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# Solutions to Math Methods for Physics and Engineering 3e by Riley

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Chapter 1: Preliminary algebra
Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 1.6 Exercise 1.7 Exercise 1.8 Exercise 1.9
Exercise 1.10 Exercise 1.11 Exercise 1.12 Exercise 1.13 Exercise 1.14 Exercise 1.15 Exercise 1.16 Exercise 1.17 Exercise 1.18
Exercise 1.19 Exercise 1.20 Exercise 1.21 Exercise 1.22 Exercise 1.23 Exercise 1.24 Exercise 1.25 Exercise 1.26 Exercise 1.27
Exercise 1.28 Exercise 1.29 Exercise 1.30 Exercise 1.31 Exercise 1.32 Exercise 1.33

Chapter 2: Preliminary calculus
Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 Exercise 2.7 Exercise 2.8 Exercise 2.9
Exercise 2.10 Exercise 2.11 Exercise 2.12 Exercise 2.13 Exercise 2.14 Exercise 2.15 Exercise 2.16 Exercise 2.17 Exercise 2.18
Exercise 2.19 Exercise 2.20 Exercise 2.21 Exercise 2.22 Exercise 2.23 Exercise 2.24 Exercise 2.25 Exercise 2.26 Exercise 2.27
Exercise 2.28 Exercise 2.29 Exercise 2.30 Exercise 2.31 Exercise 2.32 Exercise 2.33 Exercise 2.34 Exercise 2.35 Exercise 2.36
Exercise 2.37 Exercise 2.38 Exercise 2.39 Exercise 2.40 Exercise 2.41 Exercise 2.42 Exercise 2.43 Exercise 2.44 Exercise 2.45
Exercise 2.46 Exercise 2.47 Exercise 2.48 Exercise 2.49 Exercise 2.50

Chapter 3: Complex numbers and hyperbolic functions
Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.6 Exercise 3.7 Exercise 3.8
Exercise 3.9 Exercise 3.10 Exercise 3.11 Exercise 3.12 Exercise 3.13 Exercise 3.14 Exercise 3.15 Exercise 3.16
Exercise 3.17 Exercise 3.18 Exercise 3.19 Exercise 3.20 Exercise 3.21 Exercise 3.22 Exercise 3.23 Exercise 3.24
Exercise 3.25 Exercise 3.26 Exercise 3.27 Exercise 3.28

Chapter 4: Series and limits
Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.6 Exercise 4.7 Exercise 4.8 Exercise 4.9
Exercise 4.10 Exercise 4.11 Exercise 4.12 Exercise 4.13 Exercise 4.14 Exercise 4.15 Exercise 4.16 Exercise 4.17 Exercise 4.18
Exercise 4.19 Exercise 4.20 Exercise 4.21 Exercise 4.22 Exercise 4.23 Exercise 4.24 Exercise 4.25 Exercise 4.26 Exercise 4.27
Exercise 4.28 Exercise 4.29 Exercise 4.30 Exercise 4.31 Exercise 4.32 Exercise 4.33 Exercise 4.34 Exercise 4.35 Exercise 4.36

Chapter 5: Partial differentiation
Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.6 Exercise 5.7 Exercise 5.8 Exercise 5.9
Exercise 5.10 Exercise 5.11 Exercise 5.12 Exercise 5.13 Exercise 5.14 Exercise 5.15 Exercise 5.16 Exercise 5.17 Exercise 5.18
Exercise 5.19 Exercise 5.20 Exercise 5.21 Exercise 5.22 Exercise 5.23 Exercise 5.24 Exercise 5.25 Exercise 5.26 Exercise 5.27
Exercise 5.28 Exercise 5.29 Exercise 5.30 Exercise 5.31 Exercise 5.32 Exercise 5.33 Exercise 5.34 Exercise 5.35

Chapter 6: Multiple integrals
Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.5 Exercise 6.6 Exercise 6.7 Exercise 6.8
Exercise 6.9 Exercise 6.10 Exercise 6.11 Exercise 6.12 Exercise 6.13 Exercise 6.14 Exercise 6.15 Exercise 6.16
Exercise 6.17 Exercise 6.18 Exercise 6.19 Exercise 6.20 Exercise 6.21 Exercise 6.22 Exercise 6.23

Chapter 7: Vector algebra
Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.6 Exercise 7.7 Exercise 7.8 Exercise 7.9
Exercise 7.10 Exercise 7.11 Exercise 7.12 Exercise 7.13 Exercise 7.14 Exercise 7.15 Exercise 7.16 Exercise 7.17 Exercise 7.18
Exercise 7.19 Exercise 7.20 Exercise 7.21 Exercise 7.22 Exercise 7.23 Exercise 7.24 Exercise 7.25 Exercise 7.26 Exercise 7.27

Chapter 8: Matrices and vector spaces
Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4 Exercise 8.5 Exercise 8.6 Exercise 8.7 Exercise 8.8 Exercise 8.9
Exercise 8.10 Exercise 8.11 Exercise 8.12 Exercise 8.13 Exercise 8.14 Exercise 8.15 Exercise 8.16 Exercise 8.17 Exercise 8.18
Exercise 8.19 Exercise 8.20 Exercise 8.21 Exercise 8.22 Exercise 8.23 Exercise 8.24 Exercise 8.25 Exercise 8.26 Exercise 8.27
Exercise 8.28 Exercise 8.29 Exercise 8.30 Exercise 8.31 Exercise 8.32 Exercise 8.33 Exercise 8.34 Exercise 8.35 Exercise 8.36
Exercise 8.37 Exercise 8.38 Exercise 8.39 Exercise 8.40 Exercise 8.41 Exercise 8.42 Exercise 8.43

Chapter 9: Normal modes
Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5
Exercise 9.6 Exercise 9.7 Exercise 9.8 Exercise 9.9 Exercise 9.10

Chapter 10: Vector calculus
Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.5 Exercise 10.6 Exercise 10.7 Exercise 10.8
Exercise 10.9 Exercise 10.10 Exercise 10.11 Exercise 10.12 Exercise 10.13 Exercise 10.14 Exercise 10.15 Exercise 10.16
Exercise 10.17 Exercise 10.18 Exercise 10.19 Exercise 10.20 Exercise 10.21 Exercise 10.22 Exercise 10.23 Exercise 10.24

Chapter 11: Line, surface and volume integrals
Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.5 Exercise 11.6 Exercise 11.7
Exercise 11.8 Exercise 11.9 Exercise 11.10 Exercise 11.11 Exercise 11.12 Exercise 11.13 Exercise 11.14
Exercise 11.15 Exercise 11.16 Exercise 11.17 Exercise 11.18 Exercise 11.19 Exercise 11.20 Exercise 11.21
Exercise 11.22 Exercise 11.23 Exercise 11.24 Exercise 11.25 Exercise 11.26 Exercise 11.27 Exercise 11.28

Chapter 12: Fourier series
Exercise 12.1 Exercise 12.2 Exercise 12.3 Exercise 12.4 Exercise 12.5 Exercise 12.6 Exercise 12.7
Exercise 12.8 Exercise 12.9 Exercise 12.10 Exercise 12.11 Exercise 12.12 Exercise 12.13 Exercise 12.14
Exercise 12.15 Exercise 12.16 Exercise 12.17 Exercise 12.18 Exercise 12.19 Exercise 12.20 Exercise 12.21
Exercise 12.22 Exercise 12.23 Exercise 12.24 Exercise 12.25 Exercise 12.26

Chapter 13: Integral transform
Exercise 13.1 Exercise 13.2 Exercise 13.3 Exercise 13.4 Exercise 13.5 Exercise 13.6 Exercise 13.7
Exercise 13.8 Exercise 13.9 Exercise 13.10 Exercise 13.11 Exercise 13.12 Exercise 13.13 Exercise 13.14
Exercise 13.15 Exercise 13.16 Exercise 13.17 Exercise 13.18 Exercise 13.19 Exercise 13.20 Exercise 13.21
Exercise 13.22 Exercise 13.23 Exercise 13.24 Exercise 13.25 Exercise 13.26 Exercise 13.27 Exercise 13.28

Chapter 14: First-order ordinary differential equations
Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.5 Exercise 14.6 Exercise 14.7 Exercise 14.8
Exercise 14.9 Exercise 14.10 Exercise 14.11 Exercise 14.12 Exercise 14.13 Exercise 14.14 Exercise 14.15 Exercise 14.16
Exercise 14.17 Exercise 14.18 Exercise 14.19 Exercise 14.20 Exercise 14.21 Exercise 14.22 Exercise 14.23 Exercise 14.24
Exercise 14.25 Exercise 14.26 Exercise 14.27 Exercise 14.28 Exercise 14.29 Exercise 14.30 Exercise 14.31

Chapter 15: Higher-order ordinary differential equations
Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.4 Exercise 15.5 Exercise 15.6 Exercise 15.7 Exercise 15.8
Exercise 15.9 Exercise 15.10 Exercise 15.11 Exercise 15.12 Exercise 15.13 Exercise 15.14 Exercise 15.15 Exercise 15.16
Exercise 15.17 Exercise 15.18 Exercise 15.19 Exercise 15.20 Exercise 15.21 Exercise 15.22 Exercise 15.23 Exercise 15.24
Exercise 15.25 Exercise 15.26 Exercise 15.27 Exercise 15.28 Exercise 15.29 Exercise 15.30 Exercise 15.31 Exercise 15.32
Exercise 15.33 Exercise 15.34 Exercise 15.35 Exercise 15.36 Exercise 15.37

Chapter 16: Series solutions of ordinary differential equations
Exercise 16.1 Exercise 16.2 Exercise 16.3 Exercise 16.4 Exercise 16.5 Exercise 16.6 Exercise 16.7 Exercise 16.8
Exercise 16.9 Exercise 16.10 Exercise 16.11 Exercise 16.12 Exercise 16.13 Exercise 16.14 Exercise 16.15 Exercise 16.16

Chapter 17: Eigenfunction methods for differential equations
Exercise 17.1 Exercise 17.2 Exercise 17.3 Exercise 17.4 Exercise 17.5 Exercise 17.6 Exercise 17.7 Exercise 17.8
Exercise 17.9 Exercise 17.10 Exercise 17.11 Exercise 17.12 Exercise 17.13 Exercise 17.14 Exercise 17.15

Chapter 18: Special functions
Exercise 18.1 Exercise 18.2 Exercise 18.3 Exercise 18.4 Exercise 18.5 Exercise 18.6 Exercise 18.7 Exercise 18.8
Exercise 18.9 Exercise 18.10 Exercise 18.11 Exercise 18.12 Exercise 18.13 Exercise 18.14 Exercise 18.15 Exercise 18.16
Exercise 18.17 Exercise 18.18 Exercise 18.19 Exercise 18.20 Exercise 18.21 Exercise 18.22 Exercise 18.23 Exercise 18.24

Chapter 19: Quantum operators
Exercise 19.1 Exercise 19.2 Exercise 19.3 Exercise 19.4 Exercise 19.5
Exercise 19.6 Exercise 19.7 Exercise 19.8 Exercise 19.9 Exercise 19.10

Chapter 20: Partial differential equations: general and particular solutions
Exercise 20.1 Exercise 20.2 Exercise 20.3 Exercise 20.4 Exercise 20.5 Exercise 20.6 Exercise 20.7
Exercise 20.9 Exercise 20.8 Exercise 20.10 Exercise 20.11 Exercise 20.12 Exercise 20.13 Exercise 20.14
Exercise 20.15 Exercise 20.16 Exercise 20.17 Exercise 20.18 Exercise 20.19 Exercise 20.20 Exercise 20.21
Exercise 20.22 Exercise 20.23 Exercise 20.24 Exercise 20.25

Chapter 21: Partial differential equations: separation of variables and other methods
Exercise 21.1 Exercise 21.2 Exercise 21.3 Exercise 21.4 Exercise 21.5 Exercise 21.6 Exercise 21.7
Exercise 21.9 Exercise 21.8 Exercise 21.10 Exercise 21.11 Exercise 21.12 Exercise 21.13 Exercise 21.14
Exercise 21.15 Exercise 21.16 Exercise 21.17 Exercise 21.18 Exercise 21.19 Exercise 21.20 Exercise 21.21
Exercise 21.22 Exercise 21.23 Exercise 21.24 Exercise 21.25 Exercise 21.26 Exercise 21.27 Exercise 21.28

Chapter 22: Calculus of variations
Exercise 22.1 Exercise 22.2 Exercise 22.3 Exercise 22.4 Exercise 22.5 Exercise 22.6 Exercise 22.7 Exercise 22.8
Exercise 22.9 Exercise 22.10 Exercise 22.11 Exercise 22.12 Exercise 22.13 Exercise 22.14 Exercise 22.15 Exercise 22.16
Exercise 22.17 Exercise 22.18 Exercise 22.19 Exercise 22.20 Exercise 22.21 Exercise 22.22 Exercise 22.23 Exercise 22.24
Exercise 22.25 Exercise 22.26 Exercise 22.27 Exercise 22.28 Exercise 22.29

Chapter 23: Integral equations
Exercise 23.1 Exercise 23.2 Exercise 23.3 Exercise 23.4 Exercise 23.5 Exercise 23.6 Exercise 23.7 Exercise 23.8
Exercise 23.9 Exercise 23.10 Exercise 23.11 Exercise 23.12 Exercise 23.13 Exercise 23.14 Exercise 23.15 Exercise 23.16

Chapter 24: Complex variables
Exercise 24.1 Exercise 24.2 Exercise 24.3 Exercise 24.4 Exercise 24.5 Exercise 24.6 Exercise 24.7 Exercise 24.8
Exercise 24.9 Exercise 24.10 Exercise 24.11 Exercise 24.12 Exercise 24.13 Exercise 24.14 Exercise 24.15 Exercise 24.16
Exercise 24.17 Exercise 24.18 Exercise 24.19 Exercise 24.20 Exercise 24.21 Exercise 24.22

Chapter 25: Applications of complex variables
Exercise 25.1 Exercise 25.2 Exercise 25.3 Exercise 25.4 Exercise 25.5 Exercise 25.6 Exercise 25.7 Exercise 25.8
Exercise 25.9 Exercise 25.10 Exercise 25.11 Exercise 25.12 Exercise 25.13 Exercise 25.14 Exercise 25.15 Exercise 25.16
Exercise 25.17 Exercise 25.18 Exercise 25.19 Exercise 25.20 Exercise 25.21 Exercise 25.22 Exercise 25.23

Chapter 26: Tensors
Exercise 26.1 Exercise 26.2 Exercise 26.3 Exercise 26.4 Exercise 26.5 Exercise 26.6 Exercise 26.7 Exercise 26.8
Exercise 26.9 Exercise 26.10 Exercise 26.11 Exercise 26.12 Exercise 26.13 Exercise 26.14 Exercise 26.15 Exercise 26.16
Exercise 26.17 Exercise 26.18 Exercise 26.19 Exercise 26.20 Exercise 26.21 Exercise 26.22 Exercise 26.23 Exercise 26.24
Exercise 26.25 Exercise 26.26 Exercise 26.27 Exercise 26.28 Exercise 26.29

Chapter 27: Numerical methods
Exercise 27.1 Exercise 27.2 Exercise 27.3 Exercise 27.4 Exercise 27.5 Exercise 27.6 Exercise 27.7
Exercise 27.9 Exercise 27.8 Exercise 27.10 Exercise 27.11 Exercise 27.12 Exercise 27.13 Exercise 27.14
Exercise 27.15 Exercise 27.16 Exercise 27.17 Exercise 27.18 Exercise 27.19 Exercise 27.20 Exercise 27.21
Exercise 27.22 Exercise 27.23 Exercise 27.24 Exercise 27.25 Exercise 27.26 Exercise 27.27

Chapter 28: Group theory
Exercise 28.1 Exercise 28.2 Exercise 28.3 Exercise 28.4 Exercise 28.5 Exercise 28.6 Exercise 28.7 Exercise 28.8
Exercise 28.9 Exercise 28.10 Exercise 28.11 Exercise 28.12 Exercise 28.13 Exercise 28.14 Exercise 28.15 Exercise 28.16
Exercise 28.17 Exercise 28.18 Exercise 28.19 Exercise 28.20 Exercise 28.21 Exercise 28.22 Exercise 28.23

Chapter 29: Representation theory
Exercise 29.1 Exercise 29.2 Exercise 29.3 Exercise 29.4 Exercise 29.5 Exercise 29.6 Exercise 29.7
Exercise 29.9 Exercise 29.8 Exercise 29.10 Exercise 29.11 Exercise 29.12 Exercise 29.13

Chapter 30: Probability
Exercise 30.1 Exercise 30.2 Exercise 30.3 Exercise 30.4 Exercise 30.5 Exercise 30.6 Exercise 30.7 Exercise 30.8
Exercise 30.9 Exercise 30.10 Exercise 30.11 Exercise 30.12 Exercise 30.13 Exercise 30.14 Exercise 30.15 Exercise 30.16
Exercise 30.17 Exercise 30.18 Exercise 30.19 Exercise 30.20 Exercise 30.21 Exercise 30.22 Exercise 30.23 Exercise 30.24
Exercise 30.25 Exercise 30.26 Exercise 30.27 Exercise 30.28 Exercise 30.29 Exercise 30.30 Exercise 30.31 Exercise 30.32
Exercise 30.33 Exercise 30.34 Exercise 30.35 Exercise 30.36 Exercise 30.37 Exercise 30.38 Exercise 30.39 Exercise 30.40

Chapter 31: Statistics
Exercise 31.1 Exercise 31.2 Exercise 31.3 Exercise 31.4 Exercise 31.5 Exercise 31.6 Exercise 31.7
Exercise 31.8 Exercise 31.9 Exercise 31.10 Exercise 31.11 Exercise 31.12 Exercise 31.13 Exercise 31.14
Exercise 31.15 Exercise 31.16 Exercise 31.17 Exercise 31.18 Exercise 31.19 Exercise 31.20