Mathematical methods for mechanical sciences
By: Michael Howe, Boston University, USA
Published: 2016
Language: eng
Number of pages: 319
ISBN-13: 9781783266647
Subjects: Differential equations; Engineering; Engineering mathematics; Study and teaching (Higher); Textbooks; Mathematical models
Description: "A mathematical model of a physical system provides the engineer with the insight and intuitive understanding required to make efficient system design changes or other modifications. A simple formula is often worth a thousand numerical simulations, and can reveal connections between control parameters that might otherwise take hours or weeks to deduce from a computational analysis. This book supplies the undergraduate engineer with the basic mathematical tools for developing and understanding such models. It is also suitable as a review for professional engineers and graduate students. A firm grasp of the topics covered should enable the working engineer (educated to bachelor's degree level) to understand, write and otherwise make sensible use of technical reports and papers."--Back cover.
Notes: Includes bibliographical references (pages 307-310) and index.
Table of contents: title: 1.; title: Linear Ordinary Differential Equations -- -- 1.1.; title: First-Order Equations -- -- 1.2.; title: Second-Order Equations with Constant Coefficients -- -- 1.3.; title: Euler's Homogeneous Equation -- -- 1.4.; title: Method of Reduction of Order -- -- 1.5.; title: Particular Integrals of Second-Order Equations -- -- 1.6.; title: Method of Variation of Parameters -- -- 1.7.; title: Method of Frobenius -- -- 1.8.; title: Bessel Functions of Integer Order -- -- 1.9.; title: The Sturm-Liouville Equation -- -- 1.10.; title: Fourier Series -- -- 1.11.; title: Generalised Functions and Green's Function -- -- 2.; title: Vector Calculus -- -- 2.1.; title: Elementary Operations with Vectors -- -- 2.2.; title: Scalar and Vector Fields -- -- 2.3.; title: The Divergence and the Divergence Theorem -- -- 2.4.; title: Stokes' Theorem and Curl -- -- 2.5.; title: Green's Identities -- -- 2.6.; title: Orthogonal Curvilinear Coordinates -- -- 2.7.; title: Evaluation of Line and Surface Integrals -- -- 2.8.; title: Suffix Notation -- -- 3.; title: Complex Variables -- -- 3.1.; title: Complex Numbers -- -- 3.2.; title: Functions of a Complex Variable -- -- 3.3.; title: Integration in the Complex Plane -- -- 3.4.; title: Cauchy's Theorem -- -- 3.5.; title: Cauchy's Integral Formula -- -- 3.6.; title: Taylor's Theorem -- -- 3.7.; title: Laurent's Expansion -- -- 3.8.; title: Poles and Essential Singularities -- -- 3.9.; title: Cauchy's Residue Theorem -- -- 3.10.; title: Applications of the Residue Theorem to Evaluate Real Integrals -- -- 3.11.; title: Contour Integration Applied to the Summation of Series -- -- 3.12.; title: Conformal Representation -- -- 3.13.; title: Laplace's Equation in Two Dimensions -- -- 3.14.; title: Applications to Hydrodynamics -- -- 4.; title: Partial Differential Equations -- -- 4.1.; title: Classification of Second-Order Equations -- -- 4.2.; title: Boundary Conditions for Well-Posed Problems -- -- 4.3.; title: Method of Separation of Variables -- -- 4.4.; title: Problems with Cylindrical Boundaries -- -- 4.5.; title: Application of Green's Second Identity: Green's Function -- -- 4.6.; title: The Dirac Delta Function in Three Dimensions -- -- 4.7.; title: The Method of Images -- -- 4.8.; title: Green's Function for the Wave Equation -- -- 4.9.; title: Fourier Transforms -- -- 4.10.; title: Application of Fourier Transforms to the Solution of Partial Differential Equations -- -- 5.; title: Special Functions -- -- 5.1.; title: The Gamma Function ¿(x) -- -- 5.2.; title: The Beta Function -- -- 5.3.; title: Legendre Polynomials -- -- 5.4.; title: The Error Function erf(x) -- -- 6.; title: Matrix Algebra and Linear Equations -- -- 6.1.; title: Definitions -- -- 6.2.; title: Algebra of Matrices -- -- 6.3.; title: Linear Equations -- -- 6.4.; title: Further Discussion of Compatibility -- -- 6.5.; title: Determinants -- -- 6.6.; title: Inverse of a Square Matrix -- -- 6.7.; title: Cramer's Rule -- -- 6.8.; title: Eigenvalue Problems -- -- 6.9.; title: Real Symmetric Matrices -- -- 6.10.; title: The Cayley-Hamilton Equation -- -- 7.; title: Variational Calculus -- -- 7.1.; title: Taylor's Theorem for Several Variables -- -- 7.2.; title: Maxima and Minima -- -- 7.3.; title: Constrained Maxima and Minima: Lagrange Multipliers -- -- 7.4.; title: Stationary Definite Integrals -- -- 7.5.; title: Isoperimetric Problems --; title: Useful formulae --; title: Bibliography --; title: Index.