Instructor: Piotr Hajlasz
Office Hours: MoWe 12:00-1:00 & 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 and I will keep sending you updated notes by email.
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 submitted on Canvas. The problems must be typed in LaTeX and submitted as a pdf file. Late homework will not be accepted. Selected problems will be graded by Anthony Cappello.
Course content Metric spaces, Banach contraction principle, Arzela-Ascoli theorem, Stone-Weierstrass theorem, differentiability of functions of sseveral variables, inverse function theorem, implicit function theorem, Lagrange multipliers, integration (whatever it means) etc.
Problems (LaTeX file) Problems (pdf file) No deanline, not required, Canvas
HW#1 (LaTeX file) HW#1 (pdf file) February 7 (my birthday), Canvas.
HW#2 (LaTeX file) HW#2 (pdf file) February 14 (celebration of my x years + 7 days), Canvas.
HW#3 (LaTeX file) HW#3 (pdf file) February 21, Canvas.
HW#4 (LaTeX file) HW#4 (pdf file) February 28, Canvas.
HW#5 (LaTeX file) HW#5 (pdf file) March 18, Canvas.
HW#6 (LaTeX file) HW#6 (pdf file) April 2, Canvas.
HW#6 (LaTeX file) HW#6 (pdf file) Not available yet.
HW#6 (LaTeX file) HW#6 (pdf file) Not available yet.
HW#6 (LaTeX file) HW#6 (pdf file) Not available yet.