NOTE: The links on this page were updated in October, 2021. If you saved the old links you will need to resave them.
The following are lectures for Calculus III - Multivariable. They are mostly in Adobe pdf format. Clicking on a link will take you to Google Docs. You should be able do view these files on Google Docs or download them.
You will need to download the PowerPoint lectures in order to view them correctly. Because of the mathematical formulas and graphics involved, the PowerPoint lectures cannot be viewed directly in Google Drive. To download the PowerPoint lectures, after the link takes you to the Google Drive page, click on File in the upper left corner, and then select Download, Microsoft PowerPoint.
A few of these lectures are PowerPoint presentations. To view them on an iPad, download the free SlideShark application from iTunes.
Notes:
Some of these lectures reference the TI-89 graphing calculator.
Lectures with an N after the lecture number have been rewritten to reference the TI-nspire graphing calculator.
11.01 Parametric Equations 11.01N
11.02a Calculus with Parametric Curves
11.02b Area and Arc Length of Parametric Curves
11.02c Parametric Curves and Surface Area
11.04 Areas and Lengths in Polar Coordinates
11.06b Polar Equations of Conics 11.06bN
12.01a Sequences Part 1 (PowerPoint) 12.1aN
12.02 Series (PowerPoint) VIDEO YOUTUBE
12.03 The Integral Test and Estimates of Sums
12.05 Alternating Series 12.05N
12.06 Absolute Convergence and Root Tests (PowerPoint)
12.07 Strategy for Testing Series
Series Convergence Flow Chart (handout)
12.09 Representations of Functions as Power Series
12.10a Taylor Series (PowerPoint) 12.10aN
12.10b Taylor's Theorem - Error Analysis for Series (PowerPoint)
12.10d Multiplication and Division of Power Series 12.10dN
12.11a Applications of Taylor Series
13.01 Three-Dimensional Coordinate Systems
Cross and Dot Products on the TI-89 (handout)
13.04b Triple Products, Torque, Vectors & Determinants on the TI-nspire (PowerPoint)
13.04b Triple Products & Torque (PDF)
13.06 Cylinders and Quadric Surfaces
14.01a Vector Functions and Space Curves
14.01b Using Computers to Draw Space Curves (PowerPoint) VIDEO YouTube
14.02 Derivatives and Integrals of Vector Functions
14.03a Arc Length (PowerPoint)
14.03a Arc Length (PDF)
14.03c Normal and Binormal Curves 14.03c N
14.04a Motion in Space: Velocity and Acceleration
14.04b Tangential and Normal Components of Acceleration
15.01 Functions of Several Variables (PowerPoint) 15.01N
15.02a Limits and Epsilon-Delta Proofs
15.02a 3-D Graphs (PowerPoint)
15.03 Partial Derivatives (PowerPoint)
15.04 Tangent Planes and Linear Approximations
15.05b Implicit Differentiation
15.06a Directional Derivatives and Gradient Vectors
15.06b Tangent Planes to Level Surfaces
15.06bH Handout for problems 36 & 38
15.07a Maximum and Minimum Values
16.02 Iterated Integrals (PowerPoint)
16.03 Double Integrals Over General Regions
16.04 Double Integrals in Polar Coordinates
16.05 Applications of Double Integrals
16.07 Triple Integrals in Cylindrical Coordinates (PowerPoint)
16.08 Triple Integrals in Spherical Coordinates
16.09b Change of Variables Continued
17.03 The Fundamental Theorem for Line Integrals
17.06b Tangent Planes and Surface Area
18.01 Second-Order Linear Differential Equations