| 1 |
Introduction |
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| 2 |
Measures |
Assignment 1 due (one day after Lecture 2) |
| 3 |
Chebyshev's Inequality |
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| 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 |
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| 7 |
Linearity |
Assignment 4 due (one day after Lecture 7) |
| 8 |
Fatou's Lemma |
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| 9 |
Integrable Functions |
Assignment 5 due (one day after Lecture 9) |
| 10 |
Bessel's Inequality |
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| 11 |
Convergence of Fourier Series |
Assignment 6 due (one day after Lecture 11) |
| 12 |
Completeness |
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| 13 |
First In-class Test |
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| 14 |
Riesz Representation Theorem |
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| 15 |
Schwartz Functions |
Assignment 7 due (one day after Lecture 15) |
| 16 |
Fourier Transform |
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| 17 |
Approximation |
Assignment 8 due (one day after Lecture 17) |
| 18 |
Harmonic Oscillator |
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| 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 |
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| 22 |
Wave Equation |
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| 23 |
Bounded Operators |
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| 24 |
Compact Operators |
Assignment 11 due (one day after Lecture 24) |
| 25 |
Spectral Theorem |
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| 26 |
Hilbert-Schmidt Operators |
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| 27 |
Final Exam |
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