Euclidean geometry | Functions and mappings | Transformation (function) | Linear algebra
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new coordinate system has coordinates (h, k) in the original system. The positive x' and y' directions are taken to be the same as the positive x and y directions. A point P has coordinates (x, y) with respect to the original system and coordinates (x', y') with respect to the new system, where or equivalently In the new coordinate system, the point P will appear to have been translated in the opposite direction. For example, if the xy-system is translated a distance h to the right and a distance k upward, then P will appear to have been translated a distance h to the left and a distance k downward in the x'y'-system . A translation of axes in more than two dimensions is defined similarly. A translation of axes is a rigid transformation, but not a linear map. (See Affine transformation.) (Wikipedia).
A formal look at the method of translation of axis when doing double integrals. We have seen how to translate the axis from an XY Cartesian coordinate system to a polar grid, but a translation to any grid system is possible.
From playlist Advanced Calculus / Multivariable Calculus
14_11 The Translation of Axes in Triple Integrals
An introduction to the translation of axes in triple integrals.
From playlist Advanced Calculus / Multivariable Calculus
Transformations of Graphs A Level Maths - Translation 1 - Quadratics and Cubics
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From playlist AS Level Maths Pure - AQA, Edexcel and OCR MEI
via YouTube Capture
From playlist Further Work with Functions (related content)
14_12 Translation to Cylindrical Coordinates
Translating to Cylindrical Coordinate Axes in Triple Integrals.
From playlist Advanced Calculus / Multivariable Calculus
Apply a translation vector to translate a figure ex 1
👉 Learn how to apply transformations of a figure and on a plane. We will do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the fi
From playlist Transformations
http://www.youtube.com/vinteachesmath This video focuses on translations in the plane. In particular, this video focuses on the definition of a translation and two methods for translating a point in the Cartesian Plane. This video is appropriate for a student taking a course in Geometry
From playlist Geometry
Vertical Translation, Amplitude, Period, Phase Shift, and Range of Cosine and Sine Functions
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Vertical Translation, Amplitude, Period, Phase Shift, and Range of Cosine and Sine Functions
From playlist Trigonometry
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We learn how to find the solutions of nonhomogeneous systems. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Submit your questions on Reddit: http://bit.ly/1GwZZrP #LinearAlgebra #Algebra #UniversityMath #
From playlist Linear Algebra
Thermodynamics and Chemical Dynamics 131C. Lecture 06. The Rotational Partition Function.
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From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
MIT 3.60 | Lec 12a: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
MIT 3.60 | Lec 14b: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
Chemistry 107. Inorganic Chemistry. Lecture 05
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From playlist Chem 107: Week 2
MIT 3.60 | Lec 11b: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
MIT 3.60 | Lec 14a: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
MIT 3.60 | Lec 4b: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
MIT 3.60 | Lec 5a: Symmetry, Structure, Tensor Properties of Materials
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
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From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
14_8 The Volume of a Cylinder Revisited
Now that we have had a formal look at the translation of axes, let's revisit the calculation of the volume of a cylinder using our newfound knowledge.
From playlist Advanced Calculus / Multivariable Calculus