# Math 215 Demonstrations

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
UMMath Math 215 Lecture Demos