This subsite of Mathematics Tutorials and Problems (with applets) (see http://www.merlot.org/merlot/viewMaterial.htm?id=317524 ) is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions. Here the user will find applets with guided exercises and many examples and worked out problems applicable to the first year of Calculus.
Type of Material:
This material is designed as tutorials, but many of the applets could also be used as simulations.
This material is designed as tutorials but many of the applets could also be used in classroom demonstrations.
A Java-enabled Web browser.
Identify Major Learning Goals:
To provide tutorials in various areas of mathematics, including pre-calculus, calculus, geometry and statistics.
Target Student Population:
Undergraduate students taking Calculus.
Prerequisite Knowledge or Skills:
Evaluation and Observation
This site is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions.
1. Interactive Tutorials
There are 15 tutorials. Each one consists of an applet accompanied by a brief discussion of the math concept, an explanation of how to use the applet, and a series of guided exercises. The intent of the guided exercises is to provide the student with a more in-depth understanding of the concept rather than to solve a particular problem. For example in the Concavity of Polynomial Functions tutorial, the student is guided to discover that the first derivative is increasing in an interval where the function is concave up, thus explaining why f ''(x) > 0 corresponds to concave up on the graph. Topics covered in the Interactive Tutorials include derivatives, concavity, Mean Value Theorem, Runge Kutta Method, Riemann Sums, the natural logarithm, and Fourier Series.
2. Calculus Problems
There are 13 problem areas, but some of areas contain more than one problem. Each of these is a typical calculus textbook problem. For example, one asks for the dimensions of the base of a pyramid that minimizes the surface area for a given volume. Another problem is that of finding all points on a polynomial with horizontal tangent. Graphs, diagrams, and detailed solutions are provided. The problems in this section are limited to differential Calculus.
3. Calculus Questions, Answers and Solutions
This section deals with examples that are quite similar to the Calculus Problems discussed above. Nearly 50 topics are listed, and each topic contains two or three examples (worked-out exercises). Many are typical textbook problems, like find the derivative of the inverse of a given function or use implicit differentiation to find dy/dx for a given implicitly defined function. The areas of Calculus covered include differential, integral, and ordinary differential equations.
Potential Effectiveness as a Teaching Tool
This site should be quite effective for students seeking help in the first year of calculus or introductory ordinary differential equations. While some of the more sophisticated interactive tutorials that use experimentation and discovery may require the aid of an instructor, the majority of the material should be quite accessible to most Calculus students. The math concepts are well-explained, the solutions are quite detailed and thorough, and ample instructions are provided for operating the Java applets. The site should also be quite useful for classroom demonstrations.
Ease of Use for Both Students and Faculty
Most of the Java applets are intuitive and easy to use. There is quite adequate instruction provided for the technical aspects throughout the site, and the problems and solutions are well-explained. Even in the non-interactive parts, one finds a great number of illustrative graphs.
Initially, some of the applets would not work in Firefox. After upgrading Java and then re-installing the upgrade, these difficulties seem to be resolved. Internet Explorer played all the applets without a hitch.
There is an apparent font problem in rendering some of the pages in FireFox. In particular, the arrow symbols in limits appear correctly on some pages but not on others. No such difficulties occurred with Internet Explorer.
Also, this site would definitely benefit from a hyperlinked subject index that can make navigation a lot easier.