The following links will lead you to applications of differential equations using particular software
It should be pointed out from the very beginning that any software is only a tool. As a very important tool, it is more useful if its user has thought through the details of the task for which the tool is designed. Once you have learned the concepts behind the differential equations (which is the topic of the course) and know how to set up a specific problem, software will be of great help in understanding the material. There are many computing resources available that will aid in your exploration and understanding of differential equations. The main software packages that we recommend are
All these packages have the syntax commands closely related to traditional pen-and-paper mathematical language. According to the National Council of Teachers of Mathematics, the goal of teaching mathematics is to help all students develop mathematical concepts including the abilities of students in converting symbolic information into graphical and technology. This can be achieved and constructed using programming that is useful at any stage of mathematical thinking especially in conjecturing. In our days, computational thinking should be considered a fundamental analytic skill in education, along with reading, writing, and arithmetic. This is a vision for the twenty-first century supported by both, the National Research Council of the Academy of Science and the National Council of Teachers of Mathematics.
The author feels deeply that computing should be an integral part of any differential equation course. The graphics capabilities alone warrant its use, whether for plotting solutions, direction fields, phase plane portraits, or any of the other interesting and often necessary auxiliary functions that arise in the theory. Of course. technology is not a substitute for actual knowledge of material. Technology is a tool to gain insights into complex problems and it can be a valuable tool to better understand difficult concepts and learn the scientific methods of inquiry. The author believes that computing brings additional insight and helps to develop curiosity that theory alone cannot achieve. As a result, the qualitative aspects of differential equations could be explored in greater depth.
Exams & Solutions