Maple worksheets on the numerical evaluation of mathematical functions |
Numerical methods topics:
- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes
The following Maple worksheets can be downloaded.
They are all compatible with Classic Worksheet Maple 10.
A procedure for calculating square roots - sqrt.mws
- Newton's method for calculating square roots.
- Hero's formula for calculating square roots.
- Starting approximation for a general square root procedure.
- A procedure for calculating the square root of a number: squareroot.
Evaluating the sine function from its Maclaurin series - sine_MS.mws
- Graphing partial sums of the Maclaurin series for sin(x).
- A procedure for evaluating the sine function from its Maclaurin series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the sine function.
Evaluating the cosine function from its Maclaurin series - cosine_MS.mws
- Graphing partial sums of the Maclaurin series for cos(x).
- A procedure for evaluating the cosine function from its Maclaurin series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the cosine function.
Evaluating the exponential function from its Maclaurin series - exp_MS.mws
- Graphing partial sums of the Maclaurin series for exp(x).
- A procedure for evaluating the exponential function from its Maclaurin series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the exponential function.
Evaluating the natural logarithm function from its Maclaurin series - natlog_MS.mws
- Graphing partial sums of the Maclaurin series for ln(1+x).
- A procedure for evaluating the natural logarithm function from a Taylor series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the natural logarithm function.
Evaluating the inverse tangent function from its Maclaurin series - arctan_MS.mws
- Graphing partial sums of the Maclaurin series for arctan(x).
- A procedure for evaluating the inverse tangent function from its Maclaurin series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the inverse tangent function.
Evaluating the inverse sine function from its Maclaurin series - arcsin_MS.mws
- Graphing partial sums of the Maclaurin series for arcsin(x).
- A procedure for evaluating the inverse sine function from its Maclaurin series.
- Argument reduction.
- An arbitrary precision procedure for evaluating the inverse sine function.
Procedures for evaluating the sine function - sine.mws
- A fixed (low) precision procedure for evaluating the sine function.
- A general procedure for evaluating the sine function: sine.
Procedures for evaluating the sine and cosine functions - sincos.mws
- Arbitrary precision procedures for evaluating the sine and cosine functions.
- Fixed precision procedures for evaluating the sine and cosine functions.
- General procedures for evaluating the sine and cosine functions: sin_, cos_ .
Procedures for evaluating the tangent function - tan.mws
- Argument reduction.
- An arbitrary precision procedure for evaluating the tangent function.
- Fixed precision procedures for evaluating the tangent function.
- A general procedure for evaluating the tangent function: tan_.
Procedures for evaluating the exponential function - exp.mws
- Evaluating the exponential function via the function f(x)=x*(exp(x)+1)/(exp(x)-1).
- Fixed precision procedures for evaluating the exponential function.
- A general procedure for evaluating the exponential function: exp_.
Procedures for evaluating the natural logarithm function - natlog.mws
- Evaluating the natural logarithm function via the function f(x)=ln((1+x)/(1-x)).
- Argument reduction.
- An arbitrary precision procedure for evaluating the natural logarithm function.
- Fixed precision procedures for evaluating natural logarithm function.
- A general procedure for evaluating the natural logarithm function: ln_.
Procedures for evaluating the inverse tangent function - arctan.mws
- Fixed precision procedures for evaluating the inverse tangent function.
- A general procedure for evaluating the inverse tangent function: arctan_.
Procedures for evaluating the inverse sine function - arcsin.mws
- Fixed precision procedures for evaluating the inverse sine function.
- A general procedure for evaluating the inverse sine function: arcsin_.
Procedures for evaluating the inverse cosine function - arccos.mws
- Evaluating arccos(x) by using arcsin(x).
- A general procedure for evaluating the inverse cosine function: arccos_.
Procedures for evaluating the hyperbolic sine and cosine functions - sinhcosh.mws
- Arbitrary precision procedures for evaluating sinh(x) and cosh(x).
- Fixed (low) precision procedures for evaluating sinh(x) and cosh(x).
- General procedures for evaluating the sinh(x) and cosh(x): sinh_,cosh_.
Procedures for evaluating the hyperbolic tangent function - tanh.mws
- A fixed (low) precision procedure for evaluating the hyperbolic tangent function.
- A general procedure for evaluating the hyperbolic tangent function: tanh_.
Procedures for evaluating the inverse hyperbolic sine and cosine functions - invhyp.mws
- Graphing partial sums of the Maclaurin series for arcsinh(x).
- A fixed (low) precision procedure for evaluating arcsinh(x).
- A general procedure for evaluating arcsinh(x) and arccosh(x): arcsinh_,arccosh_.
Procedures for evaluating the inverse hyperbolic tangent function - arctanh.mws
- Graphing partial sums of the Maclaurin series for arctanh(x).
- Fixed precision procedures for evaluating the inverse hyperbolic tangent function.
- A general procedure for evaluating the inverse hyperbolic tangent function: arctanh_.
Examples involving the numerical functions - fcnexamp.mws
Evaluation of functions using continued fractions - contfrac.mws
- Introductory example of a continued fraction.
- Evaluation of continued fractions.
- Lentz's method for the evaluation of continued fractions.
- Argument reduction for the inverse tangent function.
- A procedure for evaluating arctan(x) using a continued fraction expansion: atanCF.
- A procedure for evaluating ln(x) using a continued fraction expansion: lnCF.
Procedures for the numerical evaluation of functions - numfcn.zip