An online derivative calculator that computes symbolic derivatives of mathematical expressions. User input and results are typeset as graphical formulas.

Encyclopedia of STEM education is a free resource with 50,000 problems/solutions covering 13 math subjects, 13 science subjects and 13 engineering subjects for self study learning, classroom teaching, tutoring and teacher training.

This site provides information on solutions to various classes of mathematical equations. There are exact solutions and methods for solving ordinary differential equations, partial differential equations, integral equations, and other classes of functions and transforms. The Equation Archive allows authors to post equations and exact solutions, first integrals, and transformations. There is also an index of named algebraic, ordinary differential, partial differential, integral, and functional equations. Other materials include links to online forums, information on mathematical software, and links to educational materials, publications, and related websites.

The General Purpose Math Visualizer Package performs mathematical tasks that are commonly encountered in physics: plotting, animating, numerically differentiating and integrating, and solving systems of coupled algebraic equations. For examples of how this package can be used to explore various physics problems, see the chapter "Using the Computer as a Black Box" at http://www.compadre.org/osp/items/detail.cfm?ID=11330. A significantly revised and expanded version of this package’s function plotting program is also available at http://www.compadre.org/osp/items/detail.cfm?ID=11593. The General Purpose Math Visualizer Package was developed using the Easy Java Simulations (Ejs) modeling tool.   It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_GeneralPurposeMath.jar file will run the program if Java is installed. An alternate version (ejs_GeneralPurposeMath_lowres.jar) is also included below that should fit on the screen more nicely when using a display set to a low resolution.

An online integral calculator supporting definite integrals, indefinite integrals (antiderivatives) and improper integrals. User input and results are typeset as graphical formulas.

This work takes an experimental approach to understanding mathematics through the use of interactive Java simulations. Suggestions for experiments to perform are included for over 60 interactive EJS models created by the author and a collection of over 2000 java simulations in physics. Topics covered include infinitesimal calculus, partial differential equations, fractals and much more. Intervention and customization of the calculation programs is possible using the EJS (Easy Java Simulation) simulation technology. A module library also allows users to engage in further development. In the electronic version of the text, the examples can be accessed directly from the text and operated online or from an installed package. The interactive format is an ideal tool to help users visualize and understand mathematics and physics and their simulation techniques.

Extracted from its web site: "Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions.... Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was revolutionary in its day, and many later systems, such as Maple and Mathematica, were inspired by it." Maxima is available free of charge under the GNU General Public License. There are versions for Linux, Windows, MaC OS X, as well as other operating systems. The Windows version installation includes the popular graphical environment wxMaxima which was specifically developed for it.

We designed a sequence of seven lessons to facilitate learning of integration in a physics context. We implemented this sequence with a single college sophomore, “Amber,” who was concurrently enrolled in a first-semester calculus-based introductory physics course which covered topics in mechanics. We outline the philosophy underpinning these lessons, which characterizes integration in terms of layers and representations. We describe how Amber learned to give oral presentations in which she told a story about how integration comes from products, sums, and limits in a variety of physics contexts. We conclude that by the end of our lessons, Amber was able to conceptualize and explain integrals using multiple representations. In one case, she was able to solve a novel problem about integration in an unfamiliar context (center of mass.) Based on our previous research about integration, we suggest that these achievements would have been unattainable with the use of a single one or two hour lesson.

In this calculus activity, learners use a classic problem of geometrical probability to find an important mathematical constant (pi). Learners explore Buffonäóťs needle problem (which asks the probability of a needle hitting a line if it is thrown at a group of evenly spaced parallel lines) by physically throwing toothpicks and graphing the results.

Chapter 1 of Open Source tools for Computational Physics: An introduction to EJS and Python. This chapter introduces the use of the computer as a “black box” (i.e., without programming) for solving a variety of physics and engineering problems, making use of the General Purpose Math Visualizer Package. Using this package, the reader is asked to create and analyze plots and animations, numerically differentiate and integrate functions of relevance to physical problems, and numerically solve systems of coupled linear algebraic equations.

The derivative of a function is always less smooth than the function. Because of this any noise in our data is magnified when we differentiate it.