Analytical and Computational Methods of Advanced Engineering Mathematics
Springer Science & Business Media, Sep 25, 1998 - Mathematics - 733 pages
(NOTES)This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts: 1. The text has a large number of examples and problems - a typical section having 25 quality problems directly related to the text. 2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to real-world problems, each treated completely and in sufficient depth to be self-contained. 3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications. 4.The authors have used and updated the book as a course text over a 10 year period. 5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie. 6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 1300-1500 pages.
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algebra algorithm applied boundary value problem calculation Chapter coefficients column Compute constant convergence theorem coordinates curve defined derivative det(A determined Dirichlet Boundary Condition eigenfunctions eigenpairs eigenvalue eigenvectors equivalent Euler's method exact example Exercises Figure Find finite formula Fourier integral Fourier sine Fourier sine series fundamental theorem given gives graph heat diffusion heat equation Hence homogeneous implies initial value problem interval Laplace transform linear linearly independent mathematical Moreover multiplication Neumann Neumann boundary conditions Newton's nonzero notation obtained orthogonal oscillator parameters plane polynomial prescribed function product solutions proof properties quadratic interpolation row echelon rule satisfies scalar second-order Section 1.2 sectionally continuous separation of variables shown sin(nx solution basis solved steady-state string Sturm-Liouville problem subspace surface system Ax Table temperature unique solution uniqueness theorem vector field vector space verify vibrating voltage xi(t xp(t zero