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 vii
... elastic rod . Traffic flow on a freeway Seepage flow through a porous medium Diffusion in a stationary medium page xiii xvii 1 1 4 6 7 10 12 12 15 23 2 Classification of equations with two independent variables 2.1 A first - order ...
... elastic rod . Traffic flow on a freeway Seepage flow through a porous medium Diffusion in a stationary medium page xiii xvii 1 1 4 6 7 10 12 12 15 23 2 Classification of equations with two independent variables 2.1 A first - order ...
Page viii
... elastic beam on an elastic foundation 114 6.5.1 Formulation of the beam problem 114 6.5.2 Beam under a sinusoidal concentrated load 117 6.6 Fundamental solutions 121 6.7 Green's function in a finite domain 124 6.8 Adjoint operator and ...
... elastic beam on an elastic foundation 114 6.5.1 Formulation of the beam problem 114 6.5.2 Beam under a sinusoidal concentrated load 117 6.6 Fundamental solutions 121 6.7 Green's function in a finite domain 124 6.8 Adjoint operator and ...
Page ix
... elastic ground 145 7.5.1 Field equations for plane elasticity 145 7.5.2 Half plane under surface load 147 7.5.3 Response to a line load 149 7.6 Fourier sine and cosine transforms 153 7.7 Diffusion in a semi - infinite domain 154 7.8 ...
... elastic ground 145 7.5.1 Field equations for plane elasticity 145 7.5.2 Half plane under surface load 147 7.5.3 Response to a line load 149 7.6 Fourier sine and cosine transforms 153 7.7 Diffusion in a semi - infinite domain 154 7.8 ...
Page x
... elasticity 318 12.1 12.2 Riemann - Hilbert problem and Plemelj's formulas Solution to the Riemann - Hilbert problem 318 320 12.3 Linearized theory of cavity flow 322 12.4 Schwarz's principle of reflection 327 12.5 * Complex formulation ...
... elasticity 318 12.1 12.2 Riemann - Hilbert problem and Plemelj's formulas Solution to the Riemann - Hilbert problem 318 320 12.3 Linearized theory of cavity flow 322 12.4 Schwarz's principle of reflection 327 12.5 * Complex formulation ...
Page xi
... Elastic spring with weak nonlinearity 363 13.6 Theory of homogenization 367 13.6.1 Differential equation with periodic coefficient 367 13.6.2 * Darcy's law in seepage flow 370 13.7 * Envelope of a propagating wave 376 13.8 Boundary ...
... Elastic spring with weak nonlinearity 363 13.6 Theory of homogenization 367 13.6.1 Differential equation with periodic coefficient 367 13.6.2 * Darcy's law in seepage flow 370 13.7 * Envelope of a propagating wave 376 13.8 Boundary ...
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