Titlebook: Understanding Mathematical Concepts in Physics; Insights from Geomet Sanjeev Dhurandhar Book 2024 The Editor(s) (if applicable) and The Aut

狂热语言

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

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

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

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Buttress

吵闹

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

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

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阴郁

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

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