- This course is the continuation of APPM 5440, with the same instructor and same book. The biggest change is that we are no longer using D2L for grades and homework solutions; instead, we are using canvas. Visit our course's canvas website.
- We cover chapters 7, 8, 9, 11, and 12 of Hunter and Nachtergaele's book (APPM 5440 covered chapters 1--6), skipping chapters 10 and 13.
- The class meets in ECCR 131 every Monday/Wednesday/Friday from 1 PM to 1:50 PM
- Note: this is not the same time/location as last semester
- The final exam is Sunday May 6 from 7:30 PM to 10 PM
- If you have any issues with this date, let the instructor know immediately
- Since you have months of advance warning, there are very few valid reasons to miss it!
- Dropping the course
- After Jan 31 2018, if you drop the course, a "W" shows up on the transcript and you are charged for the class (last day to add a class is Jan 24 2018)
- After Mar 23 2018, the course cannot be dropped automatically online; you need to petition the dean for approval (which is unlikely to happen except in extenuating circumstances).
Text: Applied Analysis by by J. Hunter and B. Nachtergaele, World Scientific Publishing, 1st ed., 2001, ISBN 978-9812705433.
Syllabus: APPM 5450 syllabus (last updated 1/17/18)
Prelim exam: this course is designed to partially prepare you for the Analysis prelim exam (Analysis prelim exam, old website) for graduate students in the applied math department (you should also know advanced calculus and the first semester of this course; in addition, independent studying is recommended).
||MWF 1 to 1:50
||TBD first week of class
Homework solutions are to uploaded to Canvas.
||Friday, Jan 26 2018
There are no mid-term exams, only a final (in-class). Half of the homework are "no collaboration" homeworks, which serve as mid-term exam scores.
The final exam is in accordance with the standard CU Final Exam schedule and is Sunday, May 6 2018 from 7:30 PM to 10:00 PM
Handouts for 5450:
some handouts from the 2016 version of 5450:
Handouts from 5440:
Supplemental (non-required) texts/resources:
The material we cover is quite standard, so there are lots of references. If you were to get one additional reference, I'd suggest Kreyszig.
- Royden's classic Real Analysis
- Kolmogorov and Fomin's Introductory Real Analysis, which is highly readable and not too long
- Kreyszig's Introductory Functional Analysis with Applications
- Kreyszig is a particularly good book for self-study because (1) he is rather conversational with good insight, (2) the topics are rather close to our syllabus, in that he covers the contraction mapping theorem, basic differential equations, and Fourier analysis, and (3) there are answers to odd-numbered exercises in the back, so you can check your work.
- There are not a lot of books on applied functional analysis (meaning that the Fourier transform, distributions and Green's functions are discussed), and many of them have a physics bent. Applied functional analysis by D. H. Griffel is in similar spirit to our book and quite readable (and cheap on Amazon), so it comes recommended as a supplement. There is a book by J. T. Oden and L. F. Demkowicz with the same title which may also be useful, though not quite as cheap.
- Applied Functional Analysis: Applications to Mathematical Physics by E. Zeidler is available on SpringerLink, so you have free access to the PDF version if you are on campus. I am not familiar with this book so no endorsement, but amazon reviews are positive.
- Elementary Functional Analysis by B. MacCluer, also available on SpringerLink (no endorsements)
- A course in Functional Analysis by John B. Conway (not Comway as Springer/Amazon say, nor the John H. Conway) goes into more detail in some places
- (2nd ed.1990, 1997 revised 4th printing)
- For a whirlwind tour of all of analysis (covers a lot, but not too deeply), see the Hitch-hiker's guide to analysis (2005), free download via SpringerLink if you are on campus
- Reed and Simon's Methods of Mathematical Physics, vol. 1: functional analysis, which is a bit condensed and focuses on some applications particularly relevant for applied mathematics
- Apostol's Mathematical Analysis covers real analysis and Fourier series
- For a modern, more conversational perspesctive, two good online sources from respected mathematicians are the following class notes:
- Topics specific to the second semester (5450):
Note: you may not use theorems/lemmas/etc. from any of the above references in a homework problem without proof unless explicitly mentioned (with the exception of the Hunter/Nachtergaele book, from which you may use any stated fact from the current or previous chapters).
Previous versions the 5450 course:
- spring semester APPM 5450 (2015) and 2016, taught by Prof. Becker (links are probably dead as WebExpress automatically unpublishes old course webpages)
- spring semester APPM 5450 (taught by Prof Martinsson): 2006, 2007, 2008, 2010, 2011, 2013, 2014, 2017 (these links should still be active)
Previous versions the 5440 course: