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- 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.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/05%3A_Differential_Calculus_with_Parametric_CurvesThis page introduces parametric equations, highlighting their advantages in representing curves beyond traditional methods. It emphasizes their application in describing motion in two and three dimens...This page introduces parametric equations, highlighting their advantages in representing curves beyond traditional methods. It emphasizes their application in describing motion in two and three dimensions and covers graphing, analysis, and differential calculus aspects like tangent slopes, arc lengths, and areas. Exercises for deeper comprehension are included, authored by contributors from MIT and Harvey Mudd, and published under a Creative Commons license.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.03%3A_Elementary_MechanicsThis section discusses applications to elementary mechanics involving Newton's second law of motion. The problems considered include motion under the influence of gravity in a resistive medium, and de...This section discusses applications to elementary mechanics involving Newton's second law of motion. The problems considered include motion under the influence of gravity in a resistive medium, and determining the initial velocity required to launch a satellite.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.06%3A_Directional_Derivatives_and_the_Gradient/1.6E%3A_Exercises_for_Section_1.6This page includes exercises on directional derivatives and gradients for functions such as f(x,y)=5−2x2−12y2 and f(x,y)=y2cos(2x), evaluated at points like P(3,4). It a...This page includes exercises on directional derivatives and gradients for functions such as f(x,y)=5−2x2−12y2 and f(x,y)=y2cos(2x), evaluated at points like P(3,4). It also covers gradients in multiple dimensions, tangent planes, and normal lines, alongside problems related to temperature change and electric potential.
