Topics Outline for MA113 - Calculus III - 2010-11

**Note:** The topics list for
AP Freshmen in the Fall quarter is slightly different since they need to
be brought up to speed on Maple.

**Text:** Thomas's Thomas' Calculus - Early Transcendentals
Twelfth Edition - Weir, Hass

**Supplement:** Just in Time - bundled with text.

**Other supplements: ** Normal and tangential components of acceleration problems from Angel.

There should be 3 or 4 tests, perhaps a final review day or two.

**Please note that some additional time needs to be spent teaching Maple MA111 and MA112 topics for fall sections. **

Optional topics in *italics*

Topic |
Fall AP Sections |
Winter and Spring Sections |
||

Chapter Sections | Time | Chapter Sections | Time | |

Review and Maple | 1 day | no review | ||

Polar Coordinates | 11.3, 11.4, 11.7 |
2 days | 11.3, 11.4, 11.7 |
2 days |

Vectors | 12.1, 12.2, 12.3, 12.4,12.5, 12.6 |
1.5 weeks | 12.1, 12.2, 12.3, 12.4,12.5, 12.6 |
1.5 weeks |

Vectors and Motion | 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 |
1 week | 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 |
1 week |

Partial Derivatives | 14.1, 14.2, 14.3. 14.4, 14.5, 14.6, 14.7, 14.8, 14.9, 14.10 |
3 weeks | 14.1, 14.2, 14.3. 14.4, 14.5, 14.6, 14.7, 14.8, 14.9, 14.10 |
3 weeks |

Multiple Integrals | 15.1, 15.2, 15.3, 15.4, 15.5, 15.6, 15.7, 15.8 |
3 weeks | 15.1, 15.2, 15.3, 15.4, 15.5, 15.6,15.7, 15.8 |
3 weeks |

**11. Conic Sections and Polar Coordinates**

11.3 Polar Coordinates

11.4 Graphing in Polar Coordinates

* 10.7 Area and Lengths in Polar Coordinates (optional)*

**12. Vectors and the Geometry of Space **

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

* 12.6 Cylinders and Quadric Surfaces *

**13. Vector-Valued Functions and Motion in Space **

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

* 13.6 Velocity and Acceleration in Polar Coordinates (optional)*

**14. Partial Derivatives **

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

* 14.9 Taylor's Formula for Two Variables (optional)*

* 14.10 Partial Derivatives with
Constrained Variables *

**15. Multiple Integrals **

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Moments and Centers of Mass

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

* 15.8 Substitutions in Multiple
Integrals *