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  • OH.TMM.0006.Core.4
Calculus II Course Content
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The Calculus II course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in February 2019. The course is part of the Ohio Transfer Module and is also named TMM006. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadJim Fowler                                         Ohio State UniversityRita Ralph                                         Columbus State Community CollegeContent ContributorsNela Lakos                                       Ohio State UniversityBart Snapp                                       Ohio State UniversityJames Talamo                                  Ohio State UniversityXiang Yan                                         Edison State Community CollegeLibrarianDaniel Dotson                                    Ohio State University                     Review TeamThomas Needham                             Ohio State UniversityCarl Stitz                                            Lakeland Community CollegeSara Rollo                                         North Central State College

Subject:
Mathematics
Calculus
Material Type:
Full Course
Provider:
Ohio Open Ed Collaborative
Date Added:
09/26/2018
Calculus II Course Content, Absolute and conditional covergence, Absolute and conditional convergence module
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Determine if a series converges absolutely or conditionally.Answer conceptual questions about absolute convergence 

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Alternating series, Alternating series modules
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Determine if a series converges using the alternating series test.Determine if a series converges absolutely.Determine if a series converges conditionally.Determine if an alternating series diverges.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Approximating functions with polynomials, Approximating functions with polynomials module
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Compute Taylor polynomials.Use Taylor’s theorem to estimate the error of a Taylor polynomial.Determine the maximum error between a function and a given Taylor polynomial.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, A review of integration, A review of integration modules
Conditional Remix & Share Permitted
CC BY-NC
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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
Conditional Remix & Share Permitted
CC BY-NC
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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, Comparison tests, Comparison tests modules
Conditional Remix & Share Permitted
CC BY-NC
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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, Integral and divergence tests, Integral and divergence tests module
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Use the integral test to determine that a series diverges.Use integrals to estimate the value of a series within an error.Use the divergence test to determine that a series diverges.Manipulate series using the properties of convergent series.Recognize known convergent or divergent series.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Power series, Power Series Module
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Give the definition of a power series.Find the interval and radius of convergence of a power series.Express functions as power series.Express power series as closed-form functions.Differentiate and integrate power series.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Putting it all together, Putting it all together module
Conditional Remix & Share Permitted
CC BY-NC
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The various concepts associated with sequences and series are reviewed.All of the series convergence tests we have used require that the underlying sequence (an)(an) be a positive sequence. We can actually relax this and state that there must be an N>0N>0 such that an>0an>0 for all n>Nn>N; that is, (an)(an) is positive for all but a finite number of values of nn. We’ve also stated this by saying that the tail of the sequence must have positive terms. In this section we explore series whose summation includes negative terms.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Ratio and root tests, Ratio and root tests modules
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Use the ratio test to determine if a series diverges or converges.Use the root test to determine if a series diverges or converges.Determine when to use the ratio or root test.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Sequences, Sequences Modules
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Define a sequence.Write the first several terms of a sequence using an explicit formula.Write the first several terms of a sequence using a recurrence relation.Find an explicit formula for a sequence given recursively.Find a recurrence relation for a sequence given explicitly.

Subject:
Calculus
Material Type:
Module
Date Added:
07/25/2019
Calculus II Course Content, Sequences as functions, Sequences as functions module
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Recognize sequences can be generated by functions.Compute limits of sequences.Understand growth rates of basic sequences.Introduce important terminology for sequences.Apply the monotone convergence theorem 

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
Calculus II Course Content, Sums of sequences, Sums of sequences modules
Conditional Remix & Share Permitted
CC BY-NC
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After completing this section, students should be able to do the following.Define a series.Recognize a geometric series.Recognize a telescoping series.Compute the sum of a geometric series.Compute the sum of a telescoping series.

Subject:
Calculus
Material Type:
Module
Date Added:
07/26/2019
MATH 1152 CSCC Calculus 2
Unrestricted Use
CC BY
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This is a Calculus II interactive textbook with modules curated and created on The Ohio State University's Ximera platform.

The software upon which this interactive textbook was built is licensed under a GNU General Public License v.2.0, and therefore this resource caries the same license. Pursuant to this license, no warranties are made.

Review the license terms at https://github.com/XimeraProject/server/blob/master/LICENSE

Subject:
Mathematics
Calculus
Material Type:
Textbook
Provider:
Columbus State Community College
Author:
Kevin James
Lee Wayand
The Ximera Project
Tzy-Yi "Alan" Yang
Date Added:
01/10/2020