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Complex Analysis: Contour Integration
In this contour integration worksheet, students integrate complex functions of a real variable. They sketch the contour and evaluate the integral. This two-page worksheet contains eight problems, as well as explanations and examples.
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Complex Analysis: Introduction to Contours
For this contour worksheet, students compute complex valued functions of a real variable. They give examples of a parametric representation and draw a sketch of the points. This two-page worksheet contains explanations and examples, as...
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Complex Analysis: Harmonic Functions
In this harmonic function worksheet, students explore harmonic functions and construct a harmonic conjugate. This three-page worksheet contains three problems, with explanations and examples.
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Complex Analysis: Complex Variables
In this complex variable worksheet, students use functional iteration to find the fixed points of a function. This two-page worksheet explains the functional iteration, the Julia Set and the Mandelbrot set. Four problems are included.
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Complex Analysis: Complex Exponential
In this complex exponential worksheet, students answer questions about the characteristics of a function. They sketch the image in a coordinate plane. This two-page worksheet contains six problems.
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Complex Analysis: Functions
In this function worksheet, students complete complex trigonometric functions. They use hyperbolic trigonometric functions to solve problems. This two-page worksheet contains eight problems with examples and explanations.
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Complex Analysis: Branch Cuts
In this branch cuts worksheet, students define analytic branches of logs and use the Riemann surface for logs. They determine the domain of analyticity for the function. This two-page worksheet contains six problems, as well as...
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Complex Analysis: The Complex Logarithm
For this complex logarithm worksheet, students compute the log of given functions. They sketch the sketch the set of points and investigate the analyticity of the logs. This two-page worksheet contains approximately five problems, with...
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Complex Analysis: Properties of Complex Numbers
In this properties of complex numbers worksheet, students list and explain the properties and operations used to compute the value of expressions. This one-page worksheet contains six definition questions and three equations.
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Complex Analysis: Graphical Representations
In this graphical representation worksheet, students draw an Argand diagram depicting two complex numbers in a complex plane. They draw vectors to represent complex numbers. This two-page worksheet contains five equations to solve.
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Complex Analysis: Point Sets in the Complex Plane
In this point set worksheet, students explore definitions describing planar point sets. They use the definitions to describe examples of point sets. This two-page worksheet contains four problems and 15 definitions.
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Complex Analysis: Functions of Complex Variables
For this complex variable worksheet, students explore the functions of a complex variable. They map complex variables and solve complex inequalities. This three-page worksheet contains fourteen problems.
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Complex Analysis: Limits of Complex Functions
In this complex function worksheet, students identify the limits of complex functions. They explore the rules on limits and the point at infinity. This two-page worksheet contains examples and explanations, as well as seven problems.
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Complex Analysis: Cauchy-Reimann Equations
In this Cauchy-Riemann equation worksheet, students derive the Cauchy-Riemann equations by using the definition of the derivative function. This two-page worksheet contains seven problems.
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Complex Analysis: Polynomial Equations
For this polynomial equation worksheet, students explore real fractional powers of complex numbers. This three-page worksheet contains examples, explanations and approximately seven problems.
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Multivariable Calculus: Divergence
In this divergence activity, students explore the definitions of divergence and a curl. Given equations, students compute the divergence and the curl. This two-page activity contains four problems.
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Multivariable Calculus: Green's Theorem
For this Green's Theorem worksheet, students compute the value of the line integral. This two-page worksheet contains explanations, examples, and three problems to solve.
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Multivariable Calculus: Conservative Vector Fields
In this vector field worksheet, students explore the properties of conservative vector fields. They solve problems for a given field. This two-page worksheet contains explanations, examples and five equations.
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Multivariable Calculus: Change of Variables Theorem
In this change of variables worksheet, students complete integral problems through the use of Jacobi's Theorem. They use various methods to convert from Cartesian coordinates to polar, spherical and cylindrical coordinates. This...
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Multivariable Calculus: Multiple Integration
For this multiple integration worksheet, students define coordinate rectangle, explore what it means to be "bounded on a set," and define the Riemann integral. They find the volume of a graph with specified boundaries and curves. ...
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Multivariable Calculus: Iterated Integration
In this iterated integration worksheet, students evaluate iterated integrals over rectangular and non-rectangular regions. This two-page worksheet contains explanations and examples. It contains three problems for students to work.
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Multivariable Calculus: Multiple Integration
In this multiple integration activity, students identify the multiple integration of a given function. They evaluate integrals and identify their value. Students sketch a region of integration, write integrals in terms of rectangular...
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Multivariable Calculus: Introduction to Path Integrals
In this path integral worksheet, students compute line integrals under given conditions, define vector fields, and explore gradient fields, as well as a potential function. This two-page worksheet contains five problems.
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Multivariable Calculus: Extrema of Multivariable Functions
In this multivariable function worksheet, students determine the extrema of multivariable functions, classify critical points, and solve functions with given boundaries. This two page worksheet contains five multi-step problems as well...
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