This site contains various interactive applets that use a computer algebra system (webMathematica) to draw graphs of functions, take derivatives, integrate, solve equations, multiply matrices, etc. It live-computes derivatives and integrals of functions entered in standard programming language type format. For derivatives a step-by-step computation is provided. For integrals, the program only displays the result. The steps can be bought by purchasing a password. The site also draws graphs and a password can be used to access graphs with the main features (extrema, inflection points etc.) explicitly marked. On the algebraic side, the site multiplies and divides polynomials, showing all steps, and it performs a multitude of matrix operations.
Type of Material:
Checking of homework solutions, drill and practice.
Should run in any browser.
Identify Major Learning Goals:
Mostly to help with understanding certain topics in Calculus (e.g. differentiation and integration), and Linear Algebra (operations with matrices, linear equations, etc.)
Target Student Population:
Students in calculus and linear algebra classes.
Prerequisite Knowledge or Skills:
First term calculus for the calculus component of the site, basic algebra for the rest.
Solutions are correct and the live presentation of a very detailed solution process is impressive. Computations include a final step for simplification.
Potential Effectiveness as a Teaching Tool
Solid, to the point explanation of the computations with steps so elementary that it is near impossible to get lost within a computation.
The main concern is one of abuse, which is ultimately beyond the control of the builders of the site. With perfect solutions presented, the temptation to copy without understanding (worst case scenario) or the development of an inadvertent dependence even on hints from calc101 (sincere students have fallen into this type of trap in many situations) pose the same danger to the learning process that solutions manuals have posed for decades.
The elementary steps can feel a bit long-winded after a while, but that will hopefully teach the user the value of combining steps.
Ease of Use for Both Students and Faculty
The input format is standard for most programming languages and computer algebra systems. Thus, aside from learning nuts-and-bolts calculus, students will learn another way to encode symbolic functions.
Students who could benefit most from this type of service may also be a bit weak in their symbolic computing skills. This makes the input format a small issue. Overall, the format should not be a problem, however, because the detailed steps will show if an expression was entered correctly.
Using square brackets for the arguments of functions like sin[x] takes a minute to get used to.
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