Math Analysis Notes

Math Analysis Notes, Problem Sets, Playlists

These are notes, problem sets, and playlists for Math Analysis. Half of the playlists are me doing the notes. The rest of the playlists are supplementary problems and explanations. Click the top headings for the actual notes--they don't look like hyperlinks, but they are! Math Analysis is a great pre-calculus course: you learn everything you need for Calc 1, Calc 2, and Calc 3 (as well as AP Calculus AB and BC).

If you have noticed any errors in the notes, I'd really appreciate it if you'd point them out to me. You can do that using this form.

Notes 1

Radians, arc length, basic stuff about trigonometry in the plane, coterminal angles, degrees, minutes, seconds. Here's a GeoGebra file that shows radians on a circle. I recommend downloading it and playing around to get a better sense of how radians work.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of additional videos about these notes.

Notes 2

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 3

Unit Circle! Even/odd trig functions. Here's a link to a GeoGebra file that tries (tries really hard...) to show the geometry of the Unit Circle and the various trig ratios. Here's a blank copy of the Unit Circle quiz. Print it and practice a LOT!

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 4

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 5

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.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to some useful Desmos Activities and GeoGebra sketches.

Here's a link to a YouTube playlist of videos about these notes.

Notes 6

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.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 7

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 Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 8

Solving trigonometric equations.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 9

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

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 file that I use to motivate the acute-angled ambiguous case. Here's a link to the online version of the motivation for the ambiguous case.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

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!)

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 12

Complex numbers, trig/polar form, multiplying, dividing, nth powers, nth roots. Here's a link 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.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

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.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 14

Conic sections...lots and lots of conic sections...

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to some GeoGebra things.

Here's a link to a YouTube playlist of videos about these notes.

Notes 15

Parametric equations and doing stuff with them. Here's a GeoGebra file that is set up to model parametric motion (you can change the equations and then watch the particle move). Click here to go to a page with links to various GeoGebra sketches to play around with.
Click here for a detailed discussion of a problem (relevant to you by page 189).

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 16

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 17

Three-dimensional things, lines, simple planes (we do NOT cover cross product in the notes), volumes of revolution. Here's a link to some GeoGebra sketches about these sorts of things.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 18

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.

Notes 19

Limits visually, graphically, numerically.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

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! Here's a link to GeoGebra and/or Desmos things to check out.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

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.

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!
Here's a link to a YouTube playlist of videos about these notes.

Notes 22

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

Here's a link to the Problem Sets for these notes.
Here's a link to a YouTube playlist of me working through the notes. Complete solutions and explanations!

Here's a link to a YouTube playlist of videos about these notes.