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APEX Calculus
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APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

Subject:
Calculus
Material Type:
Textbook
Provider:
APEX: Affordable Print and Electronic TeXtbooks
Author:
Brian Heinold
Dimplekumar Chalishajar
Gregory Hartman
Troy Siemers
Date Added:
01/01/2014
APEX PreCalculus
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This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.

Subject:
Calculus
Material Type:
Textbook
Author:
Amy Givler Chapman
Jessica Libertini
Meagan Herald
Date Added:
04/27/2020
Active Calculus
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Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Mathematics
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matt Boelkins
Steve Schlicker
Date Added:
04/27/2020
Active Calculus Multivariable
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Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matthew Boelkins
Steven Schlicker
Date Added:
07/01/2018
Calculus
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Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.

Subject:
Mathematics
Calculus
Material Type:
Full Course
Provider:
MIT
Author:
Gilbert Strang
Date Added:
01/01/1991
Calculus-Based Physics I
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Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students.

Subject:
Calculus
Physics
Material Type:
Textbook
Provider:
Saint Anselm College
Author:
Jeffrey Schnick
Date Added:
04/27/2020
Calculus I Course Content
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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 

Subject:
Mathematics
Calculus
Material Type:
Full Course
Provider:
Ohio Open Ed Collaborative
Date Added:
09/26/2018
Calculus I Course Content, An application of limits, An application of limits modules
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After completing this section, students should be able to do the following.Compute average velocity.Approximate instantaneous velocity.Compare average and instantaneous velocity.Compute instantaneous velocity.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
06/28/2019
Calculus I Course Content, Antiderivatives, Antiderivatives Modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/03/2019
Calculus I Course Content, Antiderivatives and area, Antiderivatives and area modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/05/2019
Calculus I Course Content, Application of integrals, Application of integrals modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/05/2019
Calculus I Course Content, Applied related rates, Applied related rates modules
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After completing this section, students should be able to do the following.Identify word problems as related rates problems.Translate word problems into mathematical equations.Solve related rates word problems.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/02/2019
Calculus I Course Content, Approximating the area under a curve, Approximating the area under a curve modules
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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→∞ .

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/03/2019
Calculus I Course Content, Chain rule, Chain rule modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/02/2019
Calculus I Course Content, Computations for graphing functions, Computations for graphing functions modules
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After completing this section, students should be able to do the following.Find the intervals where a function is increasing or decreasing.Find the intervals where a function is concave up or down.Determine how the graph of a function looks without using a calculator.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/02/2019
Calculus I Course Content, Concepts of graphing functions, Concepts of graphing functions modules
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After completing this section, students should be able to do the following.Understand what information the derivative gives concerning when a function is increasing or decreasing.Understand what information the second derivative gives concerning concavity of the graph of a function.Interpret limits as giving information about functions.Determine how the graph of a function looks based on an analytic description of the function.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/02/2019
Calculus I Course Content, Continuity and the Intermediate Value Theorem, Continuity and the Intermediate Value Theorem Modules
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After completing this section, students should be able to do the following.Identify where a function is, and is not, continuous.Understand the connection between continuity of a function and the value of a limit.Make a piecewise function continuous.State the Intermediate Value Theorem including hypotheses.Determine if the Intermediate Value Theorem applies.Sketch pictures indicating why the Intermediate Value Theorem is true, and why all hypotheses are necessary.Explain why certain points exist using the Intermediate Value Theorem.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
06/28/2019
Calculus I Course Content, Definite integrals, Definite integrals modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/03/2019
Calculus I Course Content, Definition of the derivative, Definition of the derivative modules
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After completing this section, students should be able to do the following.Use limits to find the slope of the tangent line at a point.Understand the definition of the derivative at a point.Compute the derivative of a function at a point.Estimate the slope of the tangent line graphically.Write the equation of the tangent line to a graph of a function at a given point.Recognize and distinguish between secant and tangent lines.Recognize the the tangent line as a local approximation for a differentiable function near a point.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
06/28/2019
Calculus I Course Content, Derivatives as functions, Derivatives as functions modules
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After completing this section, students should be able to do the following.Understand the derivative as a function related to the original definition of a function.Find the derivative function using the limit definition.Relate the derivative function to the derivative at a point.Explain the relationship between differentiability and continuity.Relate the graph of the function to the graph of its derivative.Determine whether a piecewise function is differentiable.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
06/28/2019
Calculus I Course Content, Derivatives of inverse functions, Derivatives of inverse functions modules
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After completing this section, students should be able to do the following.Find derivatives of inverse functions in general.Recall the meaning and properties of inverse trigonometric functions.Derive the derivatives of inverse trigonometric functions.Understand how the derivative of an inverse function relates to the original derivative.Take derivatives which involve inverse trigonometric functions.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/02/2019
Calculus I Course Content, First fundamental theorem of calculus, First fundamental theorem of calculus modules
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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.

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
07/05/2019
Calculus I Course Content, Higher order derivatives and graphs, Higher order derivatives and graphs modules
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After completing this section, students should be able to do the following.Use the first derivative to determine whether a function is increasing or decreasing.Define higher order derivatives.Compare differing notations for higher order derivatives.Identify the relationships between the function and its first and second derivatives.Sketch a graph of the second derivative, given the original function.Sketch a graph of the original function, given the graph of its first or second derivative.Sketch a graph of a function satisfying certain constraints on its higher-order derivatives.State the relationship between concavity and the second derivative.Interpret the second derivative of a position function as acceleration.Calculate higher order derivatives.Given the graph of a position function, find time intervals where the velocity is positive/negativeGiven the graph of a position function, find time intervals where the velocity is increasing/decreasing

Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Date Added:
06/28/2019