Maple worksheets on Taylor series |

Approximation of functions:

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Taylor polynomials and Taylor series- taylor.mws

- Some polynomial approximations for exp(x) when x is close to zero
- General Taylor polynomial approximations for exp(x) when x is close to zero
- Linear approximations
- Quadratic approximations
- General Taylor polynomials and Taylor series

Maclaurin series and convergence of power series- maclrn.mws

- Power series
- Radius and interval of convergence of power series
- Convergence of the Maclaurin series for sin(x)
- Some standard Maclaurin series and their intervals of convergence
- Why does a power series have a radius of convergence?

Experimental determination of the radius of converge- radconv.mws

- Experimental determination of the radius of convergence of a Maclaurin series
- Examples

Using Taylor series to approximate integrals- taylrint.mws

- Introductory example
- More examples

Using Taylor series to calculate pi- calcpi.mws

- Newton's approximation for pi
- Using the Maclaurin series for arctan(x) to calculate pi
- 19 th century computation of pi by Johann Dase

Manipulation of of power series- diffpow.mws

- Introductory examples of adding power series
- Formal addition of power series
- Multiplying a power series by a polynomial
- Differentiating power series
- Integrating power series

The even and odd parts of a function- evenodd.mws

- Even and odd functions
- The even and odd parts of a function

Hyperbolic functions- hyperbolic.mws

- The hyperbolic sine and cosine functions
- Two points on the graph of cosh and sinh

Multiplication of power series- multpow.mws

- From multiplying polynomials to multiplying power series
- Examples of multiplying power series

Bernoulli numbers and the Maclaurin series for x/(exp(x)-1)- bernum.mws

- An introduction to Bernoulli numbers via the sums of powers of positive integers
- The Bernoulli numbers via the series for x/(exp(x)-1)
- A summation formula involving the Bernoulli numbers
- Calculation of the Bernoulli numbers
- Procedures for computing the Bernoulli numbers
- Ada Lovelace and the first computer program

Euler numbers and the Maclaurin series for sech(x)- eulnum.mws

- The Euler numbers
- A summation formula involving the Euler numbers
- Calculation of the Euler numbers
- Procedures for computing the Euler numbers

Radius of convergence of the series for x/(exp(x)-1) and sech(x)- maclrn2.mws

- The Maclaurin series for x/(exp(x)-1)
- The Maclaurin series for sech(x)

Some Maclaurin series involving Bernoulli and Euler numbers- maclrn3.mws

- The Maclaurin series for coth(x)-1/x
- The Maclaurin series for tanh(x)
- The Maclaurin series for tan(x)
- The Maclaurin series for sec(x)

More Maclaurin series involving Bernoulli numbers- maclrn4.mws

- The Maclaurin series for x/sinh(x)
- The Maclaurin series for x/sin(x)
- The Maclaurin series for ln(sinh(x)/x)
- The Maclaurin series for ln(sin(x)/x)