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: 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
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.
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.
After completing this section, students should be able to do the following.Find the area of a region bound by a polar curve.Find the intersection points of two polar curves.Find the area of a region bound by two polar curves.
After completing this section, students should be able to do the following.Convert between polar and Cartesian coordinates.Plot basic curves in polar coordinates.Use the Cartesian to polar method to plot polar graphs.
Vector-valued functions are parameterized curves.
After completing this section, students should be able to do the following.Sketch a parametric curve.Eliminate a parameters of a parametric equation.Represent a graph with parametric equations.Find the derivative of a parametric curve.
This is a Calculus II interactive textbook with modules curated and created on The Ohio State University's Ximera platform.
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