# Calc C Notes and Videos

## Notes 01

Partial fraction decomposition (leading to integrals, of course!); non-repeating linear factors; repeated linear factors; quadratic factors.

## Notes 02

Introduction to Taylor polynomials; error of Taylor polynomials for approximations. Not Yet Here’s a link to a GeoGebra file that shows a Taylor Polynomial with variable center and order.

## Notes 03

Sequences; some properties of sequences; limits of sequences; linking sequences to series

## Notes 04

Introduction to series; geometric series; telescoping series; properties of convergent series; nth term test for divergence

## Notes 05

Series Tests: Integral test; p-series

## Notes 06

Series Tests: Direct comparison test; limit comparison test.

## Notes 07

Series Tests: Ratio Test (best test ever!); Root Test.

## Notes 08

Alternating Series; Alternating Series Test; Error for Alternating Series; Absolute Convergence vs. Conditional Convergence

## Notes 09

Power Series; Interval of Convergence; new series from old series via integration and differentiation

## Notes 10

Taylor Series; working with the known series for e^x, sin(x), cos(x), and 1/(1-x); applications of series; Lagrange Error Bound; identifying the function to which a series converges.

## Notes 11

Integrals of powers of trig functions; saving a power; using Pythagorean Identities.

## Notes 12

Arc Length for functions

## Notes 13

Euler’s Method. Not Yet Here’s a link to a GeoGebra file that demonstrates Euler’s Method (change the initial point, the size of dx, and the number of steps; also view the solution curve). Several interesting/useful videos in the playlist.

## Notes 14

Logistic Differential Equation. Not Yet Here’s a link to a GeoGebra file of a logistic curve with a slope field and some things you can manipulate. Here’s a fun activity that generates a nice logistic curve (we do it in class, you don’t need to print it). Here’s the spreadsheet we’ll use to track the activity.

## Notes 15

Integration by Trig Substitution; integrating lots of things with radicals of a certain form; introducing a radical to make it work; drawing reference triangles. (This is not actually a topic that’s on the AP Calculus BC Exam, but I really think you should know it!)

## Notes 16

Calculus of parametric equations; vector-valued functions; calculus of vector-valued functions. Not Yet Here’s a link to a GeoGebra file that shows a curve, dx/dt, dy/dt, dy/dx, and the second derivative of the parametric equations. You might want to review Notes 15 from Math Analysis. The videos for those notes are here.

## Notes 17

Calculus of polar coordinates. First you need to really get good at non-calculus related polar coordinates. You might want to review Notes 16 from Math Analysis for basic, non-calculus stuff. Here’s the videos for those. In these notes: common graphs, tangent lines, interpreting derivatives dy/dx, dy/dt, dx/dt, and dr/dt, polar areas.

Nothing after this point will be on the AP Calculus BC Exam! ***

# Calc D Notes and Videos

## Notes 01

3D vectors; distance, midpoint, spheres; dot product; components and projections; cross products; distance from a point to a line; scalar triple product; parallelepipeds. Here’s a proof about a relationship between sine and the cross product.

• 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!
• Here’s a link to some tech things (probably GeoGebra sketches!) about these notes.

## Notes 02

vector, parametric, and symmetric equations of a line in 3-dimensions; angle between lines; planes; normal vectors to planes.

## Notes 03

The various quadratic surfaces and their traces; cylindrical coordinates (basically polar); spherical coordinates. If you follow along with the videos about spherical coordinates, you can find the problems, some work, and some things to type in here.

## Notes 04

Intersections of surfaces; domains; limits; derivatives; tangent lines; arc length parameterizations; curvature

## Notes 05

Domains; partial derivatives; mixed partial derivatives; the Chain Rule; Direction Derivative and Gradient; tangent planes and normal lines. See the videos for a bunch of examples. Here’s a write up of directions on how to look at partial derivatives graphically using GeoGebra 3D.

## Notes 06

Critical points; Second Derivative Test; Global extrema (absolute max/min); constrained optimization; Lagrange Multipliers.

## Notes 07

Riemann sums leading to double integrals; evaluating iterated integrals; changing the order of integration; determining the bounds; polar coordinates; triple integrals; cylindrical coordinates; spherical coordinates. Here’s a video of how to use your TI-Nspire CAS to help you find double (or triple) integrals. Here’s a video example of how to reverse the order of integration. Here’s a link to a GeoGebra sketch that tries to show Riemann Sums for double integrals in rectangular on GeoGebra.org. (It is very slow to update as you change things because it is doing a lot of work!)

## Notes 08

Gradient vector fields and potential functions; conservative vector fields; curl; line integrals; work; Fundamental Theorem of Line Integrals; path independence. Here’s a video example of a line integral of a scalar function. Here’s a video example of a line integral of a vector field.

## Calc D Assignments Video Solutions

This is an ongoing project of mine, but the videos are all in this playlist.