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- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/15%3A_Multiple_Integration/15.08%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_373%3A_Trigonometry_for_Calculus/05%3A_Graphs_of_the_Trigonometric_Functions/5.02%3A_Non-Rigid_TransformationsThis section covers non-rigid transformations of graphs of trigonometric functions, focusing on vertical and horizontal stretching, compressing, and reflecting. It explains how these transformations a...This section covers non-rigid transformations of graphs of trigonometric functions, focusing on vertical and horizontal stretching, compressing, and reflecting. It explains how these transformations affect the amplitude and period of the fundamental trigonometric functions. This section also provides examples and visual aids to help understand how altering parameters in trigonometric functions modifies their graphs, enhancing comprehension of the dynamic behavior of these functions.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.07%3A_TransformationsThis section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in...This section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in function equations affect their graphs. The section provides examples and visual aids to illustrate vertical and horizontal shifts, reflections over the axes, and scaling of graphs. These concepts help understand how functions can be manipulated to model different real-world scenarios.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/05%3A_Eigenvalues_and_Eigenvectors/5.3%3A_SimilarityThis page explores similar matrices defined by the relation A=CBC−1, focusing on their geometric interpretations, eigenvalues, eigenvectors, and properties as an equivalence relation. It expl...This page explores similar matrices defined by the relation A=CBC−1, focusing on their geometric interpretations, eigenvalues, eigenvectors, and properties as an equivalence relation. It explains how to compute matrix powers, emphasizing transformations and changes of coordinates between different systems. The relationship between matrices A and B is examined, highlighting how they share characteristics like trace and determinant but may differ in eigenvectors.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/15%3A_Multiple_Integration/15.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Workbench/De_Anza-_Math_1D/02%3A_Multiple_Integration/2.08%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/04%3A_Multiple_Integration/4.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/04%3A_Multiple_Integration/4.07%3A_Change_of_Variables_in_Multiple_IntegralsWhen solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double inte...When solving integration problems, we make appropriate substitutions to obtain an integral that becomes much simpler than the original integral. We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/01%3A_Functions_-_Fundamental_Concepts/1.05%3A_TransformationsIn this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad c...In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/10%3A_Graphs_of_the_Trigonometric_Functions/10.02%3A_Non-Rigid_TransformationsThis section covers non-rigid transformations of graphs of trigonometric functions, focusing on vertical and horizontal stretching, compressing, and reflecting. It explains how these transformations a...This section covers non-rigid transformations of graphs of trigonometric functions, focusing on vertical and horizontal stretching, compressing, and reflecting. It explains how these transformations affect the amplitude and period of the fundamental trigonometric functions. This section also provides examples and visual aids to help understand how altering parameters in trigonometric functions modifies their graphs, enhancing comprehension of the dynamic behavior of these functions.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.00%3A_Prelude_to_Linear_Transformations_and_Matrix_AlgebraThis page explores the non-linear complexities of a robot arm's joint movements and hand positions through the transformation function f(θ,ϕ,ψ). It discusses the relationship between ma...This page explores the non-linear complexities of a robot arm's joint movements and hand positions through the transformation function f(θ,ϕ,ψ). It discusses the relationship between matrices and transformations, covering how transformations can be expressed with matrices, their properties, and how matrix multiplication relates to composition. The chapter culminates in understanding matrix arithmetic and solving matrix equations.
