| Edition |
1st ed |
| Descript |
1 online resource (259 pages) |
|
text txt rdacontent |
|
computer c rdamedia |
|
online resource cr rdacarrier |
| Note |
Cover -- Title page -- Copyright page -- Contents -- Preface -- 1: Problem Formulation and Model Development -- Introduction -- Algebraic Equations from Vapor-Liquid Equilibria (VLE) -- Macroscopic Balances: Lumped-Parameter Models -- Force Balances: Newton's Second Law of Motion -- Distributed Parameter Models: Microscopic Balances -- Using the Equations of Change Directly -- A Contrast: Deterministic Models and Stochastic Processes -- Empiricisms and Data Interpretation -- Conclusion -- Problems -- References -- 2: Algebraic Equations -- Introduction -- Elementary Methods -- Newton-Raphson (Newton's Method of Tangents) -- Regula Falsi (False Position Method) -- Dichotomous Search -- Golden Section Search -- Simultaneous Linear Algebraic Equations -- Crout's (or Cholesky's) Method -- Matrix Inversion -- Iterative Methods of Solution -- Simultaneous Nonlinear Algebraic Equations -- Pattern Search for Solution of Nonlinear Algebraic Equations -- Algebraic Equations with Constraints -- Conclusion -- Problems -- References -- 3: Vectors and Tensors -- Introduction -- Manipulation of Vectors -- Force Equilibrium -- Equating Moments -- Projectile Motion -- Dot and Cross Products -- Differentiation of Vectors -- Gradient, Divergence, and Curl -- Green's Theorem -- Stokes' Theorem -- Conclusion -- Problems -- References -- 4: Numerical Quadrature -- Introduction -- Trapezoid Rule -- Simpson's Rule -- Newton-Cotes Formulae -- Roundoff and Truncation Errors -- Romberg Integration -- Adaptive Integration Schemes -- Simpson's Rule -- Gaussian Quadrature and the Gauss-Kronrod Procedure -- Integrating Discrete Data -- Multiple Integrals (Cubature) -- Monte Carlo Methods -- Conclusion -- Problems -- References -- 5: Analytic Solution of Ordinary Differential Equations -- An Introductory Example -- First-Order Ordinary Differential Equations |
|
Nonlinear First-Order Ordinary Differential Equations -- Solutions with Elliptic Integrals and Elliptic Functions -- Higher-Order Linear ODEs with Constant Coefficients -- Use of the Laplace Transform for Solution of ODEs -- Higher-Order Equations with Variable Coefficients -- Bessel's Equation and Bessel Functions -- Power Series Solutions of Ordinary Differential Equations -- Regular Perturbation -- Linearization -- Conclusion -- Problems -- References -- 6: Numerical Solution of Ordinary Differential Equations -- An Illustrative Example -- The Euler Method -- Modified Euler Method -- Runge-Kutta Methods -- Simultaneous Ordinary Differential Equations -- Some Potential Difficulties Illustrated -- Limitations of Fixed Step-Size Algorithms -- Richardson Extrapolation -- Multistep Methods -- Split Boundary Conditions -- Finite-Difference Methods -- Stiff Differential Equations -- Backward Differentiation Formula (BDF) Methods -- Bulirsch-Stoer Method -- Phase Space -- Summary -- Problems -- References -- 7: Analytic Solution of Partial Differential Equations -- Introduction -- Classification of Partial Differential Equations and Boundary Conditions -- Fourier Series -- A Preview of the Utility of Fourier Series -- The Product Method (Separation of Variables) -- Parabolic Equations -- Elliptic Equations -- Application to Hyperbolic Equations -- Applications of the Laplace Transform -- Approximate Solution Techniques -- Galerkin MWR Applied to a PDE -- The Rayleigh-Ritz Method -- Collocation -- Orthogonal Collocation for Partial Differential Equations -- The Cauchy-Riemann Equations, Conformal Mapping, and Solutions for the Laplace Equation -- Conclusion -- Problems -- References -- 8: Numerical Solution of Partial Differential Equations -- Introduction -- Finite-Difference Approximations for Derivatives -- Boundaries with Specified Flux |
|
Elliptic Partial Differential Equations -- An Iterative Numerical Procedure: Gauss-Seidel -- Improving the Rate of Convergence with Successive Over-Relaxation (SOR) -- Parabolic Partial Differential Equations -- An Elementary, Explicit Numerical Procedure -- The Crank-Nicolson Method -- Alternating-Direction Implicit (ADI) Method -- Three Spatial Dimensions -- Hyperbolic Partial Differential Equations -- The Method of Characteristics -- The Leapfrog Method -- Elementary Problems with Convective Transport -- A Numerical Procedure for Two-Dimensional Viscous Flow Problems -- MacCormack's Method -- Adaptive Grids -- Conclusion -- Problems -- References -- 9: Integro-Differential Equations -- Introduction -- An Example of Three-Mode Control -- Population Problems with Hereditary Influences -- An Elementary Solution Strategy -- VIM: The Variational Iteration Method -- Integro-Differential Equations and the Spread of Infectious Disease -- Examples Drawn from Population Balances -- Particle Size in Coagulating Systems -- Application of the Population Balance to a Continuous Crystallizer -- Conclusion -- Problems -- References -- 10: Time-Series Data and the Fourier Transform -- Introduction -- A Nineteenth-Century Idea -- The Autocorrelation Coefficient -- A Fourier Transform Pair -- The Fast Fourier Transform -- Aliasing and Leakage -- Smoothing Data by Filtering -- Modulation (Beats) -- Some Familiar Examples -- Turbulent Flow in a Deflected Air Jet -- Bubbles and the Gas-Liquid Interface -- Shock and Vibration Events in Transportation -- Conclusion and Some Final Thoughts -- Problems -- References -- 11: An Introduction to the Calculus of Variations and the Finite-Element Method -- Some Preliminaries -- Notation for the Calculus of Variations -- Brachistochrone Problem -- Other Examples -- Minimum Surface Area -- Systems of Particles -- Vibrating String |
|
Laplace's Equation -- Boundary-Value Problems -- A Contemporary COV Analysis of an Old Structural Problem -- Flexing of a Rod of Small Cross Section -- The Optimal Column Shape -- Systems with Surface Tension -- The Connection between COV and the Finite-Element Method (FEM) -- Conclusion -- Problems -- References -- Index -- EULA |
|
Prepare students for success in using applied mathematics for engineering practice and post-graduate studies moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques Uses different examples from chemical, civil, mechanical and various other engineering fields Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters |
|
Description based on publisher supplied metadata and other sources |
|
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
| Link |
Print version: Glasgow, Larry A. Applied Mathematics for Science and Engineering
Somerset : John Wiley & Sons, Incorporated,c2014 9781118749920
|
| Subject |
Engineering mathematics.;Technology -- Mathematical models
|
|
Electronic books
|
|
