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Applied Mathematics In Hydraulic Engineering : An Introduction To Nonlinear Differential Equations - Kazumasa Mizumura

Applied Mathematics In Hydraulic Engineering

An Introduction To Nonlinear Differential Equations

Hardcover

Published: 31st May 2011
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Applied Mathematics in Hydraulic Engineering is an excellent teaching guide and reference to treating nonlinear mathematical problems in hydraulic, hydrologic and coastal engineering. Undergraduates studying civil and coastal engineering, as well as analysis and differential equations, are started off applying calculus to the treatment of nonlinear partial differential equations, before given the chance to practice real-life problems related to the fields. This textbook is not only a good source of teaching materials for teachers or instructors, but is also useful as a comprehensive resource of mathematical tools to researchers.

Prefacep. v
Introduction
Quadratic Curvesp. 1
Trigonometric Functionsp. 3
Infinite Seriesp. 6
Differentiations
Derivatives and Differentiationsp. 13
Mean Value Theorem and Taylor Seriesp. 14
Partial Derivatives and Applicationsp. 16
Finite Difference Method and Newton Methodp. 18
Various Slopes of Unconfined Groundwater Flowp. 20
Integrations
Indefinite Integralsp. 25
Definite Integralsp. 26
Double and Triple Integralsp. 28
Taylor's Diffusion Theoryp. 30
Vector and Tensor
Vector Algebrap. 35
Tensorp. 39
Curvilinear Coordinate Systemp. 41
Vector Analysisp. 46
Application to Navier-Stokes Equationsp. 48
Ordinary Differential Equations
Method of Separation of Variablesp. 51
Linear Differential Equations of the First-Orderp. 52
Linear Differential Equations of the Second-Orderp. 57
Operational Methodp. 60
The Method of Undetermined Coefficientsp. 65
Linear Ordinary Differential Equations of the Higher Ordersp. 67
Variation of Parametersp. 70
Ordinary Differential Equations and Integral Equationsp. 73
Complex Functions and Complex Integrals
Complex Functionsp. 75
Complex Integralp. 78
Application of Complex Integralp. 84
Conformal Mapping
Conformal Mapping by Elementary Functionsp. 91
Schwartz-Christoffel Transformationp. 98
Applications to Hydraulic Engineeringp. 102
Partial Differential Equation of the First-Order
Generalp. 121
Charpit's Methodp. 126
Application to Hydrologyp. 128
Special Functions
Gamma, Beta, and Error Functionsp. 133
Bessel Functionp. 138
Legendre Functionp. 144
Elliptic Functionp. 148
Orthogonality Principlep. 152
Fourier Series and Integral
Fourier Seriesp. 155
Fourier Integralp. 161
Fourier Transform and Its Applicationsp. 164
Laplace Transform
Definition of Laplace Transformp. 169
Inverse Laplace Transformp. 171
Applications to Ordinary Differential Equationsp. 178
Applications to Partial Differential Equationsp. 180
Green's Functionsp. 184
Wave Equations
Classification of Partial Differential Equations of the Second-Orderp. 193
Fundamental Partial Differential Equationsp. 196
One-Dimensional Wave Equationp. 200
Water Surface Oscillations of Rectangular Lakep. 204
Water Surface Oscillations of Circular Lakep. 209
Saint Venant Equationsp. 212
Long Wave Transform on Slopep. 217
Side Outflow from Steep Open Channel Flowp. 221
Potential Equations
Fundamental Equationsp. 229
Surface Wave of Infinitesimally Small Amplitudep. 232
Groundwater Flowp. 236
Motion of a Sphere in Fluidp. 238
Two-Dimensional Stratified Flow into a Sinkp. 241
Analysis of Sand Wavesp. 245
Diffusion Equations
Governing Equationsp. 251
Rayleigh Problemp. 254
Flow near Oscillatory Platep. 257
Distribution of Suspended Load in Flowp. 259
Well Hydraulicsp. 263
Water Content Distribution in Groundp. 266
Modeling of Coastal Changesp. 268
Solution of Nonlinear Equations
Cubic Equationp. 273
Quintic Equationp. 276
Newton Methodp. 278
Solution of Differential Equation and Secant Methodp. 280
Hardy-Cross Methodp. 283
Method of Characteristicsp. 286
Lax-Wendroff Schemep. 289
Linearization Methods
Fundamentals in Linearizationp. 291
Stokes Wavep. 292
KdV Equationp. 296
Stokes Equationp. 303
Burgers Equationp. 308
Series Solutionp. 311
Approximate Solution of Nonlinear Ordinary Differential Equationp. 317
Method of Boundary-Layer Theory
Boundary-Layer Equationp. 321
Two-Dimensional Jetp. 326
Two-Dimensional Wakep. 332
Boundary-Layer Induced by Wave Motionp. 338
Plane Boundary-Layer and Ekman Layerp. 340
Variational Method
Ritz Methodp. 347
Galerkin Methodp. 351
Transform of Partial Differential Equation to Ordinary Differential Equationp. 354
Eigen Value Problemp. 357
Application to Groundwater Flowp. 360
Least Squares Method and Collocation Methodp. 362
The Method of Momentsp. 365
Perturbation Methods
Parameter Perturbationp. 367
Matched Asymptotic Expansionp. 374
Free Surface Flow over Wavy Bedp. 379
Application to Kinematic Wave Methodp. 384
Averaging Methodp. 389
Stability Analysis in Fluid Flowp. 392
Nonlinear Systems Analysis
Vector Calculationp. 395
Phase Plane Analysisp. 398
Property of Singular Pointp. 402
Referencesp. 417
Indexp. 421
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789814299558
ISBN-10: 9814299553
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 436
Published: 31st May 2011
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 23.5 x 15.24  x 2.54
Weight (kg): 0.74