Mathematical analysis in engineering : how to use the basic tools
"This user-friendly text shows how to use mathematics to formulate, solve, and analyze physical problems." "Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at center stage; that is, it starts with the problem, finds the mathematics that suits it, and ends with a mathematical analysis of the physics. The emphasis throughout is on engineering applications rather than mathematical formalities." "Physical examples are selected primarily from applied mechanics, a field central to many branches of engineering and applied science, and they range from the simple to the more sophisticated. Among mathematical topics included in the book 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."--Jacket
eBook, English, 1995
Cambridge University Press, Cambridge [England], 1995
1 online resource (xvii, 461 pages) : illustrations
9780511810749, 9780521587983, 0511810741, 0521587980
817931035
Unbounded domains and Fourier transforms
7.1 Exponential Fourier transform
7.2 One-dimensional diffusion
7.3 Forced waves in one dimension
7.4 Seepage flow into a line drain
7.5 Surface load on an elastic ground
7.6 Fourier sine and cosine transforms
7.7 Diffusion in a semi-infinite domain
7.8 Potential problem in a semi-infinite strip
Bessel functions and circular boundaries
8.1 Circular region and Bessel's equation
8.2 Bessel function of the first kind
8.3 Bessel function of the second kind for integer order
8.4 Some properties of Bessel functions
8.5 Oscillations in a circular region
8.6 Hankel functions and wave propagation
8.7 Modified Bessel functions
8.8 Bessel functions with complex argument
8.9 Pipe flow through a vertical thermal gradient
8.10 Differential equations reducible to Bessel form
Complex variables
9.1 Complex numbers
9.2 Complex functions
9.3 Branch cuts and Riemann surfaces
9.4 Analytic functions
9.5 Plane seepage flows in porous media
9.6 Plane flow of a perfect fluid
9.7 Simple irrotational flows
9.8 Cauchy's theorem
9.9 Cauchy's integral formula and inequality
9.10 Liouville's theorem
9.11 Singularities
9.12 Evaluation of integrals by Cauchy's theorems
9.13 Jordan's lemma
9.14 Forced harmonic waves and the radiation condition
9.15 Taylor and Laurent series
9.16 More on contour integration
Laplace transform and initial value problems
10.1 The Laplace transform
10.2 Derivatives and the convolution theorem
10.3 Coupled pendula
10.4 One-dimensional diffusion in a strip
10.5 A string-oscillator system
10.6 Diffusion by sudden heating at the boundary
10.7 Sound diffraction near a shadow edge
10.8 *Temperature in a layer of accumulating snow
Conformal mapping and hydrodynamics. 11.1 What is conformal mapping?
11.2 Relevance to plane potential flows
11.3 Schwarz-Christoffel transformation
11.4 An infinite channel
11.5 A semi-infinite channel
11.6 An estuary
11.7 Seepage flow under an impervious dam
11.8 Water table above an underground line source
Riemann-Hilbert problems in hydrodynamics and elasticity
12.1 Riemann-Hilbert problem and Plemelj's formulas
12.2 Solution to the Riemann-Hilbert problem
12.3 Linearized theory of cavity flow
12.4 Schwarz's principle of reflection
12.5 *Complex formulation of plane elasticity
12.6 *A strip footing on the ground surface
Perturbation methods
the art of approximation
13.1 Introduction
13.2 Algebraic equations
13.3 Parallel flow with heat dissipation
13.4 Freezing of water surface
13.5 Method of multiple scales for an oscillator
13.6 Theory of homogenization
13.7 *Envelope of a propagating wave
13.8 Boundary-layer technique
13.9 Seepage flow in an aquifer with slowly varying depth
13.10 Water table near a cracked sheet pile
13.11 *Vibration of a soil layer
Computer algebra for perturbation analysis
14.1 Getting started
14.2 Algebraic and trigonometric operations
14.3 Exact and perturbation methods for algebraic equations
14.4 Calculus
14.5 Ordinary differential equations
14.6 Pipe flow in a vertical thermal gradient
14.7 Duffing problem by multiple scales
14.8 Evolution of wave envelope on a nonlinear string
Appendices
Bibliography
Index
English
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