Motivation for Derivatives

Langara College - Department of Mathematics and Statistics

Internet Resources for the Calculus Student

Derivatives

Why Slopes? -- A Calculus Preview for Algebra Students
Stressed Out - Slope as Rate of Change
Derivatives -- Introduction -- Curved Mirrors
The Coffeecup Caustic
Cool Math - Calculus 1 Links

Intro to Concept and Definition

Introduction to Derivative Concept (@ubc)

Intro to Derivative from Hofstra project

Derivatives Intro @PWS
'Derivative' entry in Eric Weisstein's CRC Encyclopedia of Mathematics

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

Applications of Derivatives

Limits

L'Hopital's rule@ies

Rates of Change

Motion

Trace of Shadow@ies
Rolling Ball Applet (@uPenn)
Projectile Applet byDanSloughter@furman
DampedHarmonic Motion (mass on spring)
Motion of a piston - An application of differential calculus in robotics(@bcit)

Related Rates

Approximation

Affine Approx Applet byDanSloughter@furman
(graphics.h...fferential)byDougArnold@pennState
(graphics-j...fferential)byDougArnold@pennState
Newton's Method Applet byDanSloughter@furman
Newton's Method(@ubc)
Calculus Online@ubc: M100Lab 5(N'sMethod, &Euler's)
Calculus Online@ubc: M100Lab 5 - Grades and Solutions
Calculus Online@ubc: M100Lab 6(Lin,Quad,&Taylor)
Calculus Online@ubc: M100Lab 6 - Grades and Solutions
Calculus Online@ubc: M101Lab 6(TaylorPolys&Series)
Calculus Online@ubc: M101Lab 6 Solutions
Taylor Series @Eric'sTreasureTroves
Taylor Polys Applet byDanSloughter@furman: Bisection Method Tutorial

Optimization

MathsOnlineGallery (@uVienn.austria) SimpleMaxAreaProblem
f+1/f &AGMineq@ies
EquilibriumTheory for Econ byOsborne@UofT
Optimization for Economics byOsborne@UofT
VisualFit Applet (re LeastSquares)byTaur@JSE

Graphing

PrecalPolars@langara

Miscellaneous

Derivatives-- Introduction -- Curved Mirrors
The Zebra Danio and its escape response(@ubc)
Two examples of differential calculus in electronics(@bcit)
An Application of Differential Calculus to Food Technology(@bcit)

Review Contents of Math&Stats Dep't Website

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