TEMATH(Tools for Exploring Mathematics) is a mathematics exploration environment useful for investigating a broad range of mathematical problems. It is effective for solving problems in calculus, differential equations, linear algebra, numerical analysis, and math modeling. TEMATH contains a powerful grapher, a matrix calculator, an expression calculator, a differential equation solver, a facility for handling and manipulating data, numerical mathematical tools, and visual and dynamic exploration tools, and a capability for importing a digital background image or a sequence of background images. A student or researcher can use TEMATH as a laboratory to conduct mathematical experiments to study and discover properties of functions, discrete data, and mathematical systems. As a visualization tool TEMATH can search for patterns that will inspire mathematical conjectures.

Graphing

Rational Function   Piecewise Function   Parametric Curve   Polar Curve   Level Curves   Nonlinear Inequality   Fractal   Linear Program   Sample Graphs

TEMATH's grapher can plot functions, implicit equations, inequalities, conics, fractals, parameterized families of functions, and data. Graphs can easily be rescaled and resized. The grapher automatically finds vertical asymptotes and jump discontinuities of functions. Conics are graphed with their foci, vertex axes, and asymptotes (if there are any). Plots can easily be zoomed-in or zoomed-out. TEMATH's grapher can also plot functions and data in polar coordinates as well as parameterized curves.

Numerical Tools

TEMATH's numerical tools can find the roots, relative maxima and minima, fixed points, asymptotes, intersections, and lengths of curves. The tangent to a point on a curve can be drawn, and its slope calculated. Both the definite integral of a function and the definite integral of the difference of two functions can be found. Curves can be traced and annotated with labels and points. TEMATH has a moving tangents tool, a dynamic integrator, and a fixed-point iterator.

Matrix Calculator

With the matrix calculator, you can enter matrices, perform matrix arithmetic and matrix operations (such as transpose, inverse, determinant, norm, and elementary row or column operations), and solve systems of linear equations. Eigenvalues, eigenvectors, characteristic polynomials, and singular value decompositions can also be found. With the matrix calculator, you can step through the solution of a linear programming problem, find its initial simplex tableau, or its final solution. The matrix calculator contains four memory registers for storing intermediate results. The matrix calculator is an easy-to-use tool for exploring problems in linear algebra.

Data Analysis Tools

Nautilus Shell Fit

Data tables can easily be entered using the TEMATH interface. Data can be generated or transformed using any function that you specify. You can find the maximum, minimum, average value, and standard deviation of a set of data. Riemann sums and forward, backward and central differences can be found with the click of the mouse. A data table can be graphed, fitted with a line or curve, or interpolated with a polynomial. Data can be imported from spreadsheets and TI calculators.

Differential Equation Solver

Logistic Equation Second-Order Eqn Predator-Prey System Vertical Family Phase Plane X,Y Solutions

With TEMATH's differential equation solver, you can plot the solution of first and second order differential equations using various numerical methods. Slope fields, phase lines, and phase planes are also easily plotted. With TEMATH's system of differential equations solver, a click of the mouse plots the solution of a system of two first-order differential equations.

Expression Calculator

TEMATH's expression calculator can be used to perform simple arithmetic or to evaluate functions, algebraic expressions, sums, products, or complicated mathematical expressions.

Classroom Demonstration Features

TEMATH was also designed with the teacher in mind. Its windows are resizable, it can be used in color mode or black and white mode, and it supports large-sized fonts and different font styles. These features make it easy for the teacher to present clear classroom demonstrations. In fact, the menu-icon style interface of the software encourages spur of the moment demonstrations inspired by the dynamics of the classroom. The traditional classroom lecture can now become a community of learners and explorers.

Audience

Because TEMATH is a general mathematical problem-solving environment, it can be used by students of

• Exploring properties of functions
• Exploring distance and slope
• Graphing, finding roots, local max and min, and points of intersection
• Finding numerical solutions of applied problems
• Solutions of linear systems of equations
• Modeling data with mathematical functions
• Discovering patterns and making conjectures

• Visualizing slope, limits, and the derivative
• Finding tangents, maxima, and minima
• Plotting complete graphs
• Evaluation of definite integrals and arc length
• Exploring analytic geometry
• Visually verifying the definitions of the conics
• Exploring parametric and polar functions
• Simulating physical phenomena
• Applying exponential growth and decay models

• Exploring elementary row and column operations
• Exploring algebraic matrix operations
• Calculation of trace, determinant, and inverse
• Exploring rank, nullity, and matrix norms
• Solving systems of linear equations
• Calculating eigenvalues and solving applied problems

• Sampling curves and generating data
• Fitting data
• Transforming data
• Analyzing and solving differential equations
• Using Markov chains
• Analyzing and solving linear programs

• Solving homework problems
• Analyzing experimental data
• Building mathematical models

Copyright 2000-2008 Adam O. Hausknecht and Robert E. Kowalczyk