Many examples.įourier series via inner products. Orthogonal expansions with Legendre, Hermite, Laguerre, and Chebyshev polynomials.įourier series as an example of Sturm-Liouville theory. This contains Mathematica commands and functions for investigating these coordinate systems, but it is by no means self-contained.Ī notebook illustrating Laplace transforms and using them to solve some differential equations.Ī review of the properties of even and odd functions in anticipation of orthogonal expansions and Fourier series. Streamlines, equipotential curves, and a bit of complex functions.Ī notebook illustrating arc length, flows, surface area, flux.Ī notebook with functions to look at orthogonal coordinate systems and the div, grad, curl, in these coordinate systems. This is a new and improved version of veccalc.nb. This has some Mathematica basics about vectors along with some functions for plotting vectors and lists of vectors.Ī notebook illustrating parametric curves, gradient, divergence and much more. This made things easy on me and my students. Evaluate this before each vector calculus session. I collected all of the functions and packages that I need for vector calculus in this one notebook. Right click on the download button to save. The notebooks are listed in the order I assign them. Fourier Integral, Fourier Transform, Partial Differential Equations.Fourier Series, Partial Differential Equations.Line integrals, flows, Green's Theorem, potential theory, surface integrals, flux, Divergence Theorem, Stokes' TheoremĮigenfunction expansions, orthogonal polynomials Vector functions, curves, velocity, acceleration, curvature, vector fields, streamlines, gradient, divergence, curl The order of topics of the course I teach is:ĭot product, cross product, abstract vector spaces Please Note: The links to the HTML versions are not working right now. This is a course that typically uses a book with a title like "Advanced Engineering Mathematics". These notebooks are used in the course Advanced Mathematics for Applications at Indiana University of Pennsylvania. Most have some "discovery learning" built in. These Mathematica notebooks are all used for teaching and illustrating concepts. Advanced Mathematics for Applications Mathematica Notebooks Advanced Mathematics for Applications Mathematica Notebooks
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