# Math Analysis Notes and Videos

## Notes 01

Radians, arc length, basic stuff about trigonometry in the plane, coterminal angles, degrees, minutes, seconds.

## Notes 02

Right triangle trigonometry, review of special right triangles, introduction of reciprocal functions, using a calculator, co-functions.

## Notes 03

Unit Circle! Even/odd trig functions. Here’s a blank copy of the Unit Circle quiz. Print it and practice a LOT!

## Notes 04

Reference angles, circular definitions of trigonometric functions, “point” problems, trig and slope of a line

## Notes 05

Periodic functions, graphing all of the trig functions (with all of the transformations), equations from graphs, equations from tables of data. Here’s a link to a GeoGebra file that illustrates how the Unit Circle relates to the graphs of sine and cosine.

## Notes 06

Inverse trig functions, domains/ranges, compositions. Here’s a link to a GeoGebra sketch that lets you figure out how the Unit Circle generates the graphs of sine and cosine. Making sine 1-to-1 and making cosine 1-to-1.

## Notes 07

Trigonometric identities, verifying identities; using co-functions, tables, and identities. You’ll also need these eventually, so print them when you print the notes. (Sorry, have to be in my class to get them!)

• Here’s a link to the notes.
• Here’s a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
• There are currently no Problem Sets for these notes.

## Notes 08

Solving trigonometric equations.

## Notes 09

The 14 Formulas! (sum/difference/double angle/half angle/Euler’s Formula).

## Notes 10

Law of Sines/Law of Cosines, Heron’s Formula, general area of a triangle. Here’s a link (must be logged in to ) to a google spreadsheet that will solve triangles so you can check answers. Here’s a link to the GeoGebra sketch that I use to motivate the acute-angled ambiguous case.

## Notes 11

All kinds of stuff about two-dimensional vectors. Here’s a link to a GeoGebra page that finds the parallel and orthogonal vectors that sum to a given vector. (If you’ve done the notes, you know the problem!)

## Notes 12

Complex numbers, trig/polar form, multiplying, dividing, nth powers, nth roots. Here’s a link Not Yet to a GeoGebra file for visualizing the nth roots of a complex number. Here’s a link to a little p5.js sketch for area of regular polygon.

## The Inexcusable Problem Set!

This is a collection of some big ideas type questions that you should definitely be able to solve by the end of Notes 12, which we’ve now reached. Note that it’s inexcusable not to be able to solve them…that doesn’t mean you will be able to–just that there’s no excuse for not being able to, really.

## Notes 13

Random stuff about functions, rational functions, that kind of stuff…some basic limits at infinity. Here’s a little write up about how to graph two different rational functions.

## Notes 14

Conic sections…lots and lots of conic sections…

## Notes 15

Parametric equations and doing stuff with them. Here’s a link to a detailed discussion of a problem (relevant to you by page 189).

## Notes 16

Polar coordinates. Converting polar to rectangular; graphing in polar coordinates; common polar curves.

## Notes 17

Three-dimensional things, lines, simple planes (we do NOT cover cross product in the notes), volumes of revolution.

## Notes 18

More on volumes of revolution, area problems, start tying it all into limits. Here’s a link to a supplement on using summations for arc length. Here’s a link to some GeoGebra sketches about these sorts of things.

## Notes 19

Limits visually, graphically, numerically.

## Notes 20

Limits and almost all the algebra you’ll need to do them. We don’t cover pages 8, 9, and 10 in class. Try them on your own and then watch the videos in the playlist if you don’t know what you’re doing!

## Notes 21

IVT; limit definition of a derivative; power, product, and quotient rules; some notation stuff; higher derivatives. Consider listening to Episode 01 of this podcast for some info on Newton, Leibniz, and the beginnings of calculus.

## Notes 22

Extreme Values; Candidates Test; First & Second Derivative Tests; Curve Sketching; some basic optimization problems.

## AP Calculus Summer Assignment

This is not actually a summer assignment that you’re required to do if you’re in my class, but I made it after a bunch of people asked!

• Here’s a link to the pdf of the summer assignment.
• Here’s a link to a YouTube video of me working through the problems. Complete solutions and explanations!
• Here’s a link to a YouTube video of me doing an overview of the concepts you need to master to succeed in AP Calculus.