Some Desmos Demonstrations for Introductory Math/Stats Courses

Here are some of the Desmos demonstrations I've used in my classes. I'll simply link to most of them, and embed a few that are my favourites :)

They are loosely grouped in the following categories:

• Pre-Calculus
• Differential Calculus
• Integral Calculus
• Probability
• Others

Please feel free to adapt them for your own use. If you have any questions/comments/bug reports about these demonstrations, or would simply like to let me know that you find them useful, please feel free to e-mail me at Pau@mathQ.usask.caR (with P,Q, and R removed).

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Pre-Calculus

• Some basic graph transformations (translations, stretches/compressions, and reflections). (Link to Demonstration)
• Geometric illustrations of the six common trig. functions on the unit circle. (Link to Demonstration)
• Graphs of the six common trig. functions and the corresponding inverse trig functions. (Link to Demonstration)

Differential Calculus

• From secant lines to tangent lines. (Link to Demonstration)
• Illustrating $\frac{d}{dx}\ln(x) = \frac{1}{x}$ as a consequence of $\frac{d}{dx}e^x=e^x$ and that $\ln(x)$ is the inverse function of $e^x$.

(Link to Demonstration)

• Visualizing Newton’s method for approximating zeros of functions (Link to Demonstration)

• Taylor polynomials:

  • Plotting Taylor polynomials of up to order 3 for an arbitrary function. (Link to Demonstration)
  • Visualizing the Taylor polynomials of $e^x$, $\cos(x)$, and $\sin(x)$ about $x=0$. (Link to Demonstration)

Integral Calculus

• Visualizing Riemann Sums (right endpoint approximation, even subintervals). (Link to Demonstration)
• Illustrating the average value of a continuous function over a closed interval. (Link to Demonstration)
• Illustrating area functions of the form $g(t) = \displaystyle\int_{a}^t f(x)~dx$ (where $a$ is a constant). (Link to Demonstration)
• Some specific examples of area functions where the bounds of integration are themselves non-trivial functions. (Link to Demonstration)
• Visualizing the improper integral $\displaystyle\int_1^{\infty} \frac{1}{x^p}~dx$ for various values of $p$. (Link to Demonstration)
• Showing that any 3 distinct points on the plane uniquely determines a parabola. (This goes here since I usually bring it up when motivating Simpson's approximation.) (Link to Demonstration)
• Illustrating some numerical integration approximations (right/left endpoint, midpoint, trapezoidal, and Simpson's).

(Link to Demonstration)

• Volume of objects of revolution:

  • Via slicing, rotating about a horizontal line.

(Link to Demonstration) * Via cylindrical shells, rotating about a vertical line. (Link to Demonstration) * Via slicing, rotating about a vertical line. (Link to Demonstration) * Via cylindrical shells, rotating about a horizontal line. (Link to Demonstration)

• Finding the arc length of the curve $y=f(x)$ over $[a,b]$. (Link to Demonstration)
• Visualizing the surface area integral for object of revolution via approximations by slanted cylindrical shells. (Link to Demonstration)
• Motivating moments and the centre of mass.

(Link to Demonstration)

• A simplistic Sun-Earth-Mars model that shows the orbit of Mars in the perspective of the Earth via parametric equations.

(Link to Demonstration)

• Motivating the computation of slope of tangent lines and arc lengths for parametric curves.

(Link to Demonstration)

• Illustrating the cycloid. (Link to Demonstration)
• Plotting points in Cartesian versus polar coordinates. (Link to Demonstration)
• Some common polar curves. (Link to Demonstration)
• Visualizing the approximation of polar areas via sectors.

(Link to Demonstration)

Probability

• A 6/49 Lottery simulator. (Link to Demonstration)

• A coin-flip simulator that allows for biased coins. (Link to Demonstration)

• Visualizing some common discrete probability distributions:

  • The binomial distribution.

(Link to Demonstration) * The hypergeometric distribution. (Link to Demonstration) * The negative binomial distribution. (Link to Demonstration) * The Poisson distribution. (Link to Demonstration)

• Several demos related to the normal distribution:

  • Visualizing the probability related to the normal distribution as the area underneath a curve. (Link to Demonstration)
  • Computing $P(Z<k)$ given $k$. (Link to Demonstration)
  • Given $0 < p < 1$, finding $k$ (to 4 decimal places) where $P(Z<k)$ is the closest to $p$.

(Link to Demonstration)

Others

• Some basic linear algebra things (because I haven't learnt Geogebra yet):

  • Dot products of vectors in $\mathbb{R}^2$. (Link to Demonstration)
  • Orthogonal projections in $\mathbb{R}^2$. (Link to Demonstration)
  • Vector equations of lines in $\mathbb{R}^2$. (Link to Demonstration)

• Introducing complex numbers:

  • The complex plane, conjugate, and magnitude. (Link to Demonstration)
  • Visualizing complex number multiplication. (Link to Demonstration)
  • Constructing Pythagorean triples via squaring complex numbers.

(Link to Demonstration)

• Generating random 2-edge colourings of the complete graph $K_n$.

(Link to Demonstration)

• Illustrating the definition of convex functions (Link to Demonstration)

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