Instructor: Piotr Hajlasz
Office Hours: MW 4:30-5:30pm and by appointment.
Office: 622 Thackeray Hall
Email: hajlasz@pitt.edu
Textbook: The course will be based mainly on my notes that I will be posting online. In addintion to that we will use the textbook
Elementary Classical Analysis , Second Edition, by J. E. Marsden and M. J. Hoffman
Additional reading:
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. Principles of Mathematical Analysis, by W. Rudin
3. Mathematical Analysis, Second Edition, by T. M. Apostol
4. 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 Zhuomin Liu. Late homework will not be accepted.
What is it about? We start from the Stone-Weierstrass theorem, the Arzela-Ascoli theorem and the Banach contraction principle. Then we move to the analysis of functions of several variables in the Euclidean spaces. Topics will cover differentiation, implicit function theorem, submanifolds, Lagrange multiplier theorem, multiple variable integration, and integration on curves and surfaces (Green's theorem, Gauss' theorem, Stoke's theorem).
Advanced Calculus II (pages 1-233)
Advanced Calculus II (additional pages 1-34)
HW#1 Due Tuesday, January 20, recitations.
HW#2 Due Tuesday, February 10, recitations.
HW#3 Due Tuesday, February 17, recitations.
HW#4 Due day, March 17.
Advanced Calculus I (pages 1-296)
Advanced Calculus I (supplementary materials)
Midterm Exam 1 Midterm Exam 2 (fire alarm) Midterm Exam 2 Final Exam