# Book 4 Resources

In the navigation panel you can download a zip file containing **all**
the resources for Book 4, or you can click on the links below to download them individually.
(You may need to right-click and choose** 'save link as ...'**).

**vectors_and_curves.xlsm**. Relates to Chapter 1. This Excel spreadsheet shows how some of the Chapter 1 problems can be done numerically.**partial_derivatives.mw**. Relates to Chapter 2. This Maple worksheet shows how some of the Chapter 2 problems can be done analytically.**gradient_descent.xlsm**. Relates to Example 2.4. This Excel spreadsheet hows how going down the gradient will take us to a local minimum.**diffusion.xlsm**. Relates to Problem Set 2.1, #6. The diffusion equation is a partial differential equation that describes heat flow. This Excel spreadsheet contains computer code that can solve this equation under various boundary conditions.**2d_integrals_examples.mw**. Relates to Section 3.3. This Maple worksheet shows how to do double integrals as iterated integrals.**two_charges.mw**. Relates to Example 4.8. This Maple worksheet shows how to plot the electric field and the voltage field around an electric dipole.**greens_theorem.xlsm**. This Excel spreadsheet models Green's theorem. It uses an irregularly shaped region and any vector field.**surface_integrals.mw**. This Maple worksheet shows how to do the surface integrals in Examples 7.2, 7.6 and 7.7.**gauss_stokes.pdf**. A PDF sample of Chapter 8 of the text.**gauss_theorem_on_hemisphere.mw**. This Maple worksheet solves Problem Set 8.1, #3 with a hemisphere of any radius and any vector field.**gauss_on_hemisphere_using_parameters.mw**. This Maple worksheet also solves Problem Set 8.1, #3 but parameterizes the surface using the method of Kreyzig.**stokes_theorem_on_plane_triangle.mw**. This Maple worksheet solves Problem Set 8.2, #1 with any plane triangle surface and any vector field.**stokes_theorem_on_plane_disk.mw**. This Maple worksheet solves Problem Set 8.2, #3 with any plane disk surface and any vector field.