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♦ Course Videos

General Videos:

Review of Calculus I and II: part I part II (right click to download)

How to switch orders of integration (by Cam)

Tangent lines

Introduction to LaTex

Introduction to Mathematica

Lectures: PLAYLIST: https://www.youtube.com/playlist?list=PLcWNuL61dIBjye9hIa8T8Yd0R8WJfr8av

First day lecture: http://youtu.be/Sabcuhsxekg (February 7, 2014: Introduction, Pythagoras)
- 2/2/18: Sec 1: https://youtu.be/h8UiShlawOs Sec 2: https://youtu.be/8At4WaOLZkU
Second day lecture: (February 10, 2014: Definition and properties of vectors, through dot product)
- Part 1: http://youtu.be/fghStY0cqIg Part 2: http://youtu.be/AA2UEYbnkRw
- 2/5/18: Sec 1: https://youtu.be/WsStSGvorgE Sec 2: https://youtu.be/qNn9bs7ETWQ
Third day lecture: http://youtu.be/aIZmP640Sn4 (February 12, 2014: Dot Products, Cross Products, Determinants, Areas)
- 2/7/18: Sec 1: https://youtu.be/toKszypxiKE Sec 2: https://youtu.be/N8_I5Ao6B24
Fourth day lecture: http://youtu.be/ft2zViDFXcY (February 17, 2014: Lines)
- Slides: Slides from lecture on 2/17/2014 (lines and art).
- 2/9/18: Sec 1: https://youtu.be/0WH7jdUKizQ Sec 2: https://youtu.be/B3a_Bn1mmFs
Fifth day lecture: http://youtu.be/np_Icg33Lug (February 19, 2014: Coordinate systems, level sets)

2/12/18: Sec 1: https://youtu.be/r5SGAMFiVdE Sec 2: https://youtu.be/IkEGfXhbhhc

Sixth day lecture: http://www.youtube.com/watch?v=71_8kHSAE4w (February 21, 2014: Limits, Defn Partial Derivatives)
- 2/14/18: Sec 1: https://youtu.be/aKPWpMW0lYM Sec 2: https://youtu.be/SxF7Eg0RY7g
Seventh day lecture: http://www.youtube.com/watch?v=S6wiYRCiQhs (March 3, 2014: Derivatives)
- 2/19/18: Sec 1: https://youtu.be/BxqloF6FNLg Sec 2: https://youtu.be/vA071GquwGo Mathematica Notebook
Eighth day lecture: http://www.youtube.com/watch?v=L1WUWmjvnE0 (March 5, 2014: Optimization)

2/21/19: Sec 1: https://youtu.be/hS1XXbXTdNk Sec 2: https://youtu.be/u4R6NRIEWwA

BONUS LECTURE: Programming: Sec 1: https://youtu.be/2xmH6w7xdyo Sec 2: https://youtu.be/2xmH6w7xdyo

Ninth day lecture: (March 7, 2014: Method of Least Squares)

2/26/18: Sec 1 and Sec 2: https://youtu.be/Wnth5d0oT1I

Tenth day lecture: http://youtu.be/Da0cO905Aj8 (March 10, 2014: Linear Approximation)
- 2/28/18: Sec 1: https://youtu.be/Q8WuIoT06dI Sec 2: https://youtu.be/ap-JM19by2A
Eleventh day lecture: http://youtu.be/cgIoKYr11sY (March 12, 2014: Chain Rule)
- 3/2/18: Sec 1: https://youtu.be/g1ZO1k3gzdA Sec 2: https://youtu.be/SSCik_ejvaw
Twelfth day lecture: Part I: http://youtu.be/FbwGZfkf9P8 Part II: http://youtu.be/RbhK3a308sg (March 14, 2014: Directional Derivatives, Exp Fn, Trig in a Day)

3/5/18: Sec 1: https://youtu.be/Ici6M_UJvwk Sec 2: https://youtu.be/4Nopzrgq6Z8

Thirteen

th day lecture: http://youtu.be/pgwC2vOwRuE (March 17, 2014: Lagrange Multipliers)

3/7/18: Sec 2: https://youtu.be/8YOXUPcvP-U

Fourteenth day lecture: http://www.youtube.com/watch?v=Q1TQtH6POyI (March 19, 2014: Fundamental Theorem of Calculus in a Day)
- 3/9/18: Sec 1: https://youtu.be/0bkHRFEwIe0 Sec 2: https://youtu.be/BbAil7J0UGg
Supplemental lecture: Fractals: From Khan to Frozen (March 20, 2014: Mathematics of Fractals and applications to films)
Fifteenth day lecture: http://youtu.be/N8nFFWG_6J4 (April 7, 2014: Integration in two variables)
- 3/12/18: Sec 1: https://youtu.be/2mLTZRtSAq0 Sec 2: https://youtu.be/U1PEPt1If4Q
Sixteenth day lecture: http://youtu.be/G9d9lcYevnM (April 9, 2014: Iterated integrals, changing order)
- 3/14/18: Sec 1: https://youtu.be/SIej3SZ4p7M Sec 2: https://youtu.be/M6pvAWfNlgU
Seventeenth day lecture: http://youtu.be/JP78q_ri-4o (April 11, 2014: Polar Change of Variables, Circles and Spheres)
- 4/4/18: Sec 1: https://youtu.be/UBnjwxaTkXg Sec 2: https://youtu.be/IsXFx7ikzIs
Eighteenth day lecture: http://youtu.be/Nz7ahXOMTus (April 14, 2014: Monte Carlo Integration, Change of Variables for Ellipses)
- No class, traveling
Nineteenth day lecture: http://youtu.be/t3Pt4E1BeUTwt (April 16, 2014: Cylindrical and Spherical Coordinates, Newton's Shell Theorem)
- 4/9/18: Sec 1: https://youtu.be/qVmHBnisZW4 Sec 2: recording issue
Extra lecture: Probability and Spheres: Sec 1: https://youtu.be/1PwQevlIoW8 Sec 2: https://youtu.be/0TeX4c2E43A
Twentieth day lecture: http://youtu.be/gFDly_6qOn4 (April 18, 2014: Sabermetrics and Multivariable Calculus - Lecture from 2013)
Twenty-first day lecture: http://youtu.be/MN80UyR2Rh8 (April 21, 2014: Gamma Function and Calc I/II/III review)
Twenty-second day lecture: http://youtu.be/tZ9lcdk6hLOUt (April 23, 2014: Review Class: Perimeter Ellipse, Word Problems, Viewing Algebra)
Twenty-third day lecture: http://youtu.be/aigdKmu-5ow (April 28, 2014: Geometric and Harmonic Series, Memoryless Processes)
- 4/16/18: Sec 1: https://youtu.be/pVwg8eg-Qi4 Sec 2: https://youtu.be/ZplES7XRkjg
Twenty-fourth day lecture: http://youtu.be/6bf9fjwMs2o (May 2, 2014: Comparison Test, Implications of Limits of Terms)
- 4/18/18: Sec 1: https://youtu.be/C5FpOCX3eR4 Sec 2: https://youtu.be/XnAIGqDrtaQ
- Bonus lecture on sequences and series: http://youtu.be/QZ1_5SmxUo8
Lecture from 4/20/2018:
- 4/20/18: Sec 1: https://youtu.be/TJWuCwp1tUo Sec 2: https://youtu.be/tRHtA6U-YsQ
Twenty-fifth lecture: https://youtu.be/fa4X1AcGFOA (May 4, 2014: Comparison Test, Implications of Limits of Terms: II)
- 4/20/18: Sec 1: https://youtu.be/TSvffHyFHgM Sec 2: https://youtu.be/tHDtnF8cf4k Review: https://youtu.be/8EZQKzoWxEo
Twenty-fifth day lecture: http://youtu.be/u3BbXey5dVY (May 5, 2014: Ratio Test, Patton Movie Clip)
Twenty-sixth day lecture: http://youtu.be/ujJbUpCab6M (May 7, 2014: Root Test, Integral Test)
No class on May 9, watched streaming video lecture from last year: https://www.youtube.com/watch?v=WjnHNHPhJtU
5/2/18: Sec 1: https://youtu.be/gaC6R01aTjs (Sec 2 was outside)
Twenty-seventh day lecture: http://youtu.be/yr01SLw9t4c (May 12, 2014: Taylor Series: Should have already watched)
- 5/4/18: Sec 1: https://youtu.be/ultVUCHrl1c Sec 2: https://youtu.be/ss-uBM3lY2g
- 5/7/18: Sec 1: https://youtu.be/Mepc9GWlQB0
- 5/9/18: M&M game: Lecture from Probability: M&M Game: https://youtu.be/DFobthridWI (slides) (paper)
- 5/11/18: Review: Sec 1: Spherical Integral, Lagrange Multipliers, Level Sets: https://youtu.be/Jgb3z3E58Zw; Sec 2: Spherical Integral, Changing Orders, Series: https://youtu.be/Jgb3z3E58Zw
Twenty-eighth day lecture: http://youtu.be/UfL8o_IetYQ (May 12, 2014: Review by Partitioning: Not doing 2018)
- Bonus clip on Tangent Lines: http://youtu.be/lEJ06epMLEQ
Twenty-ninth day lecture: http://youtu.be/4OcxtpxuSJw (May 14, 2014: Special Series, Alternating Series, Pi formulas, Birthday Problem: Not doing 2018)
Review sessions:
- Day 1: Change of Variables, Odd/Even Functions, Bounding Functions, Comparison Test: http://youtu.be/8EZQKzoWxEo
- Day 2: Mostly series test (one series and we apply all four tests!): http://youtu.be/HANb4mVLOOc

Videos of the week:

Week 1: Fibonacci numbers (click here for more on the Fibonacci numbers).
Week 2: Light cycle scene from Tron.
Week 3: Flatland trailer. (The full movie is available here for class purposes only.) There's also projections of 4-dimensional cubes in our 3-dimensional space.
Week 4: The Battle of Trafalgar: Animated battle clip Facts on the battle Best animated re-enactment I could find (For more on this see the Additional Comments.)
Week 5: Mandelbrot zoom: video 1, video 2. Here's a cubic fractal zoom. (other copies: Videos: Mandelbrot set Newton Fractal (cubic) )
- Mathematica notebook for Newton's Method (pdf version here)
Week 6: Trick shots in pool (directions and constraints!).
- Week 6: Audio of the semester: I'm my own Grandpa; graphical version here (don't view this until you try to graph it!). Actually, this is a much better illustration of the relationships.
Week 7: coin sorting (this leads to Lebesgue's Measure Theory).
Week 8: Pacman (actually Ms. Pacman) You can play Pacman online here.
Week 9: Stacking blocks
Week 10: Conway's Game of Life: Gosper's glider gun, and a breeder leaving Gosper glider guns in its wake.
Week 11: The video of the week is a TED lecture (these are great talks, and worth hearing). We'll do Malcolm Gladwell on Spaghetti Sauce (but only a snippet starting around 5 minutes).

♦ Interesting news articles involving math (see also the course disclaimer about not suing me!)

Election fraud:

♦ Interesting videos

TED Lectures: http://www.ted.com/talks

Did You Know (2009 version)

Yes, Prime Minister: Manipulation Polls (YouTube video)

♦ Course disclaimer

I may occasionally say things such as `Probability is one of the most useful courses you can take' or 'If you know probability, stats and a programming language then you'll always be able to find employment'. I really should write `you should always be able to find employment', as nothing is certain. Thus, please consider yourself warned and while you may savor the thought of suing me and/or Williams College, be advised against this! I'm saying this because of the recent lawsuit of a graduate who was upset that she didn't have a job, and sued her school!