Solutions+ Advanced Modern Engineering Mathematics by James

hi_china59

Advanced Modern Engineering Mathematics
+
Solutions Manual by Glyn James
1055 pages
Prentice Hall; 4 edition   2011  
ISBN: 0273719238

Building on the foundations laid in the companion text Modern Engineering Mathematics, this book gives an extensive treatment of some of the advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design. The philosophy of learning by doing helps students develop the ability to use mathematics with understanding to solve engineering problems. A wealth of engineering examples and the integration of MATLAB and MAPLE further support students.




Chapter 1 Matrix analysis
1.1 Introduction 2
1.2 Review of matrix algebra 2
1.2.1 Definitions 3
1.2.2 Basic operations on matrices 3
1.2.3 Determinants 5
1.2.4 Adjoint and inverse matrices 5
1.2.5 Linear equations 7
1.2.6 Rank of a matrix 9
1.3 Vector spaces 10
1.3.1 Linear independence 11
1.3.2 Transformations between bases 12
1.3.3 Exercises (1–4) 14
1.4 The eigenvalue problem 14
1.4.1 The characteristic equation 15
1.4.2 Eigenvalues and eigenvectors 17
1.4.3 Exercises (5–6) 23
1.4.4 Repeated eigenvalues 23
1.4.5 Exercises (7–9) 27
1.4.6 Some useful properties of eigenvalues 27
1.4.7 Symmetric matrices 29
1.4.8 Exercises (10–13) 30
1.5 Numerical methods 30
1.5.1 The power method 30
1.5.2 Gerschgorin circles 36
1.5.3 Exercises (14 –19) 38
1.6 Reduction to canonical form 39
1.6.1 Reduction to diagonal form 39
1.6.2 The Jordan canonical form 42
1.6.3 Exercises (20–27) 46
1.6.4 Quadratic forms 47
1.6.5 Exercises (28–34) 53
1.7 Functions of a matrix 54
1.7.1 Exercises (35– 42) 65
1.8 Singular value decomposition 66
1.8.1 Singular values 68
1.8.2 Singular value decomposition (SVD) 72
1.8.3 Pseudo inverse 75
1.8.4 Exercises (43–50) 81
1.9 State-space representation 82
1.9.1 Single-input–single-output (SISO) systems 82
1.9.2 Multi-input–multi-output (MIMO) systems 87
1.9.3 Exercises (51–55) 88
1.10 Solution of the state equation 89
1.10.1 Direct form of the solution 89
1.10.2 The transition matrix 91
1.10.3 Evaluating the transition matrix 92
1.10.4 Exercises (56–61) 94
1.10.5 Spectral representation of response 95
1.10.6 Canonical representation 98
1.10.7 Exercises (62–68) 103
1.11 Engineering application: Lyapunov stability analysis 104
1.11.1 Exercises (69–73) 106
1.12 Engineering application: capacitor microphone 107
1.13 Review exercises (1–20)

Chapter 2 Numerical Solution of Ordinary Differential Equations
2.1 Introduction 116
2.2 Engineering application: motion in a viscous fluid 116
2.3 Numerical solution of first-order ordinary differential
equations 117
2.3.1 A simple solution method: Euler’s method 118
2.3.2 Analysing Euler’s method 122
2.3.3 Using numerical methods to solve engineering problems 125
2.3.4 Exercises (1–7) 127
2.3.5 More accurate solution methods: multistep methods 128
2.3.6 Local and global truncation errors 134
2.3.7 More accurate solution methods: predictor–corrector
methods 136
2.3.8 More accurate solution methods: Runge–Kutta methods 141
2.3.9 Exercises (8 –17) 145
2.3.10 Stiff equations 147
2.3.11 Computer software libraries and the ‘state of the art’ 149
2.4 Numerical solution of second- and higher-order
differential equations 151
2.4.1 Numerical solution of coupled first-order equations 151
2.4.2 State-space representation of higher-order systems 156
2.4.3 Exercises (18–23) 160
2.4.4 Boundary-value problems 161
2.4.5 The method of shooting 162
2.4.6 Function approximation methods 164
2.5 Engineering application: oscillations of a pendulum 170
2.6 Engineering application: heating of an electrical fuse 174
2.7 Review exercises (1–12) 179

chapter 3 Vector Calculus
3.1 Introduction 182
3.1.1 Basic concepts 183
3.1.2 Exercises (1–10) 191
3.1.3 Transformations 192
3.1.4 Exercises (11–17) 195
3.1.5 The total differential 196
3.1.6 Exercises (18–20)
3.2 Derivatives of a scalar point function 199
3.2.1 The gradient of a scalar point function 199
3.2.2 Exercises (21–30) 203
3.3 Derivatives of a vector point function 203
3.3.1 Divergence of a vector field 204
3.3.2 Exercises (31–37) 206
3.3.3 Curl of a vector field 206
3.3.4 Exercises (38–45) 210
3.3.5 Further properties of the vector operator ∇ 210
3.3.6 Exercises (46–55) 214
3.4 Topics in integration 214
3.4.1 Line integrals 215
3.4.2 Exercises (56–64) 218
3.4.3 Double integrals 219
3.4.4 Exercises (65–76) 224
3.4.5 Green’s theorem in a plane 225
3.4.6 Exercises (77–82) 229
3.4.7 Surface integrals 230
3.4.8 Exercises (83–91) 237
3.4.9 Volume integrals 237
3.4.10 Exercises (92–102) 240
3.4.11 Gauss’s divergence theorem 241
3.4.12 Stokes’ theorem 244
3.4.13 Exercises (103–112) 247
3.5 Engineering application: streamlines in fluid dynamics 248
3.6 Engineering application: heat transfer 250
3.7 Review exercises (1–21) 254

Chapter 4 Functions of a complex variable
4.1 Introduction 258
4.2 Complex functions and mappings 259
4.2.1 Linear mappings 261
4.2.2 Exercises (1–8) 268
4.2.3 Inversion 268
4.2.4 Bilinear mappings 273
4.2.5 Exercises (9–19) 279
4.2.6 The mapping w = z2 280
4.2.7 Exercises (20–23)
4.3 Complex differentiation 282
4.3.1 Cauchy–Riemann equations 283
4.3.2 Conjugate and harmonic functions 288
4.3.3 Exercises (24–32) 290
4.3.4 Mappings revisited 290
4.3.5 Exercises (33–37) 294
4.4 Complex series 295
4.4.1 Power series 295
4.4.2 Exercises (38–39) 299
4.4.3 Taylor series 299
4.4.4 Exercises (40– 43) 302
4.4.5 Laurent series 303
4.4.6 Exercises (44– 46) 308
4.5 Singularities, zeros and residues 308
4.5.1 Singularities and zeros 308
4.5.2 Exercises (47–49) 311
4.5.3 Residues 311
4.5.4 Exercises (50–52) 316
4.6 Contour integration 317
4.6.1 Contour integrals 317
4.6.2 Cauchy’s theorem 320
4.6.3 Exercises (53–59) 327
4.6.4 The residue theorem 328
4.6.5 Evaluation of definite real integrals 331
4.6.6 Exercises (60–65) 334
4.7 Engineering application: analysing AC circuits 335
4.8 Engineering application: use of harmonic functions 336
4.8.1 A heat transfer problem 336
4.8.2 Current in a field-effect transistor 338
4.8.3 Exercises (66–72) 341
4.9 Review exercises (1–24) 342

Chapter5  Laplace transform
5.1 Introduction 346
5.2 The Laplace transform 348
5.2.1 Definition and notation 348
5.2.2 Transforms of simple functions 350
5.2.3 Existence of the Laplace transform 353
5.2.4 Properties of the Laplace transform 355
5.2.5 Table of Laplace transforms 363
5.2.6 Exercises (1–3) 364
5.2.7 The inverse transform 364
5.2.8 Evaluation of inverse transforms 365
5.2.9 Inversion using the first shift theorem 367
5.2.10 Exercise (4) 369
5.3 Solution of differential equations 370
5.3.1 Transforms of derivatives 370
5.3.2 Transforms of integrals 371
5.3.3 Ordinary differential equations 372
5.3.4 Simultaneous differential equations 378
5.3.5 Exercises (5–6) 380
5.4 Engineering applications: electrical circuits and
mechanical vibrations 381
5.4.1 Electrical circuits 382
5.4.2 Mechanical vibrations 386
5.4.3 Exercises (7–12) 390
5.5 Step and impulse functions 392
5.5.1 The Heaviside step function 392
5.5.2 Laplace transform of unit step function 395
5.5.3 The second shift theorem 397
5.5.4 Inversion using the second shift theorem 400
5.5.5 Differential equations 403
5.5.6 Periodic functions 407
5.5.7 Exercises (13–24) 411
5.5.8 The impulse function 413
5.5.9 The sifting property 414
5.5.10 Laplace transforms of impulse functions 415
5.5.11 Relationship between Heaviside step and impulse functions 418
5.5.12 Exercises (25–30) 423
5.5.13 Bending of beams 424
5.5.14 Exercises (31–33) 428
5.6 Transfer functions 428
5.6.1 Definitions 428
5.6.2 Stability 431
5.6.3 Impulse response 436
5.6.4 Initial- and final-value theorems 437
5.6.5 Exercises (34 – 47) 442
5.6.6 Convolution 443
5.6.7 System response to an arbitrary input 446
5.6.8 Exercises (48–52) 450
5.7 Solution of state-space equations 450
5.7.1 SISO systems 450
5.7.2 Exercises (53–61) 454
5.7.3 MIMO systems 455
5.7.4 Exercises (62–64) 462
5.8 Engineering application: frequency response 462
5.9 Engineering application: pole placement 470
5.9.1 Poles and eigenvalues 470
5.9.2 The pole placement or eigenvalue location technique 470
5.9.3 Exercises (65–70) 472
5.10 Review exercises (1–34) 473

Chapter 6 The Z transform
6.1 Introduction 482
6.2 The z transform 483
6.2.1 Definition and notation 483
6.2.2 Sampling: a first introduction 487
6.2.3 Exercises (1–2) 488
6.3 Properties of the z transform 488
6.3.1 The linearity property 489
6.3.2 The first shift property (delaying) 490
6.3.3 The second shift property (advancing) 491
6.3.4 Some further properties 492
6.3.5 Table of z transforms 493
6.3.6 Exercises (3–10) 494
6.4 The inverse z transform 494
6.4.1 Inverse techniques 495
6.4.2 Exercises (11–13) 501
6.5 Discrete-time systems and difference equations 502
6.5.1 Difference equations 502
6.5.2 The solution of difference equations 504
6.5.3 Exercises (14–20) 508
6.6 Discrete linear systems: characterization 509
6.6.1 z transfer functions 509
6.6.2 The impulse response 515
6.6.3 Stability 518
6.6.4 Convolution 524
6.6.5 Exercises (21–29) 528
6.7 The relationship between Laplace and z transforms 529
6.8 Solution of discrete-time state-space equations 530
6.8.1 State-space model 530
6.8.2 Solution of the discrete-time state equation 533
6.8.3 Exercises (30–33) 537
6.9 Discretization of continuous-time state-space models 538
6.9.1 Euler’s method 538
6.9.2 Step-invariant method 540
6.9.3 Exercises (34–37) 543
6.10 Engineering application: design of discrete-time systems 544
6.10.1 Analogue filters 545
6.10.2 Designing a digital replacement filter 546
6.10.3 Possible developments 547
6.11 Engineering application: the delta operator and
the  transform 547
6.11.1 Introduction 547
6.11.2 The q or shift operator and the δ operator 548
6.11.3 Constructing a discrete-time system model 549
6.11.4 Implementing the design 551
6.11.5 The  transform 553
6.11.6 Exercises (38–41) 554
6.12 Review exercises (1–18) 554

Chapter 7. Fourier Series
7.1 Introduction 560
7.2 Fourier series expansion 561
7.2.1 Periodic functions 561
7.2.2 Fourier’s theorem 562
7.2.3 Functions of period 2π 566
7.2.4 Even and odd functions 573
7.2.5 Linearity property 577
7.2.6 Exercises (1–7) 579
7.2.7 Functions of period T 580
7.2.8 Exercises (8–13) 583
7.2.9 Convergence of the Fourier series 584
7.3 Functions defined over a finite interval 587
7.3.1 Full-range series 587
7.3.2 Half-range cosine and sine series 589
7.3.3 Exercises (14 –23) 593
7.4 Differentiation and integration of Fourier series 594
7.4.1 Integration of a Fourier series 595
7.4.2 Differentiation of a Fourier series 597
7.4.3 Coefficients in terms of jumps at discontinuities 599
7.4.4 Exercises (24 –29) 602
7.5 Engineering application: frequency response and
oscillating systems 603
7.5.1 Response to periodic input 603
7.5.2 Exercises (30–33) 607
7.6 Complex form of Fourier series 608
7.6.1 Complex representation 608
7.6.2 The multiplication theorem and Parseval’s theorem 612
7.6.3 Discrete frequency spectra 615
7.6.4 Power spectrum 621
7.6.5 Exercises (34 –39) 623
7.7 Orthogonal functions 624
7.7.1 Definitions 624
7.7.2 Generalized Fourier series 626
7.7.3 Convergence of generalized Fourier series 627
7.7.4 Exercises (40–46) 629
7.8 Engineering application: describing functions 632
7.9 Review exercises (1–20) 633

Chapter 8 Fourier Transform
8.1 Introduction 638
8.2 The Fourier transform 638
8.2.1 The Fourier integral 638
8.2.2 The Fourier transform pair 644
8.2.3 The continuous Fourier spectra 648
8.2.4 Exercises (1–10) 651
8.3 Properties of the Fourier transform 652
8.3.1 The linearity property 652
8.3.2 Time-differentiation property 652
8.3.3 Time-shift property 653
8.3.4 Frequency-shift property 654
8.3.5 The symmetry property 655
8.3.6 Exercises (11–16) 657
8.4 The frequency response 658
8.4.1 Relationship between Fourier and Laplace transforms 658
8.4.2 The frequency response 660
8.4.3 Exercises (17–21) 663
8.5 Transforms of the step and impulse functions 663
8.5.1 Energy and power 663
8.5.2 Convolution 673
8.5.3 Exercises (22–27) 675
8.6 The Fourier transform in discrete time 676
8.6.1 Introduction 676
8.6.2 A Fourier transform for sequences 676
8.6.3 The discrete Fourier transform 680
8.6.4 Estimation of the continuous Fourier transform 684
8.6.5 The fast Fourier transform 693
8.6.6 Exercises (28–31) 700
8.7 Engineering application: the design of analogue filters 700
8.8 Engineering application: modulation, demodulation and
frequency-domain filtering 703
8.8.1 Introduction 703
8.8.2 Modulation and transmission 705
8.8.3 Identification and isolation of the informationcarrying
signal 706
8.8.4 Demodulation stage 707
8.8.5 Final signal recovery 708
8.8.6 Further developments 709
8.9 Engineering application: direct design of digital filters
and windows 709
8.9.1 Digital filters 709
8.9.2 Windows 715
8.9.3 Exercises (32–33) 719
8.10 Review exercises (1–25) 719

Chapter 9 Partial Differential Equations
9.1 Introduction 724
9.2 General discussion 725
9.2.1 Wave equation 725
9.2.2 Heat-conduction or diffusion equation 728
9.2.3 Laplace equation 731
9.2.4 Other and related equations 733
9.2.5 Arbitrary functions and first-order equations 735
9.2.6 Exercises (1–14) 740
9.3 Solution of the wave equation 742
9.3.1 D’Alembert solution and characteristics 742
9.3.2 Separated solutions 751
9.3.3 Laplace transform solution 756
9.3.4 Exercises (15–27) 759
9.3.5 Numerical solution 761
9.3.6 Exercises (28–31) 767
9.4 Solution of the heat-conduction/diffusion equation 768
9.4.1 Separation method 768
9.4.2 Laplace transform method 772
9.4.3 Exercises (32–40) 777
9.4.4 Numerical solution 779
9.4.5 Exercises (41–43) 785
9.5 Solution of the Laplace equation 785
9.5.1 Separated solutions 785
9.5.2 Exercises (44–54) 793
9.5.3 Numerical solution 794
9.5.4 Exercises (55–59) 801
9.6 Finite elements 802
9.6.1 Exercises (60–62) 814
9.7 Integral solutions 815
9.7.1 Separated solutions 815
9.7.2 Use of singular solutions 817
9.7.3 Sources and sinks for the heat conduction equation 820
9.7.4 Exercises (63–67) 823
9.8 General considerations 824
9.8.1 Formal classification 824
9.8.2 Boundary conditions 826
9.8.3 Exercises (68–74) 831
9.9 Engineering application: wave propagation under a
moving load 831
9.10 Engineering application: blood-flow model 834
9.11 Review exercises (1–21) 838

Chapter 10 Optimization
10.1 Introduction 844
10.2 Linear programming 847
10.2.1 Introduction 847
10.2.2 Simplex algorithm: an example 849
10.2.3 Simplex algorithm: general theory 853
10.2.4 Exercises (1–11) 860
10.2.5 Two-phase method 861
10.2.6 Exercises (12–20) 869
10.3 Lagrange multipliers 870
10.3.1 Equality constraints 870
10.3.2 Inequality constraints 874
10.3.3 Exercises (21–28) 875
10.4 Hill climbing 875
10.4.1 Single-variable search 875
10.4.2 Exercises (29–34) 881
10.4.3 Simple multivariable searches 882
10.4.4 Exercises (35–39) 887
10.4.5 Advanced multivariable searches 888
10.4.6 Least squares 892
10.4.7 Exercises (40–43) 895
10.5 Engineering application: chemical processing plant 896
10.6 Engineering application: heating fin 898
10.7 Review exercises (1–26) 901

Chapter 11 Applied Probability and Statistics
11.1 Introduction 906
11.2 Review of basic probability theory 906
11.2.1 The rules of probability 907
11.2.2 Random variables 907
11.2.3 The Bernoulli, binomial and Poisson distributions 909
11.2.4 The normal distribution 910
11.2.5 Sample measures 911
11.3 Estimating parameters 912
11.3.1 Interval estimates and hypothesis tests 912
11.3.2 Distribution of the sample average 913
11.3.3 Confidence interval for the mean 914
11.3.4 Testing simple hypotheses 917
11.3.5 Other confidence intervals and tests concerning means 918
11.3.6 Interval and test for proportion 922
11.3.7 Exercises (1–13) 924
11.4 Joint distributions and correlation 925
11.4.1 Joint and marginal distributions 926
11.4.2 Independence 928
11.4.3 Covariance and correlation 929
11.4.4 Sample correlation 933
11.4.5 Interval and test for correlation 935
11.4.6 Rank correlation 936
11.4.7 Exercises (14–24) 937
11.5 Regression 938
11.5.1 The method of least squares 939
11.5.2 Normal residuals 941
11.5.3 Regression and correlation 943
11.5.4 Nonlinear regression 943
11.5.5 Exercises (25–33) 945
11.6 Goodness-of-fit tests 946
11.6.1 Chi-square distribution and test 946
11.6.2 Contingency tables 949
11.6.3 Exercises (34–42) 951
11.7 Moment generating functions 953
11.7.1 Definition and simple applications 953
11.7.2 The Poisson approximation to the binomial 955
11.7.3 Proof of the central limit theorem 956
11.7.4 Exercises (43–47) 957
11.8 Engineering application: analysis of engine performance data 958
11.8.1 Introduction 958
11.8.2 Difference in mean running times and temperatures 959
11.8.3 Dependence of running time on temperature 960
11.8.4 Test for normality 962
11.8.5 Conclusions 963
11.9 Engineering application: statistical quality control 964
11.9.1 Introduction 964
11.9.2 Shewhart attribute control charts 964
11.9.3 Shewhart variable control charts 967
11.9.4 Cusum control charts 968
11.9.5 Moving-average control charts 971
11.9.6 Range charts 973
11.9.7 Exercises (48–59) 973
11.10 Poisson processes and the theory of queues 974
11.10.1 Typical queueing problems 974
11.10.2 Poisson processes 975
11.10.3 Single service channel queue 978
11.10.4 Queues with multiple service channels 982
11.10.5 Queueing system simulation 983
11.10.6 Exercises (60–67) 985
11.11 Bayes’ theorem and its applications 986
11.11.1 Derivation and simple examples 986
11.11.2 Applications in probabilistic inference 988
11.11.3 Exercises (68–78) 991
11.12 Review exercises (1–10) 992

wangjin0215

xiexie。。。

yanzushu

The History of the Abel Prize

kylkzy

dddddddddddddddddd

yaha79479

Thanks.

sjx

waha79479

感谢感谢

mypcbok01

非常感谢

chujn

下来看看，谢谢。

allex_liu

good sharing