Chapter 1

1.1: 2-4,11,12
1.2: 1-11,13
1.3: 2
1.4: 1,4,6

Chapter 2

2.1: 1,2,5,6,9–11
2.2: 1
2.3: 1–5
2.4: 1–4,16–18 (some of the other exercises deal with various aspects needed in derivation of solution to diffusion equation - you may be interested in them)
2.5: 1 (consider the "hammer-blow" exercise 2.1.5)

Chapter 4

4.1: 2,4,5,6
4.2: 1

Chapter 5

5.1: 2,5,8,9

Chapter 6

6.1: 2,4–7,11 (remember in 3D, the book's r is our ρ (also the role of θ and Ø are switched)) For #11 you'll need the Gauss divergence theorem - see page 423 of the text.
6.2: 1,3,4,5

Chapter 10

10.1: 1–3