Investfunc (Investigation of Functions).This application contains a collection of the following functions:
allsolve : Finds all solutions of an real valued equation of one variable in a supplied interval by repeated application of fsolve. Used for the solution of algebraic equations.
fdomain : Determines the domain of an implicit real valued function of two variables. Used for the investigation of real valued functions, especially in the programs 'curdisk' and 'implicitan'.
curdisk : Determines the special points of a real valued function of only one variable (domain, zeros, poles, extrema, inflection, asymptotic, symmetry), creation of a representative plot of it. 'allsolve' is used if the function is non-polynomial. 'ratsolve' and 'ratsort' are used, to get exact results. 'fdomain' is used to determine the domain of the function. It is an addition to the students package.
ratsolve: Finds the exact roots of an univariate polynomials, otherwise find numerical solutions. Deliver sorted output. Useful in minor service in the investigation of polynomials, especially in the programs 'curdisk',' implicitan' and 'sarea'.
ratsort: sorts a list of exact and infinite numbers. It is useful in general service, especially in the programs 'curdisk', 'implicitan' and 'sarea'.
sarea: Determines the surface between two real valued functions of one variable over a supplied interval by use of 'allsolve'. It is nontrivial if nonpolynomial functions intersect more than once over the interval. This is an addition to the student package
implicitan: Determines the tangents of an implicitly given real valued function at supplied x-coordinates of the tangency points. Investigation of singular tangency points for curves of the second order and higher.
'ratsolve' and 'ratsort' are used, to get exact results. 'fdomain' is used to determine wether the x-coordinates supplied are in the domain of the implicit function. Creation of a representative plot. Useful in classical differential geometry, in addition to the student package.