Math 201B: Analysis
Winter 2007
Announcement
The Final exam is 4:00pm, Friday March 16th.
There will be a review session in 1060 Bainer from 1:40-3:30p.m. on Thursday, March 15.
Solutions to the Final exam
Here are two previous final exams:
Final from 2000
Final from 2003
Outline of topics covered in final:
- Hilbert spaces (Sec. 6.1–6.3)
- Inner product spaces
- Projection theorem
- Orthogonal direct sums
- Bessel's inequality
- Orthonormal bases
- Parseval's theorem
- Lebesgue integration (Sec. 12.1–12.6)
- Definition of measure and the integral
- Montone and dominated convergence theorems
- Fubini's theorem
- L^p-spaces
- Fourier analysis on the circle (Sec. 7.1–7.4)
- Fourier coefficients in L^1
- Riemann-Lebesgue lemma
- Convolution theorem
- Approximate identities
- Completeness of the Fourier basis in L^2
- Weak derivatives
- Sobolev spaces
- Bounded linear operators on a Hilbert space (Sec. 8.1–8.4, Sec. 8.6)
- Orthogonal projections
- Riesz representation theorem
- Adjoints
- Self-adjoint and unitary operators
- Weak convergence in a Hilbert space
- Spectral theory (Sec. 9.1–9.5)
- The spectrum of a bounded linear operator
- Point, continuous, and residual spectrum
- Compact operators
- Spectral theorem for compact self-adjoint operators
Instructor
John Hunter
e-mail: jkhunter@ucdavis.edu
Phone: (530) 752-3189
Office: MSB 3230
Office hours:M 1:30–3:00 p.m. W 1:00–2:30 p.m.
Lectures: MWF 11:00–11:50 a.m., Physics-Geology 140
Discussion session: Tu 11:00–11:50 a.m., Physics-Geology 140
Midterm: In class, Wednesday Feb 14.
Midterm solutions
Sample midterm problems
Brief solutions to sample midterm problems
Final (Code D): In class, Friday Mar 16, 4:00 p.m.–6:00 p.m., Physics-Geology 140
Important dates:
- Last day to add: Friday Jan 19
- Last day to drop: Wednesday Jan 31
- Academic Holidays: Monday Jan 15, Monday Feb 19
- Last day of instruction: Wednesday Mar 14
TAs
Hillel Raz
e-mail: hraz@math.ucdavis.edu
Office: MSB 2125
Office hours: Tu 4:30–6:00 p.m.
Zhihua Zhang
e-mail: zhangzh@math.ucdavis.edu
Office: MSB 2145
Office hours: Th 1:10 p.m.–3:00 p.m.
Grade
The course grade will be based on the Homework, Midterm, and Final scores,
weighted as follows:
- Homework: 50%
- Midterm: 20%
- Final: 30%
Text
The text for Math 201 is Applied Analysis,
by John Hunter and Bruno Nachtergaele, World Scientific, 2001.
(Corrected reprinting, 2005.)
The course this quarter will cover roughly Chapters 6–10 of the text.
You can buy a copy if you wish, or use the online copy of the book
available at these links in
postscript or
pdf formats. Either way is fine.
We welcome your comments on the text. Please send them to
jkhunter@ucdavis.edu
or
bxn@math.ucdavis.edu.
Supplementary Notes
Unordered sums
Measure theory
The heat equation
Homework Assignments
Set 1 (due in class, Friday Jan 12)
Solutions to Set 1
Set 2 (due in class, Friday Jan 19)
Solutions to Set 2
Set 3 (due in class, Friday Jan 26)
Solutions to Set 3
Set 4 (due in class, Friday Feb 2)
Solutions to Set 4
Set 5 (due in class, Monday Feb 12)
Solutions to Set 5
Set 6 (due in class, Friday Feb 23)
Solutions to Set 6
Set 7 (due in class, Friday Mar 2)
Solutions to Set 7
Set 8 (due in class, Friday Mar 9)
Solutions to Set 8
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