## Calc CD GeoGebra Files

These are the notes. If you're in my class, you shouldn't print them until I tell you to do so. If you're not in my class, do whatever you want. Notes 6 through 16 have been somewhat rewritten this year (2012)...

## Calc C GeoGebra Files

## Notes 17: Polar Coordinates

Calculus of polar coordinates. You might want to review Notes 16 from Math Analysis for basic, non-calculus stuff. Here's a link to a GeoGebra file that is designed to help you understand the connection between a rectangular graph and its polar equivalent. Here and here are two youtube videos that you might find helpful for calculating polar areas. Here's a video on graphing polar on the TI-Nspire.

## AP Free Response Video Solutions.

Not really notes, but a spreadsheet that links to each of my AP Free Response video solutions. You might find yourself consulting that frequently as you study for the exam. Make sure to always try the problems first! Watching the videos can be counter productive if you haven't yet done the problems.

## Everything after this point is beyond the scope of the AP Calculus BC Exam...

## Calc D Notes

## Notes 1: Vectors in 3D

3D vectors; distance, midpoint, spheres; dot product; components and projections; cross products; distance from a point to a line; scalar triple product; parallelepipeds.

## Notes 2: Lines and Planes in 3D

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

## Notes 3: Quadratic Surfaces, Spherical, Cylindrical Coordinates

The various quadratic surfaces and their traces; cylindrical coordinates (basically polar); spherical coordinates

## Notes 4: Calculus of Vector-Valued Functions

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

## Notes 5: Derivative Things of Functions of Several Variables

Domains; partial derivatives; mixed partial derivatives; the Chain Rule; Direction Derivative and Gradient; tangent planes and normal lines. Here's a video example of how to calculate a directional derivative.

## Notes 6: Optimization in Several Variables

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

## Notes 7: Double & Triple Integrals

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.

## Notes 8: Vector Fields & Line Integrals

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.