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Complex Analysis: Analyticity and the Cauchy-Riemann Equation
In this analyticity and Cauchy-Riemann learning exercise, students determine the domain of a function, explore its derivatives, and list its component functions. This two-page learning exercise contains eleven problems, as well as...
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Complex Analysis: Residues and Real Integrals
In this integral worksheet, students evaluate contour integrals and real integrals. This two-page worksheet contains approximately three problems. Some explanations and definitions are provided.
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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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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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Complex Analysis: Homework Set 5: Domain
In this domain activity, students determine the domain of analyticity for given functions. This one-page activity contains five multi-step equations.
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Complex Analysis: Path Independence
In this path independence worksheet, students evaluate contour integrals using the Cauchy-Goursat Theorem. This two-page worksheet contains approximately 5 problems.
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Exponents - Week 1
In this exponent worksheet, pupils add, subtract, multiply and divide exponents. They solve problems containing negative exponents, fractional exponents, and polynomials. This two-page worksheet contains eight problems.
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Complex Analysis: Cauchy's Residue Theorem
In this residue theorem worksheet, students find the poles of a function classify all singularities of a function, and compute the residues of that function. This two-page worksheet contains explanations and examples, as well as five...
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Complex Analysis: Compute Residues
In this residue worksheet, students use the Laurent series formula to compute residues. This two-page worksheet contains five problems.
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Complex Analysis: Improper Integral
In this improper integral activity, students evaluate improper integrals and its limits. They evaluate improper integrals using contour integration and define the Cauchy Principal Value. This two-page activity contains explanations and...
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Complex Analysis: Applications of Cauchy-Goursat
In this Cauchy-Goursat worksheet, students evaluate integrals, sketch the contour and explain the methods used to evaluate the problem. This two-page worksheet contains approximately six problems.
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Complex Analysis: Analyticity and Harmonic Functions
In this harmonic function worksheet, students summarize the theorems on analyticity, differentiability and the Cauch-Rieman equation. They identify the characteristics of a harmonic function. This three-page worksheet contains...
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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: Functions
In this function worksheet, students find the residues of all singularities of a given function. They use Cauchy's Second Residue Theorem to evaluate the functions. This four-page worksheet contains explanations and examples, with...
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Complex Analysis: Understanding Contour Integration
In this integration instructional activity, students evaluate contour integrals using the parameterization method. They describe various related theorems. This two-page instructional activity contains approximately eight problems.
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The Number System
Review complex numbers, real numbers, irrational and rational numbers, integers, and whole numbers with math students. Use this guide as a reference sheet or handout.
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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: Complex Variables
In this complex variable worksheet, students find the harmonic function of a problem. This two-page worksheet contains explanations and examples, as well as three problems.
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Complex Analysis: Functions
In this function activity, students complete complex trigonometric functions. They use hyperbolic trigonometric functions to solve problems. This two-page activity contains eight problems with examples and explanations.
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Complex Analysis: Homework Set 6 - Cauchy's Residue Theorem
In this residue theorem learning exercise, students find the maximum and minimum values of functions. They use Cauchy's Residue Theorem to evaluate integrals of functions. This two-page learning exercise contains eleven multi-step...
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Complex Analysis: Applications of Cauchy-Goursat Theorem
In this Cauchy-Goursat Theorem, students sketch and classify domains. They evaluate integrals and explore the analytic function. This two-page worksheet contains approximately ten problems.
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Complex Analysis: Contour Integration
In this contour integration worksheet, students identify and explain theorems used with evaluating contour integrals. This two-page worksheet contains ten problems.
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Complex Analysis: Cauchy's Integral Formula
In this integral formula worksheet, students evaluate integrals. This worksheet contains examples and explanations of Cauchy's Integral Formula, as well as higher derivatives of analytical functions. There are nine problems on this...
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Complex Analysis: Using Laurent Series
In this Laurent series worksheet, students use the Laurent Series to evaluate residues. This two-page worksheet contains five equations.
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