These are a set of fictional case studies that are designed to prompt reflection and discussion about issues at the intersection of AI and Ethics. These case studies were developed out of an interdisciplinary workshop series at Princeton University that began in 2017-18. They are the product of a research collaboration between the University Center for Human Values (UCHV) and the Center for Information Technology Policy (CITP) at Princeton. Click the title of each case study to download the full document.

Long Description:
A study of derivatives of algebraic and trigonometric functions, applications to tangents and normals, curve sketching and Maximum-Minimum word problems, curvilinear motion, related rates , Newtons method for solving equations, differentiation methods for simple algebraic functions with applications for electronics, determinants, trigonometric identities.

Word Count: 175834

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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE’s) deal with functions of one variable, which can often be thought of as time.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

Lecture Videos by Professor Arthur Mattuck.
Course Notes on every topic.
Practice Problems with Solutions.
Problem Solving Videos taught by experienced MIT Recitation Instructors.
Problem Sets to do on your own with Solutions to check your answers against when you’re done.
A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
A full set of Exams with Solutions, including practice exams to help you prepare.

Content Development
Haynes Miller 
Jeremy Orloff 
Dr. John Lewis 
Arthur Mattuck

This 10-minute video lesson provides an introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. [Differential Equations playlist: Lesson 13 of 45]

This 8-minute video lesson continues the discussion from the previous video and shows how to find the general solution. [Differential Equations playlist: Lesson 14 of 45]

This 6-minute video lesson continues the discussion from the previous videos and introduces some initial conditions to solve for the particular solution. [Differential Equations playlist: Lesson 15 of 45]

This 9-minute video lesson continues the discussion from the previous videos and provides another example using initial conditions. [Differential Equations playlist: Lesson 16 of 45]

This 10-minute video lesson looks at what happens when the characteristic equations has complex roots. [Differential Equations playlist: Lesson 17 of 45]

This 10-minute video lesson continues the discussion of what happens when the characteristic equation has complex roots. [Differential Equations playlist: Lesson 18 of 45]

This 10-minute video lesson concludes the series on complex roots of characteristic equations and demonstrates an example with initial conditions. [Differential Equations playlist: Lesson 19 of 45]

This 18-minute video lesson provides an introduction to the Dirac Delta Function. [Differential Equations playlist: Lesson 41 of 45]

This 12-minute video lesson gives the first example of solving an exact differential equation. [Differential Equations playlist: Lesson 6 of 45]

This 8-minute video lesson provides some more examples of exact equations. [Differential Equations playlist: Lesson 7 of 45]

This 10-minute vidoe lesson provides one more exact equation example [Differential Equations playlist: Lesson 8 of 45]

This 10-minute video lesson provides intuiton on exact equations including the chain rule using partial derivatives (not a proof; more intuition). [Differential Equations playlist: Lesson 4 of 45]

This 11-minute video lesson provides more intuitive building blocks for exact equations. [Differential Equations playlist: Lesson 5 of 45]

This 7-minute video lesson provides an introduction to first order homogenous equations. [Differential Equations playlist: Lesson 11 of 45]

This 8-minute video lesson provides another example of using substitution to solve a first order homogeneous differential equations. [Differential Equations playlist: Lesson 12 of 45]