Instructor: Piotr Hajlasz
Office Hours: Mo 11:00-11:50AM & Fr 2:10-3:00PM.
Office: 420 Thackeray Hall
Email: hajlasz@pitt.edu
These notes constain some errors and omissions, but I will do my best to correct and append them.
You can find here some hand written notes that I used in the past for the course. The notes also include metrial of Advanced Calculus II:
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 of Advanced Calculus I & II. 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 submitted on Canvas. The problems must be typed in LaTeX. Late homework will not be accepted. Selected problems will be graded by the TA.
Course content Logic and set theory. Axiom and construction of real numbers. Supremum, infimum, sequences, series and limits, upper and lower limits. Continuity and differentiability of functions. Riemann integral. Metric spaces, contraction principle with applications, Arzela Ascoli theorem, Stone-Weierstrass theorem.
Bonus Problems (LaTeX file)
Bonus Problems (pdf file)
No due date. I will keep adding problems and you should keep adding solutions to the same file. Some of the problems will be very difficult. You can submit solutions at any time and if you have more solutions, replace the old submission.
HW#1 (LaTeX file) HW#1 (pdf file) Sunday September 8, Canvas.
HW#2 (LaTeX file) HW#2 (pdf file) Sunday September 15, Canvas.
HW#3 (LaTeX file) HW#3 (pdf file) Sunday September 22, Canvas.
HW#4 (LaTeX file) HW#4 (pdf file) Sunday September 29, Canvas.
HW#5 (LaTeX file) HW#5 (pdf file) Sunday October 6, Canvas.
HW#6 (LaTeX file) HW#6 (pdf file) Sunday October 27, Canvas.
HW#7 (LaTeX file) HW#7 (pdf file) Sunday November 3, Canvas.
HW#8 (LaTeX file) HW#8 (pdf file) Sunday November 10, Canvas.