狂热语言
发表于 2025-3-26 23:22:09
Topology,notion of continuity on the real line, which is a familiar notion. The concept of continuity is then generalised to metric spaces and finally to topological spaces, which is the home ground of the concept (one view is that topology is a study of continuous functions). Beginning with preliminaries an
RENIN
发表于 2025-3-27 01:17:26
Hilbert Spaces, of measures, in particular the Lebsegue measure, is described as also the Lebesgue integral. The chapter then deals with function spaces .—the space of Fourier coefficients—and the . space of square-integrable functions—both of which are Hilbert spaces. Then the parallelogram law, Gram- Schmidt ort
ATOPY
发表于 2025-3-27 07:59:55
Fourier Analysis, fast Fourier transform works—the underlying group theory is explained behind its performance. It further includes sampling theory, Whittaker-Shannon sampling theorem, and aliasing in detail. For this chapter, a rudimentary knowledge of Fourier transforms at the undergraduate level is assumed, and i
Maximize
发表于 2025-3-27 10:12:04
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Buttress
发表于 2025-3-27 15:19:04
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吵闹
发表于 2025-3-27 21:43:16
Solving Differential Equations,e diffusion equation and the wave equation are solved assuming suitable boundary conditions. The Sturm-Louiville problem, the method of separation of variables, and Green’s functions are discussed in detail—volume and surface Green’s functions, etc. The content of this chapter is more or less standa
Microgram
发表于 2025-3-27 23:17:41
Differential Geometry and Tensors,gent vectors, forms, higher rank tensors as elements of tensor products of tangent and cotangent spaces, the affine connection, Riemannian metric, curvature, geodesics, and geodesic deviation. The chapter ends with a brief discussion on vector bundles. The chapter lays the foundation for understandi
清醒
发表于 2025-3-28 02:43:51
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阴郁
发表于 2025-3-28 07:49:44
Probability and Random Variables,cept of probability and probability spaces. Random variables, their distributions, independence, etc., are discussed in general. Multivariate distributions, the independence of random variables, and functions of random variables are discussed. Finally, the chapter ends with a description of moment g
Brittle
发表于 2025-3-28 11:40:43
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