) November 27, recitations HW#5 (pdf file)