Solutions Manual for Advanced Modern Engineering Mathematics, 4th Edition (James, 2011) | All Chapters 1–11 Covered

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TABLE OF CONTENTS
Solutions Manual: Advanced Modern Engineering Mathematics, 4th Edition
PR By Glyn James


Chapter 1 Matrix Analysis

Chapter 2
OVNumerical Solution of Ordinary Differential Equations

Chapter 3 Vector Calculus

Chapter 4 Functions of a Complex Variable

Chapter 5
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Laplace Transforms

Chapter 6 The z Transform _S
Chapter 7 Fourier Series

Chapter 8 The Fourier Transform

Chapter 9 Partial Differential Equations
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Chapter 10 Optimization

Chapter 11 Applied Probability and Statistics VI
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TABLE OF CONTENTS
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Page
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Chapter 1. Matrix Analysis 1
Chapter 2. Numerical Solution of Ordinary Differential Equations 86
Chapter 3. Vector Calculus 126
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Chapter 4. Functions of a Complex Variable 194
Chapter 5. Laplace Transforms 270
Chapter 6. The z Transform 369
Chapter 7. Fourier Series
_S 413
Chapter 8. The Fourier Transform 489
Chapter 9. Partial Differential Equations 512
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Chapter 10. Optimization 573
Chapter 11. Applied Probability and Statistics VI 639



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1
Matrix Analysis
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Exercises 1.3.3

1(a) Yes, as the three vectors are linearly independent and span three-
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dimensional space.


1(b) No, since they are linearly dependent
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⎡ ⎤ ⎡ ⎤ ⎡ ⎤
3 1 1
⎣ 2 ⎦ − 2⎣ 0⎦ = ⎣ 2 ⎦
5 1 3
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1(c) No, do not span three-dimensional space. Note, they are also linearly
dependent.
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2 Transformation matrix is
⎡
1 1 0 ⎤ ⎡ 1 0 0 ⎤ ⎡ √1
A? ⎤
√1 0
= 1 1 −1 0 0 1 0 = √2 − √2 2 0
A √2 ⎣ √
⎦⎣ ⎦ ⎣ 12 1 ⎦
0 0 2 0 0 1 0 0 1
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Rotates the (e1, e2) plane through π/4 radians about the e3 axis.


3 By checking axioms (a)–(h) on p. 10 it is readily shown that all cubics
ax3 + bx2 + cx + d form a vector space. Note that the space is four dimensional.
3(a) All cubics can be written in the form

ax3 + bx2 + cx + d

and {1, x, x2, x3} are a linearly independent set spanning four-dimensional space.
Thus, it is an appropriate basis.