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. |
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Page xi
... equations 13.2.1 Regular perturbations 343 343 345 345 13.2.2 Singular perturbations 347 13.3 13.4 Parallel flow with heat dissipation Freezing of water surface 349 352 ... Ordinary differential equations 426 14.6 Pipe flow in a Contents xi.
... equations 13.2.1 Regular perturbations 343 343 345 345 13.2.2 Singular perturbations 347 13.3 13.4 Parallel flow with heat dissipation Freezing of water surface 349 352 ... Ordinary differential equations 426 14.6 Pipe flow in a Contents xi.
Page xii
How to Use the Basic Tools Chiang C. Mei. 14.5 Ordinary differential equations 426 14.6 Pipe flow in a vertical thermal gradient 427 14.7 Duffing problem by multiple scales 435 14.8 Evolution of wave envelope on a nonlinear string 441 ...
How to Use the Basic Tools Chiang C. Mei. 14.5 Ordinary differential equations 426 14.6 Pipe flow in a vertical thermal gradient 427 14.7 Duffing problem by multiple scales 435 14.8 Evolution of wave envelope on a nonlinear string 441 ...
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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