Math 195 - Chapter 2

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Section 2.1 – The Tangent and Velocity Problems
- Read pp. 85 – 89
- online resources:
  1. Secant Line - http://www.math.gatech.edu/~carlen/applets/unarchived/ClassFiles/Secant.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  2. Secant Line and Tangent Line - http://www.ies.co.jp/math/java/calc/limsec/limsec.html
    This site provides a java applet designed for experimenting with secant and tangent lines.
  3. SecantTangent Applet - http://www.calvin.edu/~rpruim/courses/m161/F01/java/SecantTangent.shtml
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  4. A Secant to Tangent Applet - http://www.slu.edu/classes/maymk/Applets/SecantTangent.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  5. Army vs Navy: The Long Trip – Secants and Tangents - http://www.dean.usma.edu/math/research/mathtech/java/ArmyNavyProject/armynavyprojectpage.html
    The following applet demonstrates the relationship between secants and tangents, average rate of change and instantaneous rate of change, and average velocity and instantaneous velocity.
  6. Average Rate of Change and Derivatives - http://www.ies.co.jp/math/java/calc/heihen/heihen.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
Section 2.2 – The Limit of a Function
- Read pp. 90 – 99
- online resources:
  1. Generating Tables to Demonstrate Limits - http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/limits.html
    This site provides a java applet which demonstrates the limit of a function f(x) at x = c by generating tables of values of f(x) for values of x near c.
  2. Computing a Limit - http://mss.math.vanderbilt.edu/cgi-bin/MSSAgent/~pscrooke/MSS/limit.def
    This site provides java applet that attempts to compute the limit of a function or either directional limit.
Section 2.3 – Calculating Limits Using Limit Laws
- Read pp. 102 – 109
- online resources:
  1. What are the properties of limits? - http://cne.gmu.edu/modules/dau/calculus/limits/limits2_frm.html
    This site provides a discussion of the various limit laws.
Section 2.4 – The Precise Definition of a Limit
- Note: this section is not part of the syllabus. Here are some good references for the epsilon-delta definition of a limit
- online resources:
  1. EpsilonDelta Applet - http://math.hws.edu/javamath/config_applets/EpsilonDelta.html
    This site provides a java applet designed to help users understand the epsilon/delta definition of a limit.
  2. An EpsilonDelta Applet - http://www.slu.edu/classes/maymk/Applets/EpsilonDelta.html
    This site is desigend for a visual exploration of the Epsilon Delta definition of continuity. The user highlights an epsilon and delta band around a proposed limit of a function at a point.
Section 2.5 – Continuity
- Read pp. 122 – 130
- online resources:
  1. Java Applet: Illustrating Continuity - http://www.shu.edu/projects/reals/cont/answers/javaCont1.html
    This site provides a java applet that illustrates continuity.
  2. 2^nd Degree / 2^nd Degree - http://id.mind.net/~zona/mmts/functionInstitute/rationalFunctions/simple2Over2/2ndDegreeOver2ndDegree.html
    This site provides a java grapher that which demonstrates the behavior of a rational function including a discussion on removable discontinuities and vertical asymptotes.
  3. Continuity - http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/awl/contin-main.html
    This site provides a java applet that explores continuity of a function f(x) by comparing the value of the function at x = c to values of the function for x approaching c.
  4. Continuity Checker - http://sciris.shu.edu/thinklets/Math/Calculus/IRA/Continuity.html
    This site provides a java applet to investigate whether a given function is continuous at a point or uniformly continuous.
  5. The Intermediate Value Theorem (IVT) - http://www.sosmath.com/calculus/limcon/limcon06/limcon06.html
    This site provides a good discussion of the IVT.
  6. Bisection Method Tutorial - http://www.cs.utah.edu/~zachary/isp/applets/Root/Bisection.html
    This site provides a discussion and a java applet to explore the bisection method for finding the roots of equations. This is an application of the IVT.
  7. Proofs of Intermediate Value Theorem (IVT) and Bolzano Theorem (BT) - http://www.cut-the-knot.org/Generalization/ivt.shtml
    This site provides proofs of IVT and BT.
Section 2.6 – Limits at Infinity; Horizontal Asymptotes
- Read pp. 133 – 144
- online resources:
  1. Asymptotes of Rational Functions - http://mss.math.vanderbilt.edu/cgi-bin/MSSAgent/~pscrooke/MSS/asymptotes.def
    This site provides an applet which finds the vertical and horizontal asymptotes of a rational function. It also graphs the function.
Section 2.7 – Tangents, Velocities, and Other Rates of Change
- Read pp. 147 – 153
- online resources:
  1. Secant Line - http://www.math.gatech.edu/~carlen/applets/unarchived/ClassFiles/Secant.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  2. Secant Line and Tangent Line - http://www.ies.co.jp/math/java/calc/limsec/limsec.html
    This site provides a java applet designed for experimenting with secant and tangent lines.
  3. SecantTangent Applet - http://www.calvin.edu/~rpruim/courses/m161/F01/java/SecantTangent.shtml
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  4. A Secant to Tangent Applet - http://www.slu.edu/classes/maymk/Applets/SecantTangent.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
  5. Army vs Navy: The Long Trip – Secants and Tangents - http://www.dean.usma.edu/math/research/mathtech/java/ArmyNavyProject/armynavyprojectpage.html
    The following applet demonstrates the relationship between secants and tangents, average rate of change and instantaneous rate of change, and average velocity and instantaneous velocity.
  6. Average Rate of Change and Derivatives - http://www.ies.co.jp/math/java/calc/heihen/heihen.html
    This site provides a java applet designed for experimenting with secant lines and the secant line approximation to the tangent.
Section 2.8 – Derivatives
- Read pp. 156 – 161
- online resources:
  1. Derivative Definition Java Applet - http://www.csulb.edu/~wziemer/TangentLine/TangentLine.html
    This site provides a java applet which shows the convergence of the difference quotient to the derivative, i.e. the convergence of the secant line to the tangent line, as h tends to zero.
Section 2.9 – The Derivative as a Function
- Read pp. 163 – 170
- online resources:
  1. Graphing the Derivative - http://people.hofstra.edu/faculty/Stefan_Waner/calctopic1/derivgraph.html
    This site provides a The following example shows us how to sketch the graph of f ^'(x) from a knowledge of the graph of f(x).
  2. What does f ^'(x) say about f(x)? - http://www.dean.usma.edu/math/research/mathtech/java/FandFPrimeProject/fandfprimepage.htm
    This site provides a java applet that illustrates the relationship between a function and its derivative.

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