Cover image for Applied Mathematics in hydraulic engineering : an introduction to nonlinear differential equations
Title:
Applied Mathematics in hydraulic engineering : an introduction to nonlinear differential equations
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Physical Description:
xi, 424 pages : illustrations ; 23 cm.
ISBN:
9789814299558

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30000010280406 TC160 M59 2011 Open Access Book Book
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30000010297800 TC160 M59 2011 Open Access Book Book
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Summary

Summary

Learn crucial AutoCAD tools and techniques with this Autodesk Official Press Book Quickly become productive using AutoCAD 2014 and AutoCAD LT 2014 with this full color Autodesk Official Press guide. This unique learning resource features concise, straightforward explanations and real-world, hands-on exercises and tutorials. Following a quick discussion of concepts and goals, each chapter moves on to an approachable hands-on exercise designed to reinforce real-world tactics and techniques. Compelling, full-color screenshots illustrate tutorial steps, and chapters conclude with related and more open-ended projects to further reinforce the chapter′s lessons. Starting and ending files for the exercises are also available for download, so you can compare your results with those of professionals. You′ll follow a workflow-based approach that mirrors the development of projects in the real world, learning 2D drawing skills, editing entities, working with splines and polylines, using layers and objects, creating and editing text, dimensioning, modeling in 3D, and much more. Hands-on exercises and their downloadable tutorial files are based on the real-world task of drawing a house Covers crucial features and techniques, including 2D drawing working with layers, organizing objects with groups and blocks, using hatch patterns and gradients, using constraints and layouts, importing data, 3D modeling, and Includes content to help prepare you for Autodesk′s AutoCAD certification program AutoCAD 2014 and AutoCAD LT 2014 Essentials is the Autodesk Official Press guide that helps you quickly and confidently learn the newest version of AutoCAD and AutoCAD LT.


Table of Contents

Prefacep. v
1 Introduction
1.1 Quadratic Curvesp. 1
1.2 Trigonometric Functionsp. 3
1.3 Infinite Seriesp. 6
2 Differentiations
2.1 Derivatives and Differentiationsp. 13
2.2 Mean Value Theorem and Taylor Seriesp. 14
2.3 Partial Derivatives and Applicationsp. 16
2.4 Finite Difference Method and Newton Methodp. 18
2.5 Various Slopes of Unconfined Groundwater Flowp. 20
3 Integrations
3.1 Indefinite Integralsp. 25
3.2 Definite Integralsp. 26
3.3 Double and Triple Integralsp. 28
3.4 Taylor's Diffusion Theoryp. 30
4 Vector and Tensor
4.1 Vector Algebrap. 35
4.2 Tensorp. 39
4.3 Curvilinear Coordinate Systemp. 41
4.4 Vector Analysisp. 46
4.5 Application to Navier-Stokes Equationsp. 48
5 Ordinary Differential Equations
5.1 Method of Separation of Variablesp. 51
5.2 Linear Differential Equations of the First-Orderp. 52
5.3 Linear Differential Equations of the Second-Orderp. 57
5.4 Operational Methodp. 60
5.5 The Method of Undetermined Coefficientsp. 65
5.6 Linear Ordinary Differential Equations of the Higher Ordersp. 67
5.7 Variation of Parametersp. 70
5.8 Ordinary Differential Equations and Integral Equationsp. 73
6 Complex Functions and Complex Integrals
6.1 Complex Functionsp. 75
6.2 Complex Integralp. 78
6.3 Application of Complex Integralp. 84
7 Conformal Mapping
7.1 Conformal Mapping by Elementary Functionsp. 91
7.2 Schwartz-Christoffel Transformationp. 98
7.3 Applications to Hydraulic Engineeringp. 102
8 Partial Differential Equation of the First-Order
8.1 Generalp. 121
8.2 Charpit's Methodp. 126
8.3 Application to Hydrologyp. 128
9 Special Functions
9.1 Gamma, Beta, and Error Functionsp. 133
9.2 Bessel Functionp. 138
9.3 Legendre Functionp. 144
9.4 Elliptic Functionp. 148
9.5 Orthogonality Principlep. 152
10 Fourier Series and Integral
10.1 Fourier Seriesp. 155
10.2 Fourier Integralp. 161
10.3 Fourier Transform and Its Applicationsp. 164
11 Laplace Transform
11.1 Definition of Laplace Transformp. 169
11.2 Inverse Laplace Transformp. 171
11.3 Applications to Ordinary Differential Equationsp. 178
11.4 Applications to Partial Differential Equationsp. 180
11.5 Green's Functionsp. 184
12 Wave Equations
12.1 Classification of Partial Differential Equations of the Second-Orderp. 193
12.2 Fundamental Partial Differential Equationsp. 196
12.3 One-Dimensional Wave Equationp. 200
12.4 Water Surface Oscillations of Rectangular Lakep. 204
12.5 Water Surface Oscillations of Circular Lakep. 209
12.6 Saint Venant Equationsp. 212
12.7 Long Wave Transform on Slopep. 217
12.8 Side Outflow from Steep Open Channel Flowp. 221
13 Potential Equations
13.1 Fundamental Equationsp. 229
13.2 Surface Wave of Infinitesimally Small Amplitudep. 232
13.3 Groundwater Flowp. 236
13.4 Motion of a Sphere in Fluidp. 238
13.5 Two-Dimensional Stratified Flow into a Sinkp. 241
13.6 Analysis of Sand Wavesp. 245
14 Diffusion Equations
14.1 Governing Equationsp. 251
14.2 Rayleigh Problemp. 254
14.3 Flow near Oscillatory Platep. 257
14.4 Distribution of Suspended Load in Flowp. 259
14.5 Well Hydraulicsp. 263
14.6 Water Content Distribution in Groundp. 266
14.7 Modeling of Coastal Changesp. 268
15 Solution of Nonlinear Equations
15.1 Cubic Equationp. 273
15.2 Quintic Equationp. 276
15.3 Newton Methodp. 278
15.4 Solution of Differential Equation and Secant Methodp. 280
15.5 Hardy-Cross Methodp. 283
15.6 Method of Characteristicsp. 286
15.7 Lax-Wendroff Schemep. 289
16 Linearization Methods
16.1 Fundamentals in Linearizationp. 291
16.2 Stokes Wavep. 292
16.3 KdV Equationp. 296
16.4 Stokes Equationp. 303
16.5 Burgers Equationp. 308
16.6 Series Solutionp. 311
16.7 Approximate Solution of Nonlinear Ordinary Differential Equationp. 317
17 Method of Boundary-Layer Theory
17.1 Boundary-Layer Equationp. 321
17.2 Two-Dimensional Jetp. 326
17.3 Two-Dimensional Wakep. 332
17.4 Boundary-Layer Induced by Wave Motionp. 338
17.5 Plane Boundary-Layer and Ekman Layerp. 340
18 Variational Method
18.1 Ritz Methodp. 347
18.2 Galerkin Methodp. 351
18.3 Transform of Partial Differential Equation to Ordinary Differential Equationp. 354
18.4 Eigen Value Problemp. 357
18.5 Application to Groundwater Flowp. 360
18.6 Least Squares Method and Collocation Methodp. 362
18.7 The Method of Momentsp. 365
19 Perturbation Methods
19.1 Parameter Perturbationp. 367
19.2 Matched Asymptotic Expansionp. 374
19.3 Free Surface Flow over Wavy Bedp. 379
19.4 Application to Kinematic Wave Methodp. 384
19.5 Averaging Methodp. 389
19.6 Stability Analysis in Fluid Flowp. 392
20 Nonlinear Systems Analysis
20.1 Vector Calculationp. 395
20.2 Phase Plane Analysisp. 398
20.3 Property of Singular Pointp. 402
Referencesp. 417
Indexp. 421