{"product_id":"9783540514879","title":"Chebyshev and Fourier Spectral Methods (Lecture Notes in Engineering)","description":"\u003cp\u003e§16§The goal of this book is to teach spectral methods for solving boundary value, eigenvalue, and time-dependent problems. Although the title speaks only of Chebyshev polynomials and trigonometric functions, the book also discusses Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions. These notes evolved from a course I have taught the past five years to an audience drawn from half a dozen different disciplines at the University of Michigan: aerospace engineering, meteorology, physical oceanography, mechanical engineering, naval architecture, and nuclear engineering. With such a diverse audience, this book is not focused on a particular discipline, but rather upon solving differential equations in general. The style is not lemma-theorem-Sobolev space, but algorithms guidelines-rules-of-thumb. Although the course is aimed at graduate students, the required background is limited. It helps if the reader has taken an elementary course in computer methods and also §16§ has been exposed to Fourier series and complex variables at the undergraduate level. However, even this background is not absolutely necessary. Chapters 2 to 5 are a self contained treatment of basic convergence and interpolation theory. §04§1. Introduction.- 2. Convergence Theory.- 3. Galerkin's Method 〓04§endix B. Matrix Methods.- 1. Gaussian Elimination 〓04§ourier Cosine Series: Endpoint Grid.- 4. Fourier Sine Series: Endpoint Grid.- 5. Sinc(x): Whittaker Cardinal Functions.- 6. Chebyshev Polynomials: Extrema \u0026amp; Endpoints Grid.- 7. Chebyshev Polynomials: Interior Grid.- 8. Legendre Polynomials: Extrema \u0026amp; Endpoints Grid.- 9. Cosine Cardinal Functions on the Interior [Rectangle Rule or Roots] Grid.- 10. Sine Cardinal Functions on the Interior [Rectangle Rule or Roots] Grid.- Appendix G. Minimization of the Square of the Residual (Least Squares) for Solving Differential Equations via Nonlinear Degrees of Freedom.- 1. Introduction.- 2. Newton's Method.- 3. Linear Least-Squares Fitting and the Neglect of the Second Derivative.- 4. Evaluating the Second Derivatives for the Hessian Matrix.- 5. Steepest Descent.- 6. Convexity, Positive Definiteness, and Conditions for a Minimum.- 7. Approximations that Depend Nonlinearly on the Free Parameters.- 8. Nonlinear Approximation to the KdV Soliton: A Worked Example.- Errata.\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":52354183725367,"sku":"00000_00000_00000_00000","price":921.0,"currency_code":"MYR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0962\/3548\/7543\/files\/9783540514879-1.jpg?v=1783661160","url":"https:\/\/kinokuniya.com.my\/products\/9783540514879","provider":"Books Kinokuniya Malaysia","version":"1.0","type":"link"}