MTH243 (Calculus for Functions of Several Variables)
Recent development of various computers, from the personal computer to the super computer, involves rapid change in computer architecture and advancement in software engineering. There are many computing resources available that will aid in your exploration and understanding of material. The main software packages that we recommend are
- R (free software)
- Octave (free software, similar to Matlab)
- Maxima (free computer algebra system)
- Sage (free computer algebra system)
- SymPy (free computer algebra system)
- Python (free software)
All can be found in the general computing labs on campus and available for purchase at significantly reduced rates for students. Throughout the course, we will reference these various software packages when applicable. There are many other software packages that can be used in the differential equation courses. We mention some of them.
GeoGebra is the free and multi-platform, open-source dynamic mathematics software for education in secondary schools that joins geometry, algebra, tables, graphing, statistics, and calculus.
Newplot is a free software, which is very useful for plotting.
Slope and direction fields can be plotted using the following links:
Bluffton University on-line java script, click here
Math Scoop student resources
Nathan Grigg slope fiels application
Matlab (and its free version, Octave) is used extensively in the scientific computing community; it is fairly easy to learn, and Matlab gives quite robust offering packages for visualization, numerical linear algebra, numerical differential equations and limited sybolic computation. MuPad is a computer algebra system within Matlab based on Maple. The Matlab Live Editor provides a new way to create, edit, and run Matlab code. It creates, edits, and run code in a single interactive environment. For primers on Matlab, we recommend:
- Matlab Tutorial by Vladimir Dobrushkin
- MuPad Tutorial by Vladimir Dobrushkin
- MATLAB Live Editor by Vladimir Dobrushkin
In this course, we will use information technologies that facilitate understanding the matrial; since a computer algebra system (CAS) such as Mathematica is available for URI students for free in computer labs, I recommend to use Mathematica. Projects are created to help you learn new concepts. Mathematica is very useful in visualizing graphs and surfaces in three dimensions. The commercial software Matlab is also available at engineeering labs. Its free version is called Octave. A student can also use free CASs: Maxima, SymPy (based on Python), or Sage.