Calc III Lectures

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

11.02w74 The Silo Problem

11.03 Polar Coordinates

11.04 Areas and Lengths in Polar Coordinates

11.05 Conic Sections

11.06a Eccentricity

11.06b Polar Equations of Conics 11.06bN

12.01a Sequences Part 1 (PowerPoint) 12.1aN

12.01b Sequences Part 2

12.02 Series (PowerPoint) VIDEO YOUTUBE

12.03 The Integral Test and Estimates of Sums

12.04 The Comparison Tests

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)

12.08 Power Series

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)

12.10c Binomial Series

12.10d Multiplication and Division of Power Series 12.10dN

12.11a Applications of Taylor Series

12.11b Einstein vs Newton

13.01 Three-Dimensional Coordinate Systems

13.02 Vectors

13.03a The Dot Product

13.03b Projections

13.04a The Cross Product

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)

13.05a Equations of Lines

13.05b Equations of Planes

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)

14.03b Curvature

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)

15.02b Continuity

15.03 Partial Derivatives (PowerPoint)

15.04 Tangent Planes and Linear Approximations

15.05a The Chain Rule

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

15.07b Absolute Extremes

15.08 Lagrange Multipliers

16.01 Multiple Integrals

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

16.06 Triple Integrals

16.07 Triple Integrals in Cylindrical Coordinates (PowerPoint)

16.08 Triple Integrals in Spherical Coordinates

16.09a Change of Variables

16.09b Change of Variables Continued

17.01 Vector Fields

17.02 Line Integrals

17.03 The Fundamental Theorem for Line Integrals

17.04 Green's Theorem

17.05 Curl and Divergence

17.06a Parametric Surfaces

17.06b Tangent Planes and Surface Area

17.07a Surface Integrals

17.07b Oriented Surfaces

17.08 Stokes' Theorem

17.09 The Divergence Theorem

18.01 Second-Order Linear Differential Equations

18.02 Nonhomogeneous Linear Differential Equations

18.03a Vibrating Springs

18.03b Electric Circuits

18.04 Series Solutions