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Lyryx was an OpenStax Ally for the products listed below. The texts and supplementary resources were provided by OpenStax, and Lyryx provided corresponding online assessment and support. Principles of Accounting, Volume 1: Financial Accounting; Principles of Accounting, Volume 2: Managerial Accounting; Calculus; Introductory Statistics
OpenStax textbooks follow a traditional peer review process aimed at ensuring they meet a high quality standard before publication. Textbooks are developed and peer-reviewed by educators in an attempt to ensure they are readable and accurate, meet the scope and sequence requirements of each course, are supported by instructor ancillaries, and are available with the latest technology-based ...
If the characteristic equation has a root r 1 that is repeated k times, then it is clear that y p (x) = c 1 e r 1 x is at least one solution. [1] However, this solution lacks linearly independent solutions from the other k − 1 roots. Since r 1 has multiplicity k, the differential equation can be factored into [1]
MIT OpenCourseWare (MIT OCW) is an initiative of the Massachusetts Institute of Technology (MIT) to publish all of the educational materials from its undergraduate- and graduate-level courses online, freely and openly available to anyone, anywhere.
Connexions, later known as OpenStax CNX [1] was a global repository of educational content provided by volunteers. The open source platform was provided and maintained by OpenStax, which is based at Rice University. The collection was available free of charge, can be remixed and edited, and was available for download in various digital formats. [2]
The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters explaining functions, limits, and derivatives; an appendix of recreational calculus problems; and notes for modern readers. [1]
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]
Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the ...
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