Electronic Library: Software Alcove: Repository

If you have Derive MTH or DMO files that you wish to add to this collection, you may do so from the Submissions Center. Be sure to include comments and examples that illustrate the use of the file.

Files for Calculus

• area.mth colors the area enclosed by two curves and displays solids of revolution.
• bisect.mth shows iterations of the bisection method and produces a graphical display.
• inverse.mth calculates the inverse of some functions and plots the inverse relation for any function.
• newton.mth shows iterations of Newton's method and produces a graphical display.
• planet.mth contains data about the planets. It includes functions giving the polar equations of planetary orbits with the perihelion properly placed and functions that give the approximate location of planets a function of time. Graphs planetary orbits and the movement of planets within the orbits.
• riemann.mth calculates left-hand, right-hand, and mid-point sums as well as the trapezoidal and Simpson's rule. Provides a graphical display of all of these sums.
• secant.mth calculates secant lines and plots them.

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  Files for Linear Algebra

• diagonal.mth is a utility file for diagonalizing matrices. It includes functions that:
  1. calculate the rank of a matrix
  2. find a basis for the null space of a matrix
  3. find a basis for the eigenspace associated with a given eigenvector
  4. for diagonalizable matrices produce the diagonal and conjugating matrix
  5. calculate the minimum polynomial of a matrix
  6. solve a linear system of first order differential equations when the coefficient matrix is constant and diagonalizable
• echelon.mth calculates an echelon (as opposed to reduced echelon) form of a matrix.
• gram.mth executes the Gram-Schmidt algorithm.
• lin_comp.mth produces a graphical display of the effect of iterating a linear transformation on a vector.
• lu.mth produces the Lower-Upper decomposition for a matrix.
• qr.mth produces the QR decomposition for a matrix and executes the QR algorithm.
• reduce.mth provides partial row reduction of a matrix.

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  Files for Differential Equations

• slope.mth produces a graphical display of slope fields for differential equations. This is a modification of Derive's DIRECTION_FIELD.MTH file. The difference is that SLOPE.MTH normalizes the lengths of line segments.
• vpar.mth calculates Wronskians and executes variation of parameters for high order linear differential equations.
• dif_appr.mth uses the Runge-Kutta method to approximate the solution of high order differential equations.
• ode1.mth is one of the utility files that comes with Derive. It is copywrited but is offered here by permission of SoftWarehouse. The ODE1.MTH file that came with versions of Derive earlier than 2.6 has an error that causes the DSOLVE1_GEN and DSOLVE1 functions to report "inapplicable" to differential equations that Derive knows how to solve. If you have an early version of Derive, you can write over your old ODE1.MTH file and correct the problem.
• See also the DIAGONAL.MTH file listed under Linear Algebra