Advanced Engineering Mathematics (7th Edition) by Dennis G. Zill – Solution Manual | Complete Worked Solutions for Engineering Mathematics

All Chapters Covered
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SOLUTION MANUAL
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, TableofContents g g




Part I OrdinaryDifferentialEquations
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1 Introduction to Differential Equations g g g 1

2 First-Order Differential Equations
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3 Higher-Order Differential Equations g g 99

4 The Laplace Transform
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5 Series Solutions of Linear Differential Equations
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6 Numerical Solutions of Ordinary Differential Equations
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Part II Vectors,Matrices,andVector Calculus
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7 Vectors 339

8 Matrices 373

9 Vector Calculus
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Part III Systems of DifferentialEquations
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10 Systems of Linear Differential Equations
g g g g 551

11 Systems of Nonlinear Differential Equations
g g g g 604

Part IV FourierSeries andPartialDifferentialEquations
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12 Orthogonal Functions and Fourier Series
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13 Boundary-Value Problems in Rectangular Coordinates g g g g 680

14 Boundary-Value Problems in Other Coordinate Systems g g g g g 755

15 Integral Transform Method
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16 Numerical Solutions of Partial Differential Equations
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, Part V Complex Analysis
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17 Functions of a Complex Variableg g g g 854

18 Integration in the Complex Plane g g g g 877

19 Series and Residues
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20 Conformal Mappings g 919

Appendices
Appendix II Gamma function
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Projects
3.7 Road Mirages g 944

3.10 The Ballistic Pendulum
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8.1 Two-Ports in Electrical Circuits g g g 947

8.2 Traffic Flow g 948

8.15 Temperature Dependence of Resistivity g g g 949

9.16 Minimal Surfaces g 950

14.3 The Hydrogen Atom
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15.4 The Uncertainity Inequality in Signal Processing
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15.4 Fraunhofer Diffraction by a Circular Apertureg g g g g 958

16.2 Instabilities of Numerical Methods g g g 960

, Part I g OrdinaryDifferentialEquations g g




Introduction to
1 DifferentialEquations g
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EXERCISES 1.1 g




g Definitions and Terminology g g




1. Second order; linear g g




2. Third order; nonlinear because of (dy/dx)4
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3. Fourth order; linear g g




4. Second order; nonlinear because of cos(r + u)
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5. Second order; nonlinear because of (dy/dx)2 or
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6. Second g order; g nonlinear g because g of gR2
7. Third order; linear
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8. Second order; nonlinear because of x˙2
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9. Writing the differential equation in the form x(dy/dx) + y2 = 1, we see that it is nonlinear in y because of y2.
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g However, gwriting g it gin gthe g form g (y g− g1)(dx/dy) g+ gx g= g 0, g we g see gthat git g is glinear gin g x.
2

10. Writing the differential equation in the form u(dv/du) + (1 + u)v = ueu we see that it is linear in v. However,
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writing it in the form (v + uv − ueu)(du/dv) + u = 0, we see that it is nonlinear in u.
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11. From gyg=ge−x/2 gwe gobtain gy′ g= g−g1ge−x/2. g Then g2y′ g+ gy g= g−e−x/2g+ ge−x/2g= g0.
2
12. From y = 6 − 6 e−20t we obtain dy/dt = 24e−20t, so that
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5 5
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dy + 20y = −20t 6 6 −20t
+ − e = 24. g g

24e g g


20 5 5 g
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dt
13. From y = e3x cos 2x we obtain y′ = 3e3x cos 2x − 2e3x sin 2x and y′′ = 5e3x cos 2x − 12e3x sin 2x, so that
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y′′ − 6y′ + 13y = 0.
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14. From y = − cos x ln(sec x + tan x) we obtain y′ = −1 + sin x ln(sec x + tan x) and
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y′′ = tan x + cos x ln(sec x + tan x). Then y′′ + y = tan x.
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15. The domain of the function, found by solving x + 2 ≥ 0, is [−2, ∞). From y′ = 1 + 2(x + 2)−1/2 we have
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—1/2
(y − x)y′ = (y − x)[1 + (2(x + 2)
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—1/2
= y − x + 2(y − x)(x + 2)
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—1/2
= y − x + 2[x + 4(x + 2)1/2 −
g g g g g g g g g g x](x + 2) g g




= y − x + 8(x + 2)1/2(x + 2)−1/2 = y − x + 8.
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