The Calculus I 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 TMM005. For more information about credit transfer between Ohio colleges and universities, please visit: transfercredit.ohio.gov.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 

After completing this section, students should be able to do the following.Define linear approximation as an application of the tangent to a curve.Find the linear approximation to a function at a point and use it to approximate the function value.Identify when a linear approximation can be used.Label a graph with the appropriate quantities used in linear approximation.Find the error of a linear approximation.Compute differentials.Use the second derivative to discuss whether the linear approximation over or underestimates the actual function value.Contrast the notation and meaning of dydy versus ΔyΔy.Understand that the error shrinks faster than the displacement in the input.Justify the chain rule via the composition of linear approximations.