English Version HSC Higher Mathematics Note

English Version HSC Higher Mathematics Note. This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. If you distribute this work or a derivative, include the history of the document. This text was initially written by Patrick Keef and modified by David Guichard. This HTML version was produced using a script written by David Farmer and adapted by David Guichard. It is generated from the Tex source; the output of Tex should be treated as the definitive version.

English Version HSC Higher Mathematics Note

English Version HSC Higher Mathematics Note

EV HSC Higher Mathematics 1st Paper Note

EV HSC Higher Mathematics 2nd Paper Note

Includes the latest developments in physics- and engineering-oriented higher mathematics, such as for quantum information theory and mathematical topology for knot theory.- Exposition of mathematical concepts underlying physical phenomena.- Combines mathematical rigor with practical applications.- Offers learning and teaching aids as worked-out examples with solutions for the application of higher mathematics in physics and engineering.- Reader-friendly summaries in each chapter.

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts.

A mean-preserving spread (MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A’s probability density function while leaving the mean (the expected value) unchanged. The concept of a mean-preserving spread provides a partial ordering of probability distributions according to their dispersions: of two probability distributions, one may be ranked as having more dispersion than the other, or alternatively neither may be ranked as having more dispersion.

Sometimes, determinants are used merely as a compact notation for expressions that would otherwise be unwieldy to write down. When the entries of the matrix are taken from a field (like the real or complex numbers), it can be proven that any matrix has a unique inverse if and only if its determinant is nonzero. Various other theorems can be proved as well, including that the determinant of a product of matrices is always equal to the product of determinants; and, the determinant of a Hermitian matrix is always real.

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HSC Notes

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