Some suggested exercises:
Dimensional analysis and scaling:
Page 17: 1, 2, 3, 4, 5
Page 30: 1, 2, 10
Perturbation methods:
Page 100: 2, 8 a), 9, 16 
Page 111: 1 b), 4
Page 121: 1 a), i) 
Page 141: 2
Variational calculus:
Page 158: 1
Page 175: 2 b), 3, 5, 6
Page 184: 5 d)
Dynamical systems:
 Dynamical systems problems. 
Partial differential equations:
 Partial differential equations problems. 
Sturm-Liouville problems:
 Sturm-Liouville problems. 
Transform theory:
 Transform theory problems. 
Integral equations:
 Integral equations problems.