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Multivariable Calculus: Curvilinear Coordinates
In this curvilinear coordinate worksheet, students compute the Jacobian of standard transformations to Cartesian coordinates from polar, spherical and cylindrical coordinates. They identify the determinant of the Jacobian matrices. This...
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Multivariable Calculus: Extrema of Multivariable Functions
In this multivariable functions worksheet, students find the extrema of a function under given conditions. They find the maximum and minimum values of functions. This two page worksheet contains examples, explanations, and five problems.
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Multivariable Calculus: Multivaribale Chain Rule
In this multivariable chain rule worksheet, students use the chain rule theorem to complete given problems. This worksheet contains an example, explanations, and thirteen problems to solve.
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Multivariable Calculus: Gradient Fields and Vector Fields
In this gradient field worksheet students draw vectors which correspond to the gradient. They sketch vector fields and identify functions as a vector field or gradient fields. This two-page worksheet contains approximately five...
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Multivariable Calculus: The Gradient
In this gradient worksheet, students explore the definition of differentiable and gradient. They find the tangent approximation of given situations, and determine the directional derivative. This two-page worksheet contains examples,...
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Multivariable Calculus: The Jacobian Matrix
In this Jacobian matrix worksheet, students identify the derivative matrix of a function and use the tangent approximation to approximate vectors. This two-page worksheet contains six problems.
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Multivariable Calculus: Newton's Method
In this Newton's method worksheet, students produce a sequence of approximations. They use Newton's method to approximate solutions. This two-page worksheet contains explanations and examples. it contains two problems.
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Multivariable Calculus: Dot Product
In this dot product learning exercise, students identify the properties of the dot product. They sketch vectors and obtain expressions for diagonals. This two-page learning exercise contains examples and explanations with two problems.
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Multivariable Calculus: Introduction to Vectors
In this vector learning exercise, students find the length of vectors and the distance between two points. This two-page learning exercise contains examples, definitions, and explanations, as well as two problems.
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Multivariable Calculus: Euclidean Geometry
In this Euclidean geometry worksheet, students determine if planes are parallel or perpendicular to each other. They identify the vector position. This two-page worksheet contains definitions, examples and explanations of how to do the...
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Multivariable Calculus: Parametric Equations of Lines and Planes
In this parametric equation worksheet, learners find a parametric representation by using the vector formula. They find the equation of a plane passing through given points. This two-page worksheet contains examples, explanations and...
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Multivariable Calculus: Review of Linear Systems
In this linear system worksheet, learners determine the point of intersection between two lines, they complete linear combination problems. This two-page worksheet contains four multi-step problems.
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Multivariable Calculus: Linear Systems
In this linear systems worksheet, students perform matrix multiplication. This two-page worksheet contains examples, explanations, definitions, and four problems.
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Multivariable calculus: Partial Derivatives
In this partial derivative learning exercise, students calculate the derivative of given problems and find the equation of the tangent plane to an equation. This two-page learning exercise contains five problems.
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Multivariable Calculus: Vector Functions
In this vector function worksheet, 12th graders identify a helix and a smooth curve. They find the equation of the tangent line to a helical curve. This two-page worksheet contains examples, explanations and approximately four problems.
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Multivariable Calculus: Linear Systems
In this linear system worksheet, students compute the determinant of a given matrix. They solve systems of equations and compute the inverse of a matrix. This two-page worksheet contains examples, explanations, and three multi-step...
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Linear Systems: Fundamental Theorem
In this fundamental theorem worksheet, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page worksheet...
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Linear Systems: Projections
For this projection worksheet, students explore the intuition behind projections. They calculate the length using the norm and find the projection of a vector. This two-page worksheet contains approximately five problems.
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Linear Systems: Vector Spaces of a Matrix
In this vector space matrix worksheet, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page worksheet contains examples and approximately five problems.
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Linear Systems: Least Squares Approximations
In this least squares approximation instructional activity, students determine the number of solutions a given linear system has. They find the least square error and the equation of a line of best fit for a set of three points. Students...
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Linear Systems: Projections
In this projection worksheet, students determine the projections if a given matrix. They take a vector and project it onto a line and subspace. This four-page worksheet contains examples and approximately seven problems.
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this Eigenvalue worksheet, students examine the applications of matrix exponentiation. This four-page worksheet contains examples, explanations and approximately three problems to complete.
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Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors
In this interpretation of eigenvalues and eigenvectors worksheet, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
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Linear Systems: Introduction to Vector Space
In this vector space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples, theorems, explanations, and approximately three problems.
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