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Calculus II Course Content, Areas between curves, Areas between curves module
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After completing this section, students should be able to do the following.Apply the procedure of “Slice, Approximate, Integrate” to derive a formula for the area bounded by given curves.Understand the difference between net and total area.Find the area bounded by several curves.Set up an integral or sum of integrals with respect to xx that gives the area bounded by several curves.Set up an integral or sum of integrals with respect to yy that gives the area bounded by several curves.Decide whether to integrate with respect to xx or yy.

Subject:
Calculus
Material Type:
Module
Date Added:
07/24/2019
Calculus II Course Content, A review of integration, A review of integration modules
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After completing this section, students should be able to do the following.Compute derivatives of common functions.Compute antiderivatives of common functions.Understand the relationship between derivatives and antiderivatives.Use algebra to manipulate the integrand.Evaluate indefinite and definite integrals through a change of variables.Evaluate integrals that require complicated substitutions.Recognize common patterns in substitutions.

Subject:
Calculus
Material Type:
Module
Date Added:
07/24/2019
Calculus II Course Content, Calculus and Taylor series, Calculus and Taylor Series Module
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After completing this section, students should be able to do the following.Use Taylor series to read-off derivatives of a function.Use Taylor series to solve differential equations.Use Taylor series to compute integrals.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Calculus and vector-valued functions, Calculus and vector-valued functions module
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With one input, and vector outputs, we work component-wise.A question I’ve often asked myself is: “How do you know when you are doing a calculus problem?” The answer, I think, is that you are doing a calculus problem when you are computing: a limit, a derivative, or an integral. Now we are going to do calculus with vector-valued functions. To build a theory of calculus for vector-valued functions, we simply treat each component of a vector-valued function as a regular, single-variable function. Since we are currently thinking about vector-valued functions that only have a single input, we can work component-wise. Let’s see this in action.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Comparison tests, Comparison tests modules
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After completing this section, students should be able to do the following.Use the comparison test to determine if a series diverges or converges.Use the limit comparison test to determine if a series diverges or converges.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Derivatives of polar functions, Derivatives of polar functions module
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After completing this section, students should be able to do the following.Compute derivatives of polar curves.Determine where the derivative of a polar curve is undefined.Find the equation of a tangent lines to a polar curve.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Differential equations, Differential equations module
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After completing this section, students should be able to do the following.Identify a differential equation.Verify a solution to a differential equation.Compute a general solution to a differential equation via integration.Solve initial value problems.Determine the order of a differential equation. 

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Dot products, Dot products modules
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After completing this section, students should be able to do the following.Compute dot products.Use dot products to compute the angle between vectors.Find orthogonal projections.Find scalar projections.Use the dot product in applied settings.Find orthogonal decompositions.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Exponential models, Exponential Models Modules
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After completing this section, students should be able to do the following.Compute derivatives of common functions.Compute antiderivatives of common functions.Understand the relationship between derivatives and antiderivatives.Use algebra to manipulate the integrand.Evaluate indefinite and definite integrals through a change of variables.Evaluate integrals that require complicated substitutions.Recognize common patterns in substitutions.

Subject:
Calculus
Material Type:
Module
Date Added:
07/25/2019