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The Derivation of (Pi)
Seventh graders groups measure the diameter and circumference of each of the circular objects in the room. They record their results on their student worksheets and access a computer spreadsheet program to compile their results.
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AP Calculus Practice Exam
In this Calculus worksheet, students are provided with questions that are reflective of the content of their exam. Topics covered include derivatives, volume of a solid of rotation, local maximum and minimum, and integration. The one...
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Secant Line Approximation of the Tangent Line
Students perform operation with secant and tangent lines. In this calculus lesson, students find the derivative and relate it to the slope of a line. They differentiate between secant and tangent as they intersect a circle, using Cabri.
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Differentials
Students investigate Differential equations using derivatives. In this calculus lesson, students solve problems of differential equations by taking the derivative and explaining the changes that occurred in the equation and circle. They...
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Euler's Method
Learners identify Euler's method of graphing in this calculus instructional activity. They approximate values of a function and check their work using EM. They also differentiate equations at an exact point.
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Multivariable Calculus: Implicit Differentiation
In this implicit differentiation worksheet, students compute the determinant of the Jacobian matrix and solve equations by implicit differentiation. This two-page worksheet contains definitions, examples, and explanations. It contains...
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Recursion, Roots and Newton's Methods
In this recursion worksheet, students determine the successive approximations of square roots by using the Babylonian Algorithm. They discuss how to derive Newton's Method from the microscopic approximation. This four-page worksheet...
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Complex Analysis: Path Independence
In this path independence activity, students evaluate contour integrals using the Cauchy-Goursat Theorem. This two-page activity contains approximately 5 problems.
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Roller Coaster Robot
Students calculate the area under a curve. In this calculus instructional activity, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
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Numerical Analysis: Solving Linear Equations
In this linear equation worksheet, students compare methods to solve linear equations. This four-page worksheet contains approximately five questions.
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Numerical Analysis: Polynomials
For this polynomial worksheet, students explore functions, determine the least square error, and explore quadratic spline interpolation. This two-page worksheet contains approximately six problems.
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Complex Analysis: Theorems Following Cauchy's Integral Formulas
In this integral formula, students explore how theorems are derived. They write proofs supporting Cauchy's Inequality, Liouville's Theorem, the Fundamental Theorem of Algebra, Gauss' Mean Value Theorem and Cauchy's Residue Theorem. ...
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The Pythagorean Theorem, the Distance Formula, and Slope
Students explore the concept of the Pythagorean Theorem. For this Pythagorean Theorem lesson, students derive the distance formula and slope of a line from the Pythagorean Theorem.
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Trapezoid and Midpoint Rule
Students solve problems of area using the trapezoid and midpoint rule. In this calculus lesson, students take the derivative of the functions as they approximate the area under a curve. They calculate the exact area using the area formula.
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Numerical Analysis: Successive Over-Relaxation for Linear Systems
In this successive linear systems worksheet, students use a matrix representation of iterative schemes for linear systems. They define a positive definite matrix and explore the Kahan Theorem. This two-page worksheet contains...
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Numerical Analysis: Dimensional Vectors
In this dimensional vector worksheet, students prove dimensional vectors. They write systems of equations, verify solutions, and sketch graphs of the functions. This two-page worksheet contains approximately ten problems.
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Complex Analysis: Linear Fractional Transformations
In this transformation worksheet, students explore linear transformations and mappings. They map equations on a coordinate plane. This two-page worksheet contains approximately three problems.
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Linear Systems: Applications of Linear Algebra to Differential Equations
In this differential equations worksheet, students solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
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Finding the Extrema Graphically and Symbolically
For this extrema worksheet, students use the first derivative test and the second derivative test to determine the local extrema. They identify the local maximum and global maximum. This eight-page worksheet contains detailed...
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Exploration 3: Introduction to Definite Integrals
For this integral worksheet, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page worksheet contains approximately 40 problems.
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Calc 3 Review Problems - Function
In this integral activity, students evaluate integrals, integrate functions, find directional derivative of a function, identify the maximum and minimum values of a function, and compute Cartesian coordinates. This two-page activity...
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Multivariable Calculus: The Gradient
In this gradient activity, students explore the definition of differentiable and gradient. They find the tangent approximation of given situations, and determine the directional derivative. This two-page activity contains examples,...
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Patterns of Antiderivatives
In this antiderivative worksheet, students complete a table of basic derivatives and describe the antiderivative. This ten-page worksheet contains approximately 120 problems.
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Finding Extrema Graphically and Symbolically
In this extrema worksheet, students use graphing calculators and the optimization method to identify the maximum and minimums of a given function. They compute the first and second derivative, and graph the functions. This eight-page...