Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 30 of 33
Full-Text Articles in Physical Sciences and Mathematics
06: Reciprocal Functions, Ruth Dover
06: Reciprocal Functions, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
ReciprocalFunctions.nb asks the user to input a function. The notebook will graph the original function and its reciprocal.
10: Roots Of Unity, Ruth Dover
10: Roots Of Unity, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
RootsOfUnity.nb offers some solutions to x6 -1=0 and then graphs and labels the complex roots of unity up through x8 -1=0 .
07: Tan Animation, Ruth Dover
07: Tan Animation, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
TanAnimation.nb is a nice little animation to illustrate similar triangles to show why the graph of y = tan(x) looks the way it does.
08: Sine Transformations, Ruth Dover
08: Sine Transformations, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SineTransformations.nb allows you to use sliders to see the effects of parameters on the amplitude, period, phase shift, and vertical shift.
13: Polar Reciprocal, Ruth Dover
13: Polar Reciprocal, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolarReciprocal.nb first shows a transformation of the circle r = 3 into the circle r = 3sin (theta). Second, it shows the original and reciprocal graphs through the animation. Interesting stuff!
03: Poly Basics 2, Ruth Dover
03: Poly Basics 2, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.
15: Koch Snowflakes, Ruth Dover
15: Koch Snowflakes, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.
16: Sequences And Series, Ruth Dover
16: Sequences And Series, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.
04: Domain And Range, Ruth Dover
04: Domain And Range, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
DomainAndRange.nb allows you to graph various types of functions and shows the domain and/or range along the appropriate axis.
12: Polar Path, Ruth Dover
12: Polar Path, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.
11: Parametric Path, Ruth Dover
11: Parametric Path, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.
09: Solving Trig Equations, Ruth Dover
09: Solving Trig Equations, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SolvingTrigEquations.nb develops the idea of solving trigonometric equations with special angles by looking at a sequence of problems. The student is asked to think about solutions and to do more problems along the way.
14: Polar Vs Rectangular Animation, Ruth Dover
14: Polar Vs Rectangular Animation, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolarVsRectangularAnimation.nb allows the user to input a polar function and then relates the graphs of r = ƒ(theta) and y = ƒ(x).
02: Poly Basics 1, Ruth Dover
02: Poly Basics 1, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolyBasics1.nb deals with the graphs of polynomial functions of higher degrees. In this notebook, each factor is linear.
01: Quadratic Functions, Ruth Dover
01: Quadratic Functions, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.
02: Derivative Approximation, Ruth Dover
02: Derivative Approximation, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
DerivativeApproximation.nb contains two sections. Both allow the user to input a function and an x-window and to vary the center point. Then the value of h may be changed. The first section will show a symmetric approximation while the second shows a one-sided approximation.
11: Eulers Method, Ruth Dover
11: Eulers Method, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
EulersMethod.nb asks for a differential equation, an x-interval, a specific point, and the step size. It shows the graphical approximation given by Euler's Method. This notebook has setups that allow it to be used with one DE or with a system of two DE's.
05: Limit Definition, Ruth Dover
05: Limit Definition, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
LimitDefinition.nb asks the user to input a function. Then use the vertical slider to change the size of E. An appropriate value of 8 will be given.
09: Slope Field, Ruth Dover
09: Slope Field, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SlopeField.nb does just what it says! Enter a differential equation in the form y = … and choose the window. It is also possible to choose the number of marks in each direction.
08: Accumulator, Ruth Dover
08: Accumulator, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
Accumulator.nb takes a function ƒ and other information to sketch both the graph of ƒ and the graph of F(x) = Integral of ƒ(t) from a to x. Use the slider for the x-value to see how the accumulated area under ƒ helps to create the graph of F.
12: Parametric Path, Ruth Dover
12: Parametric Path, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.
10: Slope Fields + Solns, Ruth Dover
10: Slope Fields + Solns, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SlopeFields+Solns.nb follows similarly from the previous notebook. Here, however, there is a 2D slider that shows a specific solution function as you move the initial point.
07: Riemann Sums, Ruth Dover
07: Riemann Sums, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
RiemannSums.nb allows the user to input a function, and x-interval, and a maximum value of n, the number of rectangles. This animates Riemann and trapezoidal sums.
06: Random Riemann, Ruth Dover
06: Random Riemann, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
RandomRiemann.nb takes a function, values for xmin and xmax, and a number n that represents the number of rectangles desired. This will create random subintervals with random points inside each subinterval, and then it will draw the corresponding Riemann sum. Values for the approximation and the actual value of the integral are given. This allows students to see how close (or distant) the approximation is and to visualize a wide variety of Riemann sums. Increasing values of n should help students understand the limiting process more clearly.
13: Polar Path, Ruth Dover
13: Polar Path, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.
15: Plotting S(N), Ruth Dover
15: Plotting S(N), Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.
14: Sequences And Series, Ruth Dover
14: Sequences And Series, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.
17: Plotting S(N), Ruth Dover
17: Plotting S(N), Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.
03: Derivative Signs, Ruth Dover
03: Derivative Signs, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
DerivativeSigns.nb asks the user to input a function and a domain. It will color the graph to show where the derivative is positive and where it's negative. The second part colors the graph to show where the function is concave up and down.
01: Creating Derivative, Ruth Dover
01: Creating Derivative, Ruth Dover
Mathematica Notebooks for Pre-Calculus and Calculus
CreatingDerivative.nb takes any function and an x-window and animates a tangent line while plotting the value of the derivative.