Department of Mathematics - RHIT Topics Outline for MA113 - Calculus III - 2010-11

last posted to site: 08/19/10

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 and Text Materials

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.

Approximate Timing and Pace

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

Text Topics - Optional topics in italics

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

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