Download - (Trigonometry) Amplitude, Frequency, Phase (PreCalculus ...mathsci2.appstate.edu/~osbornejm/MathematicaDemo... · Slide1of56 (Welcome to Mathematica) Description: In this demo, some

of 56 (Welcome to Mathematica)Description: In this demo, some quick facts and examples are given to introduce you to Mathematica.

Quick Facts:* Site license for student and faculty personal machines:(http://support.appstate.edu/software/mathematica-wolfram)

* Hands-On Start to Mathematica video tutorials:(http://www.wolfram.com/broadcast/screencasts/handsonstart)

* Mathematica Demo Central written tutorials: (http://mathsci2.appstate.edu/~osbornejm/CourseLinks.html ! MathematicaDemoCentral)

Quick Examples (screen shot):

MathematicaDemoCentral.nb 3

Slide 2 of 56 (Trigonometry) Amplitude, Frequency, PhaseDescription: In this demo, you can explore the functions of the form Acos($t+%) for your choice of amplitude A, frequency $ and phase %

4 MathematicaDemoCentral.nb

Slide 3 of 56 (PreCalculus) Average Rate of ChangeDescription: In this demo, you can pick a function f(t) and exlorethe Average Rate of Change in f(t)=Δy/Δt=(y2-y1)/(t2-t1) over for various time spacings. This demo should help to lay the foundationfor the relationship of the ARoC and the instantaneous rate of change.


of 56 (PreCalculus) Power and Exponential Comparisions Description: In this demo you can explore the growth rate of a power functionto an exponential function


Slide 5 of 56 (Calculus I) Average VelocityDescription: In this demo, you can explore the Average Rate of Changein the position function of an object thrown in a uniform gravitational fieldover for various time spacings. This demo should help to lay the foundationfor the relationship of the ARoC and the instantaneous velocity.


Slide 6 of 56 (Calculus1) Position Velocity AccelerationDescription: For a defined function s(t), watch Calculus Man move left/right in position.


Slide 7 of 56 (Calculus1) Tangent LinesDescription: For a defined function, explore the concept and equation of the tangent line and relationshipof the derivative of a function to the slope of the tangent line


of 56 (CalculusI) First and Second DerivativesDescription: For a defined function, explore the relationship of the slope of the tangent line and the concavity of the function with the first and second derivatives of the function.


Slide 9 of 56 (Calculus1) Riemann SumsDescription: For a defined function and for choice of left, middle,or right endpoints, explore the idea behind Riemann sums to discover the relationship of the signed area of a large number of rectangles to the exact signed area of a function on a given interval.


Slide 10 of 56 (CalculusI) Area Function and AntiDerivatives Description: For a defined function, explore the relationship betweenthe area function (obtained by the Fundamental Theorem of Calculus)to the signed area.


Slide 11 of 56 (CalculusI) Linear and Quadratic ApproximationsDescription: For a defined function, compute the linear and quadratic approximationsto a function at various points to build understanding about why the second derivative testfor local maximan and local minima works the way it does.
