Lecture Notes

The lecture notes are courtesy of Jonathan Campbell, a student in the class. Notes for the entire course are available as a single pdf file (PDF) (Courtesy of Jonathan A. Campbell. Used with permission.), or broken into files corresponding to the lectures.

LEC # TOPICS
1 Introduction (PDF)
2 Measures (PDF)
3 Chebyshev's Inequality (PDF)
4 Law of Large Numbers (PDF)
5 Measurable Functions (PDF)
6 The Integral (PDF)
7 Linearity (PDF)
8 Fatou's Lemma (PDF)
9 Integrable Functions (PDF)
10 Bessel's Inequality (PDF)
11 Convergence of Fourier Series (PDF)
12 Completeness (PDF)
13 First In-class Test
14 Riesz Representation Theorem (PDF)
15 Schwartz Functions (PDF)
16 Fourier Transform (PDF)
17 Approximation (PDF)
18 Harmonic Oscillator (PDF)
19 Completeness of Eigenfunctions (PDF)
20 Sobolev Spaces (PDF)
21 Second In-class Test
22 Wave Equation (PDF)
23 Bounded Operators (PDF)
24 Compact Operators (PDF)
25 Spectral Theorem (PDF)
26 Hilbert-Schmidt Operators (PDF)
27 Final Exam