Mathematical Analysis in Engineering: How to Use the Basic ToolsRather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, Professor Mei puts applications at center stage. Beginning with the problem, he finds the mathematics that suits it and closes with a mathematical analysis of the physics. He selects physical examples primarily from applied mechanics. Among topics included are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions and complex function theories. Also covered are advanced topics such as Riemann-Hilbert techniques, perturbation methods, and practical topics such as symbolic computation. Engineering students, who often feel more awe than confidence and enthusiasm toward applied mathematics, will find this approach to mathematics goes a long way toward a sharper understanding of the physical world. |
From inside the book
Results 1-5 of 92
Page vii
... waves 3.1 Waves due to initial disturbances 3.2 Reflection from the fixed end of a string 3.3 Specification of initial and boundary data 3.4 Forced waves in a long string 3.5 Uniqueness of the Cauchy problem 3.6 Traffic flow a taste of ...
... waves 3.1 Waves due to initial disturbances 3.2 Reflection from the fixed end of a string 3.3 Specification of initial and boundary data 3.4 Forced waves in a long string 3.5 Uniqueness of the Cauchy problem 3.6 Traffic flow a taste of ...
Page viii
... 7.2 One - dimensional diffusion 135 7.2.1 General solution in integral form 135 7.2.2 A localized source 137 7.2.3 Discontinuous initial temperature 139 7.3 Forced waves in one dimension 141 7.4 Seepage flow viii Contents.
... 7.2 One - dimensional diffusion 135 7.2.1 General solution in integral form 135 7.2.2 A localized source 137 7.2.3 Discontinuous initial temperature 139 7.3 Forced waves in one dimension 141 7.4 Seepage flow viii Contents.
Page ix
... Wave radiation from a circular cylinder 186 8.6.2 Scattering of plane waves by a circular cylinder 190 8.7 Modified Bessel functions 192 8.8 Bessel functions with complex argument 194 8.9 Pipe flow through a vertical thermal gradient ...
... Wave radiation from a circular cylinder 186 8.6.2 Scattering of plane waves by a circular cylinder 190 8.7 Modified Bessel functions 192 8.8 Bessel functions with complex argument 194 8.9 Pipe flow through a vertical thermal gradient ...
Page xi
... wave 376 13.8 Boundary - layer technique 381 13.9 Seepage flow in an aquifer with slowly varying depth 384 13.10 Water table near a cracked sheet pile 390 13.11 * Vibration of a soil layer 395 13.11.1 Formulation 395 13.11.2 The outer ...
... wave 376 13.8 Boundary - layer technique 381 13.9 Seepage flow in an aquifer with slowly varying depth 384 13.10 Water table near a cracked sheet pile 390 13.11 * Vibration of a soil layer 395 13.11.1 Formulation 395 13.11.2 The outer ...
Page xii
... gradient 427 14.7 Duffing problem by multiple scales 435 14.8 Evolution of wave envelope on a nonlinear string 441 Appendices 447 Bibliography 453 Index 457 Preface This book originated from a one - semester course xii Contents.
... gradient 427 14.7 Duffing problem by multiple scales 435 14.8 Evolution of wave envelope on a nonlinear string 441 Appendices 447 Bibliography 453 Index 457 Preface This book originated from a one - semester course xii Contents.
Contents
Classification of equations with two independent | 20 |
Onedimensional waves | 33 |
Finite domains and separation of variables | 57 |
Elements of Fourier series | 91 |
Introduction to Greens functions | 105 |
Unbounded domains and Fourier transforms | 132 |
Bessel functions and circular boundaries | 165 |
Complex variables | 210 |
Laplace transform and initial value problems | 260 |
Conformal mapping and hydrodynamics | 289 |
RiemannHilbert problems in hydrodynamics | 318 |
Perturbation methods the art | 343 |
Computer algebra for perturbation analysis | 408 |
Appendices | 447 |
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Mathematical Analysis in Engineering: How to Use the Basic Tools Chiang C. Mei No preview available - 1995 |
Common terms and phrases
analytic function approximation Bessel functions boundary conditions boundary layer boundary-value problem C₁ Cauchy-Riemann conditions Cauchy's Cauchy's integral formula characteristic closed contour coefficients complex Consider constant curve defined denote density derivatives diffusion displacement elastic example expansion Əti Əxi finite flow fluid Fourier series Fourier transform governing equation Green function hence homogeneous initial conditions integral integrand inverse transform Jordan's lemma Laplace transform Laplace's equation linear MACSYMA mapping mathematical nonlinear ordinary differential equations orthogonality oscillation partial differential equations perturbation pressure real axis result satisfy separation of variables shown in Figure singular solution solved stress string t₁ temperature theorem upper half plane vanishes vector velocity vertical wave zero Σπί ах ди ди др ппх მა მე მთ მი მუ მყ