Calendar

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