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: 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
After completing this section, students should be able to do the following.Define an antiderivative.Compute basic antiderivatives.Compare and contrast finding derivatives and finding antiderivatives.Define initial value problems.Solve basic initial value problems.Use antiderivatives to solve simple word problems.Discuss the meaning of antiderivatives of the velocity and acceleration.
After completing this section, students should be able to do the following.Interpert the product of rate and time as area.Approximate position from velocity.Recognize Riemann sums.
After completing this section, students should be able to do the following.Given a velocity function, calculate displacement and distance traveled.Given a velocity function, find the position function.Given an acceleration function, find the velocity function.Understand the difference between displacement and distance traveled.Understand the relationship between position, velocity and acceleration.Calculate the change in the amount.Compute the average value of the function on an interval.Understand that the average value of the function on an interval is attained by the function on that interval.
After completing this section, students should be able to do the following.Express the sum of n terms using sigma notation.Apply the properties of sums when working with sums in sigma notation.Understand the relationship between area under a curve and sums of areas of rectangles.Approximate area of the region under a curve.Compute left, right, and midpoint Riemann sums with 10 or fewer rectangles.Understand how Riemann sums with n rectangles are computed and how the exact value of the area is obtained by taking the limit as n→∞n→∞ .
After completing this section, students should be able to do the following.Recognize a composition of functions.Take derivatives of compositions of functions using the chain rule.Take derivatives that require the use of multiple rules of differentiation.Use the chain rule to calculate derivatives from a table of values.Understand rate of change when quantities are dependent upon each other.Use order of operations in situations requiring multiple rules of differentiation.Apply chain rule to relate quantities expressed with different units.Compute derivatives of trigonometric functions.Use multiple rules of differentiation to calculate derivatives from a table of values.
After completing this section, students should be able to do the following.Use integral notation for both antiderivatives and definite integrals.Compute definite integrals using geometry.Compute definite integrals using the properties of integrals.Justify the properties of definite integrals using algebra or geometry.Understand how Riemann sums are used to find exact area.Define net area.Approximate net area.Split the area under a curve into several pieces to aid with calculations.Use symmetry to calculate definite integrals.Explain geometrically why symmetry of a function simplifies calculation of some definite integrals.
After completing this section, students should be able to do the following.Define accumulation functions.Calculate and evaluate accumulation functions.State the First Fundamental Theorem of Calculus.Take derivatives of accumulation functions using the First Fundamental Theorem of Calculus.Use accumulation functions to find information about the original function.Understand the relationship between the function and the derivative of its accumulation function.
After completing this section, students should be able to do the following.Use the definition of the derivative to develop shortcut rules to find the derivatives of constants and constant multiples.Use the definition of the derivative to develop shortcut rules to find the derivatives of powers of xx.Use the definition of the derivative to develop shortcut rules to find the derivatives of sums and differences of functions.Compute the derivative of polynomials.Recognize different notation for the derivative.State the derivative of the natural exponential function.State the derivative of the sine function.
After completing this section, students should be able to do the following.State the Second Fundamental Theorem of Calculus.Evaluate definite integrals using the Second Fundamental Theorem of Calculus.Understand how the area under a curve is related to the antiderivative.Understand the relationship between indefinite and definite integrals.
After completing this section, students should be able to do the following.Undo the chain rule.Calculate indefinite integrals (antiderivatives) using basic substitution.Calculate definite integrals using basic substitution.
After completing this section, students should be able to do the following.Determine when a function is a composition of two or more functions.Calculate indefinite and definite integrals requiring complicated substitutions.Recognize common patterns in substitutions.Evaluate indefinite and definite integrals through a change of variables.
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