Tutorials
Why?: Teaching is a passion of mine. I decided to write these tutorials (mostly on mathematical topics) to help support the peer tutoring I do here at Princeton, and to have a collection of some of my favorite topics. My philosophy is to explain things as simply as I can. I try not to make any assumptions on what people know (beyond the prerequisites of the courses that each topic corresponds to), and I try not to skip too many steps. Even Einstein said "If you can't explain it simply, you don't understand it well enough"
NOTE: This is obviously a work in progress...
Calculus
Tutorial Author(s) Type/Classes Description Taylor Series Chris Tralie Math 104 (Calculus 2) A light introduction to Taylor Series. I derive it from a differential and integral point of view, I show how to estimate the remainder term, and I give lots of examples, including how to approximate the square root of two and why small angle approximation works. Hopefully an intuitive and clear explanation of Taylor Series for people who are confused about it or who have never seen it before Euler's Formula Chris Tralie Math 104 (Calculus 2) A short tutorial on Euler's Formula, which ties exponentials to sinusoids through imaginary numbers. A very important prerequisite to signal processing Implicit Differentiation (Multivariable) Chris Tralie Math 201 and 203 (multivariable calculus) Implicit differentiation of multivariabled functions. This topic came up while I was tutoring math 201, and I found it tricky enough to warrant a small tutorial
Signal Processing
Coming soon....
Computer Graphics / 3D Math
Tutorial Author(s) Type/Classes Description Ray-Primitive Intersections Chris Tralie COS 426 (Introduction to computer graphics) This tutorial explains how to find the intersection between a ray and various different axis-aligned primitive 3D objects, such as spheres, cylinders, and cones. The primary application of this is ray-traced 3D rendering. This tutorial was part of an assignment I did in COS 426 which was to create a basic ray-tracing engine.
Miscellaneous
Tutorial Author(s) Type/Classes Description Recursion and Self-Similarity Chris Tralie Intro Computer Science This is a tutorial I wrote on recursion back in high school. I talk about recursive functions, the Fibonacci sequence, the Towers of Hanoi, and fractals. SLAM and Global Navigation on the iRobot Roomba using ROS Chris Tralie Robotics This is a tutorial I wrote primarily for my adviser Matt Reynolds to explain a subset of my work from the summer to him.
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Calculus
| Taylor Series | Chris Tralie | Math 104 (Calculus 2) | A light introduction to Taylor Series. I derive it from a differential and integral point of view, I show how to estimate the remainder term, and I give lots of examples, including how to approximate the square root of two and why small angle approximation works. Hopefully an intuitive and clear explanation of Taylor Series for people who are confused about it or who have never seen it before |
| Euler's Formula | Chris Tralie | Math 104 (Calculus 2) | A short tutorial on Euler's Formula, which ties exponentials to sinusoids through imaginary numbers. A very important prerequisite to signal processing |
| Implicit Differentiation (Multivariable) | Chris Tralie | Math 201 and 203 (multivariable calculus) | Implicit differentiation of multivariabled functions. This topic came up while I was tutoring math 201, and I found it tricky enough to warrant a small tutorial |
Signal Processing
Computer Graphics / 3D Math
| Ray-Primitive Intersections | Chris Tralie | COS 426 (Introduction to computer graphics) | This tutorial explains how to find the intersection between a ray and various different axis-aligned primitive 3D objects, such as spheres, cylinders, and cones. The primary application of this is ray-traced 3D rendering. This tutorial was part of an assignment I did in COS 426 which was to create a basic ray-tracing engine. |
Miscellaneous
| Recursion and Self-Similarity | Chris Tralie | Intro Computer Science | This is a tutorial I wrote on recursion back in high school. I talk about recursive functions, the Fibonacci sequence, the Towers of Hanoi, and fractals. |
| SLAM and Global Navigation on the iRobot Roomba using ROS | Chris Tralie | Robotics | This is a tutorial I wrote primarily for my adviser Matt Reynolds to explain a subset of my work from the summer to him. |
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