## Video Learning Series With Dr. Bill Stewart

#### Scholarship Central and Dr. Bill Stewart have teamed up to create the following YouTube videos.

Visualization of Functions

In mathematics and science, numerous functions are used in problem-solving. A useful skill is to be able to look at a mathematical expression and to quickly visualize and sketch the behavior of the function. In this video we deal with the family of functions from linear to trigonometric expressions.

Simple Harmonic Motion - Pendulum and Spring and Mass Systems

Vibrations and oscillations are part of everyday life and a pendulum and a mass on a spring are excellent examples of Simple Harmonic Motion. Dr. Bill Stewart conducts experiments where the students can predict what might happen as parameters are changed and can then analyze the experimental data to draw conclusions. This class would be appropriate for elementary school students as an example of conducting an experiment to learn how things work; in physical science classes as an example of two types of motions; and in a physics classes which often do a detailed study of simple harmonic motion which includes the frequency and period of oscillations.

Calculating the Area of Polygon in a Circle

In this video, Dr. Stewart shows how one can calculate the area of various polygons which are inscribed inside a circle. Specifically, the percentages of the area of the circle covered by an equilateral triangle, a square, and an octagon are calculated. The student is encouraged to calculate the pentagon, hexagon, and the septagon solutions and compare with those given in the class. Various algebraic techniques are utilized including, similar triangles, the Pythagorean Theorem, and trigonometry. These types of problems are popular on the ACT and SAT College Entrance Exams.

This video is suitable for anyone in Algebra II, PreCalculus, and Calculus.

Counting: Factorials, Permutations, and Combination

How many different ways can you arrange books on a shelf? How many diagonals can you draw in a polygon? How many different sandwiches can you buy at a local Subway?

In this video, Dr. Stewart will help you understand the power of the mathematics of counting.

Finding Volumes of Shapes

A classic problem is fitting one shape into another, such as a cube inside a sphere. Dr. Stewart shows how these types of interesting problems are approached and solved. Spheres, Cubes, and Ellipsoids are used for illustration of how you can place one shape inside another and find the wasted space that occurs in real-life packaging problems that face all E-Commerce companies.

The Kinematic Equations of Motion

The kinematic equations are fundamental to the understanding of accelerated motion. These equations are derived and then used to solve the motion problems of accelerating vehicles and falling bodies such as a penny dropped from the top of the Empire State Building in New York City.

Projectiles and Motion

Projectile motion is commonly studied following the Kinematic Equations. Projectile motion is all around us with many illustrations in sports. Most sports use some type of ball (football, soccer, baseball, basketball, golf, tennis, etc.) and athletes react to the motion of the ball and fellow competitors.

Dr. Bill Stewart presents a straightforward method for solving several kinds of projectiles by separating the motion into vertical and horizontal components. Two examples are solved, one being a ball launched at an angle and the other a vehicle driving off a cliff and falling to the ground below.