## James (Jim) Frankenfield - Academic Library

# Videos and Supporting Materials

I have been making a few videos on youtube, the links to them are below. In some cases there may be supporting materials such as excel spreadsheets and/or desmos graph links which are posted here as well, but not on youtube. If you find these helpful please like the video and the channel and it will encourage me to make more. You can also suggest or request a topic via my contact page. I will consider requests but at the moment cannot make too many videos too quickly.

Introduction Video - A bit about me, what I teach, and how I teach it (~10 minutes)

* Physics Videos* - Math Videos - Engineering Videos

**Instructional Videos **

Click the + to the left of each video to open a description which includes any supporting materials. Links will open in a new window.

## Video #1 - Projectile Motion

This was my first video and covers simple projectile motion (starting and ending height the same). I first use the simple range equation then repeat the solution using the vector equations of motion for kinematics. I address the benefits and flexibility of using the kinematics equations and mention a rocket problem but do not solve that. There is a Desmos projectile page which is built in (not created by me).

The motivation for this video came from a combination of tutoring A-Level physics which simply used the range equation and also from helping somebody on Facebook with a rocket problem which requires the kinematic equations.

## Video #2 - Constant of Integration 1

This was my second video and discusses why the constant of integration is important in applications and practice. It is limited to one integration and one initial or boundary condition to meet and does not go into multiple integrations with mutliple constants and conditions. There is a Desmos graph page I created used in this video. You can find it here.

The motivation for this video came from tutoring A-Level math and realizing that very few (if any) courses explain why this mysterious constant being tacked on is important or what it might represent.

## Video #3 - Factoring 1

This was my third video and is a comprehensive treatment of factoring a polynomial and finding it's rational roots (if any). It uses a consistent methodology to solve a variety of different cases. In order to handle a lot of repetition effectively I make use of excel rather than repeatedly carrying out calculations manually. Examples include rational roots, irrational roots, imaginary roots, and a polynomial with a leading coefficient. The emphasis is on finding rational roots. I use an excel spreadsheet you can download a copy of here and a Desmos page which you can find here.

The motivation for this video comes from the issue constantly arising on Facebook help groups. How to factor something comes up a few times a week. Answers are often not explained, and the approaches used are haphazard. This video is intended to provide insight and a clear methodology which can be used for any polynomial. A second motivation comes from a rational function I helped with where the numerator and denominator are both challenging to factor. A video on that problem will follow.

## Video #4 - Factoring 2 (Irrational Roots)

This was my fourth video and is a comprehensive treatment of factoring a polynomial and finding all real roots (rational and irrational). It uses the consistent methodology from the Factoring 1 video to find any/all rational roots. Then I find the remaining irrational roots by two methods, Newtons method and an alternative without calculus. I use an excel spreadsheet you can download a copy of here.

The motivation for this video came from a problem posted in a Facebook help group. It asked for all roots but the only other answer gave three factors and made no effort to find the irrational roots.

## Video #5 - Prime Numbers and Factors

This was my fifth video and covers prime numbers, prime factorization, and the uses for these. I also cover the Sieve of Eratosthenes for generating a list of primes. I use an excel spreadsheet you can download a copy of here. One sheet is for finding all the factors of 60 using the prime factors and the other is an implementation of the Sieve of Eratosthenes.

The motivation for this video comes from frequently seeing questions about how to reduce fractions, add fractions, simplify roots, etc. Students today do not seem to be learning to use prime factors. The result, in addition to all the questions, is that their answers are often not in the best form or just plain wrong.

## Video #6 - Rational Inequalities

This is a full length instructional video on how to handle inequalities with rational functions. This started with a problem posted on a Facebook group which became mangled when it was not approached properly. This video explains a method to use and the logic behind it. There is a Desmos page with all of the functions used. Some offer counter-examples to assumptions one might make and the last goes beyond rational expressions to show that the same method is more general than that.

This video used 6 Desmos graphs for different functions:

## Video #7 - Shear and Bending Moment Diagrams

This covers a basic skill in pre-engineering studies, usually in a Statics course. Given a load distribution on a beam you are asked to graph the shear and the bending moment within the beam. This video shows how to treat this strictly as a mathematical problem by integrating graphically to get the shape of the graph and then calculating the integrals and key points to label the graph. I also discuss where this introduction will lead later - to the actual beam deflection, and the 4th order (partial) differential equations for beams. Those are just to show where things head later and are not addressed in any detail or solved in the video. You can find the Desmos graph with the forces, shear and bending moment here.

## Video #8 - Introduction to Center of Mass

This is a web version of a 20 minute invited lecture given for a school. It begins by introducing the concept and then solves 3 problems. (This is a problem-solving lecture/video, so it's AP or university level.) The first has a few discrete masses, the second is a bar or rod with varying density and requires some simple calculus, and the third is a round plate (with uniform density) which a round section has been removed from.

## Video #9 - Triangular-Square Numbers 1

This is an introduction to triangular numbers and triangular-square numbers. This came up in a help group and I became interested in this, perhaps enough for a part 2 but we'll see. It ultimately leads into number theory but I don't go into that depth and won't. Thats an important branch of math for computer science but it's not my area of expertise. In this video I explain what these numbers are, then look for them on a spreadsheet, and finally use two programs to generate them. One in python and one in LISP. I also comment a bit on computer science vs. mere coding. Resources: Excel spreadsheet, text file with 2 programs.

**Problem Solution Videos** (These will open in a new tab or window)

- P01 - Difference Quotient of a simple Quadratic
- P02 - Subtracting Two Rational Expressions
- P03 - Subtracting Two Rational Expressions (Watch out for the domain issue!)
- P04 - Physics Boom/Cable Problem (Statics)
- P05 - Greatest Common Divisor Problem (with remainders)
- P06 - Finding an Equation for a Sinusoidal Function (Desmos Page available)
- P07 - Finding Maximum Worker Efficiency (Desmos Page available)
- P08 - Using the unit circle for a trigonometry problem
- P09 - A Simple Equality between rational expressions (integer denominators)
- P10 - A Projectile problem which defies the laws of physics (Desmos Page)
- P11 - A Quadratic with an Exponential in it (Desmos Page)
- P12 - Stationary Points of f(x,y) (Desmos Page; Desmos 3D page)
- P13 - Given 2 points find all possible 3rd points for an isosceles triangle (Desmos Page)
- P14 - Tangent plane to a function f(x,y) (Desmos Page; Graphing Calculator 3D file)
- P15 - Collision Conservation of Momentum Problem - Superman and Lois
- P16 - Graphing a Rational Function (1) (Desmos Page; Excel file from factoring)
- P17 - A Collision Problem with coefficients of restitution

**Progress Updates**

## January 12, 2022 Update

January 12, 2022 - I have made 3 videos so far. I am new to creating and editing these so they are a bit rough. However, the content is sound and they should be helpful. They are intended to be academic and instructional, not entertaining. At the moment the webcam I use for whiteboard sections is very low quality and needs replacing. The document camera and the OBS screens with various screen shares are of good quality. I tutor using these tools with little use of the whiteboard but am anxious to replace that cam for actual teaching courses.

## February 12, 2022 Update

February 12, 2022 - Since January 12 I have made one more instructional video, #4 below. The Trust webcam for the whiteboard has been replaced (but not used in video 4 anyway). I have also made two introductory videos, a short one under 3 minutes to be listed on Preply and a longer one just under 10 minutes. I also have three problem solution videos which are short and use only the document camera.

## March 4, 2022 Update

Starting with video 5 I am using a better Canyon cam I am happy with. I also have figured out how to set the resolution to the right values in all the various necessary place so I should be able to avoid the black space now and use a full 16x9 screen. The intro for the video on factoring needs to be re-recorded now.

August 25, 2022 Update

Prior to the Projectile problem which defies physics I researched the sound/mic settings for OBS and set up a few filters they offer. Starting with this video I hope the sound will be much better. In previous videos the gain was high and the quality was generally ok and understandable but not great.