Rates of Change

Langara College - Department of Mathematics and Statistics

Internet Resources for the Calculus Student

Rates of Change

You might also check our 'raw list' (of links provided without comment) to see if there are any more examples there that we haven't yet included here.

If you have come across any good web-based illustrations of these and related concepts,
please do let us know and we will add them here.

Review Contents of Math&Stats Dep't Website

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Derivatives

Intro to Concept and Definition

Introduction to Derivative Concept (@ubc)
Intro to Derivative from Hofstra project
Derivatives Intro @PWS

Tangent Slopes

Surfing(Derivatives)@ies
VisualCalculus - Tangent Lines
Animation:all the tangent lines to a curve
Deriv from TanSlope(MathCad+QT@odu)
(graphics.html#tangent)byDougArnold@pennState
(graphics-j.html#tangent)byDougArnold@pennState
MathsOnlineGallery (@uVienn.austria) derivative(asTanSlope)
Why Slopes -- A Calculus Preview for Algebra Students
Derivatives-- Introduction -- Curved Mirrors
Stressed Out - Slope as Rate of Change

Secant Approximation to Tangent Lines

derivDef@ies
Sec&TanLines@ies
DerivativeDefinition Java Applet
JavaDiff(by kThompson@OregonState)
Animation:Secant approaching the Tangent
Tangent Line Applet byDanSloughter@furman
SecantGrapher byJohnOrr@uNebraskaLincoln
Visual Calculus - Tangent as Limit of Secants
(graphics.html#secants)byDougArnold@pennState
(graphics-j.html#secants)byDougArnold@pennState
Our Own Version of the Secant -> Tangent thing
Affine Approx Applet byDanSloughter@furman
derivOneSide@ies

Avg&Inst Rates

Rolling Ball Applet (@uPenn)
Velocity@upenn(withQTmovies)
Relative Motion@upenn
(graphics.html#bounce)byDougArnold@pennState
(graphics-j.html#bounce)byDougArnold@pennState
Derivatives: Rate of change/Learn
Avg&InstRates - from PWS
Calculus Online@ubc: Lab 2(avg&inst rates)
Lab 2 Grades and Solutions

Differentiability

Continuity and Differentiability(@ubc)
MathsOnlineGallery (@uVienn.austria) NowhereDiffble
(graphics-j.html#jagged)byDougArnold@pennState
(graphics.html#jagged)byDougArnold@pennState
Calc 1 pathologies(byTVogel@TexA&M)

Interpretation

What does the derivative tell us about a function?(@ubc)
Pickthe correct derivative! by David Yuen
CurvatureCircle@ies
LnGraphCircle@ies

Some Basic Rules

ProdRule@ies
derivCubics@ies
Introduction to Derivatives Computation(@ubc)
Differentiating Linear Functions
Differentiating Sums(@ubc)
Differentiating Products(@ubc)
Differentiating Quotients(@ubc)

Exp&Log

PrecalcExp&Logs@langara
Karl's Calculus Tutor - 6.1 Be Fruitful and Multiply
S.O.S. Math - Calculus(starts with exp&log)
e(1)@ies
TheNumber e (def by exp'(0)=1)
Derivatives of Exponentials(@ubc)

Trig

PrecalcTrigFunctions@langara
DerivSin@ies
TheDerivetaive of the Sine
derivSinAnimation@odu
Derivatives of Trigonometric functions(@ubc)
Inverse Trigonometric Functions(@ubc)

Chain Rule

Relative Motion@upenn
Composite Functions@ies
ChainRule@ies
The Chain Rule(@ubc)
Implicit Differentiation(@ubc)
Applications of The Chain Rule(@ubc)

Mean Value Theorem

MVT@ies

Derivatives

L'Hopital's rule@ies
Stressed Out - Slope as Rate of Change
Why Slopes -- A Calculus Preview for Algebra Students
Surfing(Derivatives)@ies
SecTan@ies
derivDef@ies
derivOneSide@ies
derivCubics@ies
ProdRule@ies
Composite Functions@ies
ChainRule@ies
e(1)@ies
DerivSin@ies
CurvatureCircle@ies
LnGraphCircle@ies
MVT@ies