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Solutions to Applied Partial Differential Equations 5e by Haberman

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Table of Contents


Chapter 1: Heat Equation
1.2 1.3 1.4 1.5
Exercise 1 Exercise 8 Exercise 1 Exercise 1 Exercise 8 Exercise 1 Exercise 8 Exercise 15 Exercise 23
Exercise 2 Exercise 9 Exercise 2 Exercise 2 Exercise 9 Exercise 2 Exercise 9 Exercise 16 Exercise 24
Exercise 3 Exercise 3 Exercise 3 Exercise 10 Exercise 3 Exercise 10 Exercise 17 Exercise 25
Exercise 4 Exercise 4 Exercise 11 Exercise 4 Exercise 11 Exercise 18
Exercise 5 Exercise 5 Exercise 12 Exercise 5 Exercise 12 Exercise 19
Exercise 6 Exercise 6 Exercise 13 Exercise 6 Exercise 13 Exercise 20
Exercise 7 Exercise 7 Exercise 7 Exercise 14 Exercise 21

Chapter 2: Method of Separation of Variables
2.2 2.3 2.4 2.5
Exercise 1 Exercise 1 Exercise 7 Exercise 1 Exercise 7 Exercise 1 Exercise 7 Exercise 13 Exercise 19 Exercise 25
Exercise 2 Exercise 2 Exercise 8 Exercise 2 Exercise 2 Exercise 8 Exercise 14 Exercise 20 Exercise 26
Exercise 3 Exercise 3 Exercise 9 Exercise 3 Exercise 3 Exercise 9 Exercise 15 Exercise 21 Exercise 27
Exercise 4 Exercise 4 Exercise 10 Exercise 4 Exercise 4 Exercise 10 Exercise 16 Exercise 22 Exercise 28
Exercise 5 Exercise 5 Exercise 11 Exercise 5 Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 29
Exercise 6 Exercise 6 Exercise 6 Exercise 12 Exercise 18 Exercise 24

Chapter 3: Fourier Series
3.2 3.3 3.4 3.5 3.6
Exercise 1 Exercise 1 Exercise 7 Exercise 13 Exercise 1 Exercise 7 Exercise 13 Exercise 1 Exercise 7 Exercise 1
Exercise 2 Exercise 2 Exercise 8 Exercise 14 Exercise 2 Exercise 8 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 9 Exercise 15 Exercise 3 Exercise 9 Exercise 3
Exercise 4 Exercise 4 Exercise 10 Exercise 16 Exercise 4 Exercise 10 Exercise 4
Exercise 5 Exercise 11 Exercise 17 Exercise 5 Exercise 11 Exercise 5
Exercise 6 Exercise 12 Exercise 18 Exercise 6 Exercise 12 Exercise 6

Chapter 4: Wave Equation: Vibrating Strings and Membranes
4.2 4.3 4.4 4.5 4.6
Exercise 1 Exercise 1 Exercise 1 Exercise 6 Exercise 11 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 7 Exercise 12 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 8 Exercise 13 Exercise 3
Exercise 4 Exercise 4 Exercise 9 Exercise 4
Exercise 5 Exercise 5 Exercise 10 Exercise 5

Chapter 5: Sturm--Liouville Eigenvalue Problems
5.3 5.4 5.5 5.5A 5.6 5.7 5.8 5.9 5.10
Exercise 1 Exercise 1 Exercise 1 Exercise 14 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 15 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 16 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 17 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 18 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11
Exercise 12 Exercise 12
Exercise 13 Exercise 13

Chapter 6: Finite Difference Numerical Methods for Partial Differential Equations
6.2 6.3 6.4 6.5 6.6 6.7
Exercise 1 Exercise 1 Exercise 8 Exercise 15 Exercise 1 Exercise 1 Exercise 1 Exercise 8 Exercise 1
Exercise 2 Exercise 2 Exercise 9 Exercise 16 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 10 Exercise 17 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 11 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 12 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 13 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 14 Exercise 7 Exercise 7 Exercise 7

Chapter 7: Higher-Dimensional Partial Differential Equations
7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 16 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12 Exercise 12 Exercise 12
Exercise 13 Exercise 13 Exercise 13
Exercise 14 Exercise 14
Exercise 15 Exercise 15

Chapter 8: Nonhomogeneous Problems
8.2 8.3 8.4 8.5 8.6
Exercise 1 Exercise 6 Exercise 1 Exercise 6 Exercise 1 Exercise 1 Exercise 6 Exercise 1 Exercise 6
Exercise 2 Exercise 2 Exercise 7 Exercise 2 Exercise 2 Exercise 2 Exercise 7
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 8
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 9
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 10

Chapter 9: Green's Functions for Time-Independent Problems
9.2 9.3 9.4 9.5 9.6
Exercise 1 Exercise 1 Exercise 10 Exercise 19 Exercise 1 Exercise 10 Exercise 1 Exercise 10 Exercise 19 Exercise 1
Exercise 2 Exercise 2 Exercise 11 Exercise 20 Exercise 2 Exercise 11 Exercise 2 Exercise 11 Exercise 20 Exercise 2
Exercise 3 Exercise 3 Exercise 12 Exercise 21 Exercise 3 Exercise 12 Exercise 3 Exercise 12 Exercise 21 Exercise 3
Exercise 4 Exercise 4 Exercise 13 Exercise 22 Exercise 4 Exercise 13 Exercise 4 Exercise 13 Exercise 22 Exercise 4
Exercise 5 Exercise 14 Exercise 23 Exercise 5 Exercise 14 Exercise 5 Exercise 14 Exercise 23 Exercise 5
Exercise 6 Exercise 15 Exercise 24 Exercise 6 Exercise 6 Exercise 15 Exercise 24 Exercise 6
Exercise 7 Exercise 16 Exercise 25 Exercise 7 Exercise 7 Exercise 16 Exercise 7
Exercise 8 Exercise 17 Exercise 26 Exercise 8 Exercise 8 Exercise 17 Exercise 8
Exercise 9 Exercise 18 Exercise 9 Exercise 9 Exercise 18 Exercise 9

Chapter 10: Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
10.2 10.3 10.4 10.5 10.6 10.7
Exercise 1 Exercise 1 Exercise 13 Exercise 1 Exercise 1 Exercise 13 Exercise 1 Exercise 13 Exercise 1
Exercise 2 Exercise 2 Exercise 14 Exercise 2 Exercise 2 Exercise 14 Exercise 2 Exercise 14 Exercise 2
Exercise 3 Exercise 15 Exercise 3 Exercise 3 Exercise 15 Exercise 3 Exercise 15 Exercise 3
Exercise 4 Exercise 16 Exercise 4 Exercise 4 Exercise 16 Exercise 4 Exercise 16 Exercise 4
Exercise 5 Exercise 17 Exercise 5 Exercise 5 Exercise 17 Exercise 5 Exercise 17 Exercise 5
Exercise 6 Exercise 18 Exercise 6 Exercise 6 Exercise 18 Exercise 6 Exercise 18 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 19 Exercise 7 Exercise 19
Exercise 8 Exercise 8 Exercise 8 Exercise 20 Exercise 8 Exercise 20
Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 21
Exercise 10 Exercise 10 Exercise 10 Exercise 10 Exercise 22
Exercise 11 Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12 Exercise 12 Exercise 12

Chapter 11: Green's Functions for Wave and Heat Equations
11.2 11.3
Exercise 1 Exercise 4 Exercise 7 Exercise 10 Exercise 13 Exercise 1 Exercise 4 Exercise 7
Exercise 2 Exercise 5 Exercise 8 Exercise 11 Exercise 14 Exercise 2 Exercise 5 Exercise 8
Exercise 3 Exercise 6 Exercise 9 Exercise 12 Exercise 15 Exercise 3 Exercise 6

Chapter 12: Green's Functions for Wave and Heat Equations
12.2 12.3 12.4 12.5 12.6 12.7
Exercise 1 Exercise 9 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 9 Exercise 17 Exercise 1
Exercise 2 Exercise 10 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 10 Exercise 18 Exercise 2
Exercise 3 Exercise 11 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 11 Exercise 19
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 12 Exercise 20
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 13 Exercise 21
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 14 Exercise 22
Exercise 7 Exercise 7 Exercise 7 Exercise 15 Exercise 23
Exercise 8 Exercise 8 Exercise 8 Exercise 16

Chapter 13: Laplace Transform Solution of Partial Differential Equations
13.2 13.3 13.4 13.5 13.6 13.7 13.8
Exercise 1 Exercise 7 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 8 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 9 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6

Chapter 14: Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12

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