Note: for each demonstration, the Explanation provides a page that explains the demonstration. Gallery is a page with web-accessible images (only) from the Explanation which might be useful even if you do not use the full Mathematica notebook. Finally, DemoNotebook is a link to a Mathematica notebook for the demonstration.
A note on usage: the computation that some of
the Mathematica notebooks are doing is quite significant. To use
the notebooks, you will want to evaluate them in advance (from the top
menu, Evaluation->Evaluate Notebook) and save the notebook
with the graphics generated. In some case the evaluation will take a
while.
There are also a number of Mathematica notebooks from chapter 12 material (that is, vectors, etc.); these are not documented but may provide useful graphics: The Distance Formula; Cartesian Coordinates; the Cross Product; Lines and Planes; and Quadratic Surfaces.
| Book Sec | Topic | Example Description | Explanation | Gallery | DemoNotebook |
|---|---|---|---|---|---|
| 13.1 | Curves in Space | Animated graphs of parametrically defined curves in space. | 13_1_Explanation | 13_1_Gallery | 13_1_Notebook |
| 13.2 | Derivatives of Vector-Valued Functions | Graphs and animated graphs of the derivatives of parametrically defined curves in space. | 13_2_Explanation | 13_2_Gallery | 13_2_Notebook |
| 13.3 | TNB Frames | Graphs of the tangent, normal and binormal vectors for a parametrically defined curve, with the normal plane also shown. | 13_3_Explanation | 13_3_Gallery | 13_3_Notebook |
| 14.1 | Level Curves | Graphs of level curves and their projection up to a surface. | n/a | n/a | 14_1_Notebook |
| 14.3–14.4 | Partial Derivatives and Tangent Planes | Graphs of the tangent vectors determined by the partial derivatives, and resulting tangent plane. | 14_3-4_Explanation | 14_3-4_Gallery | 14_3-4_Notebook |
| Book Sec | Topic | Example Description | Explanation | Gallery | DemoNotebook |
| 14.6 | Gradients | Graphics showing the gradient vectors for a function of two variables, on the level curves and corresponding surface, the gradient vector field, and gradients on a level surface. | n/a | n/a | 14_6_Notebook |
| 14.8 | Lagrange Multipliers | Graphs and animated graphs showing constraints and surfaces, and the relationship between the constraint and level curves. | 14_8_Explanation | 14_8_Gallery | 14_8_Notebook |
| 15.1 | Double Integrals over Rectangles | Graphs of Riemann sums for double integrals. | 15_1_Explanation | 15_1_Gallery | 15_1_Notebook |
| 15.2 | Iterated Integrals and Fubini's Theorem | Animated graphs of the double integrals of a function. | 15_2_Explanation | 15_2_Gallery | 15_2_Notebook |
| 15.3 | Double Integrals over General Regions | Graphics and animations showing the integration regions for integration over general regions in different orders. | 15_3_Explanation | 15_3_Gallery | 15_3_Notebook |
| Book Sec | Topic | Example Description | Explanation | Gallery | DemoNotebook |
| 15.4 | Double Integrals in Polar Coordinates | Graphs and animations showing Riemann sums in polar coordinates. | 15_4_Explanation | 15_4_Gallery | 15_4_Notebook |
| 15.5 | Moments and Centers of Mass | Graphs and animated graphs showing laminas "balanced" on walls and points, and the effect of moving off the center of mass. | 15_5_Explanation | 15_5_Gallery | 15_5_Notebook |
| 16.2 | Line Integrals | Graphs of Riemann sums approximating line integrals, and of the line integrals with respect to x and y. | 16_2_Explanation | 16_2_Gallery | 16_2_Notebook |
| 16.5 | Curl | Graphs and animations showing the curl of a vector field. | 16_5_Explanation | 16_5_Gallery | 16_5_Notebook |
| 16.7 | Flux Integrals | Graph of a vector field and surface, showing the flux through the surface. | n/a | n/a | 16_7_Notebook |
| Book Sec | Topic | Example Description | Explanation | Gallery | DemoNotebook |