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

    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