Distribution Theory, Spring 2019
Mon 4/29: Parametrix for elliptic operators.
- Reading: Chapter 17
- No new homework
- Reading: Chapter 17
- Problems: (Due Thursday 5/2): 17.2, 17.5.
Mon 4/15: Schwartz space and tempered distributions.
- Reading: Chapter 14
- Problems: (Due Thursday 4/18): 14.1, 14.2
Mon 4/8: Fundamental Solutions continued.
- Reading: (rest of) Chapter 12
- Problems: no new problems.
Mon 4/8: Fractional integration and differentiation in 1D.
- Reading: Chapter 13.1
- Problems: (Due Thursday 4/18): 13.2, 13.3
Thu 4/4: Fundamental Solutions.
- Reading: Chapter 12
- Problems: (Due Thursday 4/11): 12.1, 12.4, 12.7, 12.11.
Mon 4/1: Convolution of Distributions continued.
- Reading: Chapter 11 (second half)
- Problems: (Due Thursday 4/4): 11.7, 11.8, 11.10
Thu 3/28: Convolution of Distributions.
- Reading: Chapter 11 (first half)
- Problems: (Due Thursday 4/4): 11.2, 11.5.
Mon 3/25: Pullback, pushforward, and invariance of distributions.
- Reading: Rest of Chapter 10
- Problems: (Due Thursday 3/28): 10.8, 10.9, 10.25
Mon 3/4: Pushforward and pullback of distributions.
- Reading: Chapter 10 (first half or so)
Thu 2/28: Multiplication by functions.
- Reading: Chapter 9
- Problems: (Due Thursday 3/7): 9.2, 9.4, 9.7
Mon 2/25: Compactly supported distributions.
- Reading: Chapter 8
- Problems: No new problems.
Thu 2/21: Localization and support of distributions.
- Reading: Chapter 7
- Problems: (Due Thursday 2/28): 7.2, 7.4, 7.6, 7.9.
Mon 2/18: Taylor approximation in several variables.
- Reading: Chapter 6.
- Problems: No new problems.
Thu 2/14: Derivatives and limits of distributions.
- Reading: Chapters 4 and 5.
- Problems: (Due Thursday 2/21) 4.1, 4.5, 5.1, 5.3.
Mon 2/11: Distributions continued.
- Reading: Second half of Chapter 3.
- Problems: (Due Thursday 2/14) 3.1, 3.2, 3.4, 3.5.
Thu 2/7: Distributions defined.
- Reading: First half of Chapter 3.
- Problems: (Due Thursday 2/14) 3.1, 3.2, 3.4, 3.5.
Mon 2/4: Test functions continued.
- Reading: Rest of Chapter 2
- Problems: No new problems.
Thu 1/31: Test functions.
- Reading: Chapter 2 (We will probably take two lectures to cover this chapter).
- Problems: (Due Thursday 2/7, along with problems to be assigned Monday): 2.2, 2.3.
Mon 1/28: Motivational examples.
- Reading: Chapter 1 (I will not cover examples 1.4 and 1.5 at this time)
- Problems: (Due Thursday 1/31): 1.1, 1.2, 1.3, 1.4