Laboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation

In this video I go over another Laboratory Project, which are very interesting math projects at the end of some of the chapters in my Calculus textbook, and this time look at Taylor Polynomials. In this particular video I go over Question 1 which looks quadratic approximation as compared to linear approximation. Recall from my earlier videos on linear approximation that we can approximate the values of a function near a particular point by zooming in and obtaining a line that is tangent to the curve. But for most functions this kind of approximation becomes very inaccurate as we move beyond that particular point. Thus to illustrate some methods of obtaining better approximations, I first how a second degree polynomial, i.e. a quadratic or parabola function, is actually a much better approximation than simple linear functions. To show this I look at the example of approximating trigonometric cosine at x = 0, which clearly shows how a parabola is a much better approximation than a line. This is a very important video to not only get a recap of linear approximation, but to illustrate a simple case in which we can approximate more accurately by increasing the degree of a polynomial, so make sure to watch this video!

Video notes and playlist:

- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh44WRn_CqoI1cv-ncg
- HIVE notes: https://peakd.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-1-quadratic-approximation
- Laboratory Projects playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GPz_diCZTkiVs6Q4mA_KHb

Related Videos:

Taylor Polynomials - Introduction and Derivation: http://youtu.be/p2EkXwkbflk
Linear Approximation - Introduction and Examples: http://youtu.be/bXEK8bkWTtM
tan(x) = sin(x) = x and cos(x) = 1 near x = 0: Linear Approximation in Physics: http://youtu.be/TPtZIxICa3Q
Differentials Notation in Linear Approximation: http://youtu.be/s0adatWiZg4
Newton's Method of Linear Approximation - Introduction: http://youtu.be/aT4b_5l50RI
Newton's Method on Linear Approximation - Examples Part 1: Where it Converges: http://youtu.be/u_Uo5aShAUs
Newton's Method on Linear Approximation - Examples Part 2: Where it fails to Converge : http://youtu.be/mDSyBPsiv1Q .

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