# Math 2210 | Calculus III

These lecture videos are organized in an order that corresponds with the current book we are using for our Math2210, Calculus 3, courses (*Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson*). We have numbered the videos for quick reference so it's reasonably obvious that each subsequent video presumes knowledge of the previous videos' material. Along with the video lecture for each topic, we have included the "pre-notes" and "post-notes" which are the notes of the lecture before we did the problems and after we worked everything out during the lecture, respectively. You may want to download the notes to use as a reference while watching the lecture video, or for later reference.

If you find an error in the lecture or a problem with the video, or if you would like to give feedback to us about these lectures, please email rebecca@math.utah.edu to do so.

**NOTE: These videos were not recorded in stereo sound. If you are listening to these videos on headphones, you may want to consider setting your sound channels to come through both sides. This document will give you an idea of how to accomplish that.**

- 1 Parametric Equations lecture video
- 2A Cartesian Coordinates in 3-Space (part 1) lecture video
- 2B Cartesian Coordinates in 3-Space (part 2) lecture video
- 3A Vectors (part 1) lecture video
- 3B Vectors (part 2) lecture video
- 4A The Dot Product (part 1) lecture video
- 4B The Dot Product (part 2) lecture video
- 4C Planes lecture video
- 5A The Cross Product (part 1) lecture video
- 5B The Cross Product (part 2) lecture video
- 6 Vector-valued Functions, Curvilinear Motion lecture video
- 7 Lines and Tangent Lines in 3-Space lecture video
- 8 Surfaces in 3-Space lecture video
- 9A Spherical and Cylindrical Coordinates (part 1) lecture video
- 9B Spherical and Cylindrical Coordinates (part 2) lecture video
- 10 Functions of Two or More Variables lecture video
- 11A Partial Derivatives lecture (part 1) video
- 11B Partial Derivatives lecture (part 2) video
- 12A Limits lecture video
- 12B Continuity lecture video
- 13 Differentiability & Gradients lecture video
- 14 Directional Derivatives lecture video
- 15 Chain Rules lecture video
- 16A Tangent Planes lecture video
- 16B Approximations lecture video
- 17A Maxima and Minima (part 1) lecture video
- 17B Maxima and Minima (part 2) lecture video
- 18A Lagrange Multipliers (part 1) lecture video
- 18B Lagrange Multipliers (part 2) lecture video
- 19A Double Integrals over Rectangles & Iterated Integrals (part 1) lecture video
- 19B Double Integrals over Rectangles & Iterated Integrals (part 2) lecture video
- 20 Double Integrals over Non-Rectangular Regions lecture video
- 21 Double Integrals in Polar Coordinates lecture video
- 22A Surface Area (part 1) lecture video
- 22B Surface Area (part 2) lecture video
- 23 Triple Integrals in Cartesian Coordinates lecture video
- 24 Triple Integrals in Cylindrical and Spherical Coordinates lecture video
- 25 The Jacobian lecture video
- 26 Vector Fields lecture video
- 27A Line Integrals (part 1) lecture video
- 27B Line Integrals & Work (part 2) lecture video
- 28 Independence of Path lecture video
- 29 Green's Theorem in the Plane lecture video
- 30 Surface Integrals lecture video
- 31 Gauss's Divergence Theorem lecture video
- 32 Stokes's Theorem lecture video

These videos were completed as a collaborative effort of Marilyn Keir and Kelly MacArthur, funded and supported by the Mathematics Department at the University of Utah.