- Stressed Out - Slope as Rate of Change
- Rate of change of slope (ie derivative of derivative or "second derivative") corresponds to curvature (See also CurvatureCircle@ies), so knowledge of the derivative and second derivative of a function can help us to produce a quick qualitatively correct picture of its graph.
- Rates of change are also useful for estimating actual changes (as eg when we estimate the actual distance travelled over a small time intercval by multiplying instantaneous speed at some point by the length of the time interval). This is also useful for controlling the errors involved in various methods of approximation.
- 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)
- 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
- 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
- PrecalParamEqs@langara
- PrecalPolars@langara
- 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)

Why Slopes -- A Calculus Preview for Algebra Students

Slopes are relevant also to problems of reflection

Derivatives
-- Introduction -- Curved Mirrors

The Coffeecup
Caustic

And the slope of a graph is undefined or zero at any extreme (high or
low) point.

So derivatives are useful for locating maxima and minima of functions.
ie for Optimization problems. See also derivCubics@ies

(see also Average
and Instantaneous Rates above)

So derivatives are useful for locating maxima and minima of functions. ie for Optimization problems. See also derivCubics@ies

Rate of change of slope (ie derivative of derivative or "second derivative") corresponds to curvature (See also CurvatureCircle@ies), so knowledge of the derivative and second derivative of a function can help us to produce a quick qualitatively correct picture of its graph.

Area Inside a Parametric Curve(MathCad+QT@odu)

- L'Hopital's
rule@ies

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 | ....... | Give Feedback | ....... | Return to Langara College Homepage |

- Introduction to Derivative Concept (@ubc)
- Intro to Derivative from Hofstra project
- Derivatives Intro @PWS
- 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
- 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
- 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)
- What does the derivative tell us about a function?(@ubc)
- Pickthe correct derivative! by David Yuen
- CurvatureCircle@ies
- LnGraphCircle@ies
- ProdRule@ies
- derivCubics@ies
- Introduction to Derivatives Computation(@ubc)
- Differentiating Linear Functions
- Differentiating Sums(@ubc)
- Differentiating Products(@ubc)
- Differentiating Quotients(@ubc)
- 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)
- PrecalcTrigFunctions@langara
- DerivSin@ies
- TheDerivetaive of the Sine
- derivSinAnimation@odu
- Derivatives of Trigonometric functions(@ubc)
- Inverse Trigonometric Functions(@ubc)
- Relative Motion@upenn
- Composite Functions@ies
- ChainRule@ies
- The Chain Rule(@ubc)
- Implicit Differentiation(@ubc)
- Applications of The Chain Rule(@ubc)
- MVT@ies