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MAC 2312: Calculus With Analytic Geometry II: Home

This guide is designed to help FSCJ students do research for their MAC 2312 Calculus class and to help students and faculty find calculus open educational resources in the library and on the Internet.

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MAC 2312: Calculus with Analytic Geometry II

MAC 2312 - Calculus With Analytic Geometry II

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FSCJ Library books, eBooks, Open Educational Resources (OERs), articles, streaming media and web sites related to Calculus with Analytic Geometry


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Objectives of This Guide

This guide contains links to information resources related to Calculus and Analytic Geometry, including indexes and databases that can be used to find publications, reference works, data resources, style guides, and pages linking to resources on specific topics in Calculus.

We hope you find it helpful for all your research needs in the study of Calculus.

Find Books

The following links will take you to books, videos and other library materials available from the library on that topic:

Find Articles

Find Videos

FSCJ Library has a great many videos on  Mathematics and Calculus through our Films on Demand Database. Simply click the link and explore our ON DEMAND Video Library.

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Quick Links

Books and eBooks

Books from the Library

Ebooks from the Library

Weblinks

Concepts

Review of Integration

Basic Integration Problems

Antiderivatives / Indefinite Integrals

Antiderivatives / Indefinite Integrals

 

A tutorial on antiderivatives and indefinite integrals. Covers the Uniqueness Theorem, inverse property and applications of indefinite integrals.

A tutorial on slope fields with an interactive JAVA applet to explore slope fields.

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus

 

Tutorial on the Fundamental Theorem of Calculus.

Applications of Integration

Area Between Two Curves

 

Tutorial on finding the area bounded by the graphs of two or more functions.
  • Using a TI-85 graphing calculator to find the area between two curves.
    Discussion [Using Flash] [Using Java]
  • Drill problems on finding the area bounded by the graphs of two or more functions.
  • Computer programs that graphically illustrate the area between two curves.
  • Tutorial on finding the area bounded by a parametric curve.
    [Using Flash] [Using Java]
  • Computer programs that graphically illustrate the area bounded by a parametric curve.
  • Computer programs that graphically illustrate the area bounded by a parametric curve.
  • Tutorial on finding the area bounded by a polar curve.
  • Computer programs that graphically illustrate the area between two curves in polar coordinates.

 

Volumes

 

Tutorial on the slab or washer method for finding volumes.
  • Animation illustrating the slab or disk method for finding volumes.
  • Computer programs that draw the solid of revolution of an area rotated about the x-axis.
  • Computer programs that graphically illustrate the slab method for finding volumes.

 

Tutorial on the cylindrical shell method for finding volumes.
  • Computer programs that graphically illustrate the cylindrical shell method for finding volumes.

 

Arc Length - 1

 

Tutorial on arc length.

 

Average Value of a Function

 

Tutorial on finding the average value of a function.

 

Work

 

Tutorial on work.

 

Moments and Center of Mass

 

Tutorial on moments and center of mass.

Areas

Areas

 

A tutorial on how to find areas and approximation to areas by using inscribed and circumscribed rectangles.
  • An animation illustrating the approximation of the area under the sine function by inscribed and circumscribed rectangles.
  • An animation illustrating the approximation of the area under a parabola by inscribed and circumscribed rectangles.
  • A computer program that illustrates the approximation of the area of a circle using inscribed polygons.
  • An animation showing the approximation of the area of a circle using inscribed polygons.
  • A computer program that graphically illustrates the Monte Carlo Method to find areas.

Definite Integrals

Definite Integrals

 

A tutorial on the definition of definite integrals, properties of definite integrals, relationship between definite integrals and areas and the use of technology to evaluate definite integrals using the definition.

Techniques of Integration

Techniques of Integration - Substitution

 

Tutorial on integration using the method of substitution.

Techniques of Integration / Integration by Parts

Techniques of Integration - Integration by Parts

 

Tutorial on using Integration by Parts.

Techniques of Integration / Reduction Formulas

Techniques of Integration - Reduction Formulas

 

Tutorial on deriving and using recursion or reduction formulas.
  • Drill problems for evaluating trigonometric integrals using recursion or reduction formulas.
  • Using Maple to obtain some reduction formulas.

Techniques of Integration / Partial Fractions

Techniques of Integration - Partial Fractions

 

Tutorial on the method of Partial Fractions.

Riemann Sums

Riemann Sums

 

A tutorial on riemann sums from the graphical point of view followed by a tutorial from a symbolic or algebraic point of view.

Numerical Integration

Numerical Integration

 

Tutorial on numerical integration.

 

Tutorial on numerical integration and error bounds.

Improper Integrals

Improper Integrals

 

Tutorial on improper integrals over unbounded intervals.

 

Tutorial on improper integrals of functions with discontinuities.

Open Educational Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

Diff. & Int. of Inverse Trig & Hyperbolic Functions

Applications of the Derivative

Differentials

Differentials

 

Tutorial on differentials.
  • Drill on using differentials to approximate expressions.

Optimization Problems

Optimization Problems

 

  • Java applets illustrating the solution to finding the maximum area of a rectangle which can be inscribed in a semicircle.
  • Java applet illustrating the solution to finding the longest ladder which can be carried through a hallway with a corner.
  • Java applet illustrating the solution to finding the shortest time to move through the desert to a town.
  • Java applet illustrating the solution to finding the shortest ladder that can lean over a fence against a building.

Derivatives of Inverse Functions

Derivatives of Inverse Functions

 

Tutorial on finding the derivatives of inverse functions.
  • Drill on finding the derivative and the tangent line to the inverse of a function.

Derivatives and Inverses of Trigonometric Functions

Derivatives and Inverses of Trigonometric Functions

 

Tutorial on finding the derivatives of the inverse trig functions.

Maxima and Minima

Maxima and Minima

 

Tutorial on finding the maxima and minima of a function on a closed interval.
  • Drill on finding the maxima and minima of a function on a closed interval.

Mean Value Theorem

Mean Value Theorem

 

Tutorial on the Mean Value Theorem; includes Rolle's Theorem and the First Derivative Test.
  • Drill on applying the Mean Value Theorem.
  • Drill on using the First Derivative Test.
  • Drill on determining the intervals of concave upward and concave downward and the inflection points of a function.
  • Computer programs that can be used to illustrate the Mean Value Theorem. Also,

Open Educational Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

More applications of integration

Volumes by shells and disks

Tutorial on the slab or washer method for finding volumes.
  • Animation illustrating the slab or disk method for finding volumes.
  • Computer programs that draw the solid of revolution of an area rotated about the x-axis.
  • Computer programs that graphically illustrate the slab method for finding volumes.

 

Tutorial on the cylindrical shell method for finding volumes.
  • Computer programs that graphically illustrate the cylindrical shell method for finding volumes.

Arc length

Tutorial on arc length.

Centroids and moments

Tutorial on moments and center of mass.

Work

Tutorial on work.

Open Educational Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

Techniques of Integration

Integration Techniques

Trig substitutions

Tutorial on integration using the method of substitution.

Integration by parts

Tutorial on using Integration by Parts.

Partial fractions

Tutorial on the method of Partial Fractions.

Review of u-substitution

Trigonometric integrals

Tutorial on improper integrals over unbounded intervals.

 

Tutorial on improper integrals of functions with discontinuities.

L’Hopital’s Rule

L'Hopital's Rule

 

  • Drill on applying L'Hopital's Rule. (Using finite limits)
  • Drill on applying L'Hopital's Rule. (Using infinite limits)

Open Education Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

Sequences and Series

Sequences

Tutorial on sequences.

Converegence/Divergence of Sequences

Tutorial on absolute convergence.

 

Drill problems on determining which test to use for convergence of a series.

Ratio Test/ Root Test

Tutorial on the Ratio Test.

Series

Tutorial on introductory material on series.

Integral Test

Tutorial on the Integral Test.

Alternating Series

Tutorial on alternating series.

Comparison Test/Limit Comparison Test

Tutorial on Comparison Test for testing convergence of series.

 

Tutorial on the Limit Comparison Test.

Taylor/Maclaurin series

Tutorial on Taylor polynomials.

Power Series

Tutorial on Power Series.

 

Tutorial on differentiation and integration of power series.

Open Education Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

Review of Differentiation

Definition of a Derivative

Definition of Derivative

 

Tutorial on the definition of derivative.

Calculus Derivatives Khan Academy

Tangent Lines

Tangent Lines

 

Tutorial on tangent lines as an introduction to the derivative.

Differentiation Formulas

Differentiation Formulas

 

Tutorial on elementary differentiation formulas, their derivation and use. Includes the Power Formula.

Derivative of the Exponential Function

Derivative of the Exponential Function

 

Tutorial on the calculation of the derivative of the exponential function.
  • A LiveMath notebook illustrating the finding of the derivative of an exponential function at x = 0.
  • JavaScript exploration of the numerical estimates of the slope of the tangent line to the exponential function.

Quotient Rule

Quotient Rule

 

Tutorial on the Quotient Rule.
  • A LiveMath notebook which illustrates the use of the quotient rule.
  • Drill problems for differentiation using the quotient rule.

Definition of a Derivative at a Point

Definition of Derivative at a Point

 

Tutorial on the definition of derivative at a point.
  • Using the definition of derivative at a point, calculate the derivative of a quadratic at a point.
    [Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer]
  • Using the definition of derivative at a point, calculate the derivative of a square root of a function at a point.
    [Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer]
  • Using the definition of derivative at a point, calculates the derivative of a rational function at a point.
    [Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer]
  • A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a quotient at a specific point.
  • A LiveMath Notebook which, using the definition of derivative at a point, investigates the derivative of x2/3 at x = 0.
  • A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a radical at a specific point.
  • Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point.
  • Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point. In this case, the function is not differentiable at the given point.
  • Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point. In this case, the function is not differentiable at the given point but the limit of the symmetric difference quotient exists.

Linear Approximations

Linear Approximations

 

Tutorial on the accuracy of a linear approximation.

Product Rule

Product Rule

 

Tutorial on the Product Rule.
  • A LiveMath notebook which illustrates the use of the product rule.
  • Drill problems for differentiation using the product rule. (Algebraic and exponential functions).

Derivatives of the Trigonometric Functions

Derivatives of the Trigonometric Functions

 

Tutorial on the calculation of the derivatives of the trigonometric functions.
  • Drill problems for differentiation using the product rule. (Emphasis on trigonometric functions).
  • Drill problems for differentiation using the quotient rule. (Emphasis on trigonometric functions).

Derivatives of Functions

Derivatives of Functions

 

The Chain Rule

The Chain Rule

 

Tutorial on the Chain Rule.

Open Educational Resources (OERs)

A great deal of the information for this LibGuide comes from Open Educational Resources (OERs). OERs are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them. OERs range from textbooks to curricula, syllabi, lecture notes, assignments, tests, projects, audio, video and animation.  This page is attributed to Visual Calculus, an OER designed for the study of teaching calculus out of the University of Tennessee. 

Plug-ins
Several plug-ins are needed to view some of the materials on this site.

 

  • There are a large number of MathView notebooks on this site. These notebooks were originally constructed using the MathView program from Maple. Maple sold this program to another company which has renamed the program LiveMath. The LiveMath plug-in is available from theLiveMath site. Even if you have the MathView plug-in, we recommend that you upgrade to the LiveMath plug-in. Eventually, we plan to upgrade each of the MathView notebooks to LiveMath format.

     

  • The Shockwave Flash plug-in is available for free from the Macromedia site. It is available for Macintosh and Windows platforms. The plug-in is now packaged with many browsers. The Flash movies on this site were created with version 4 of Flash; you will need version 4 or higher of the Flash plug-in.

     

  • The IBM TechExplorer plug-in (also known as the IBM TechExplorer Hypermedia Browser) is available from the IBM site. There are two versions: (1) the Introductory Version which is free and (2) the Professional Version which is not free and can be purchased from the IBM site mentioned above. We are in the process of modifying our pages so that either version can be used. For a short time, Maple sold Maple Explorer which contained the professional version of the IBM TechExplorer plug-in. The IBM TechExplorer plug-in is available for Windows, Linux, AIX, Solaris, Mac OS and SGI platforms.

Tutoring Resources

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