About Course

COLIN MACLAURIN (1698–1746)
The development of power series to represent functions is credited to the combined work of many seventeenth and eighteenth century mathematicians. Gregory, Newton, John and James Bernoulli, Leibniz, Euler, Lagrange, Wallis, and Fourier all contributed to this work. However, the two names that are most commonly associated with power series are Brook Taylor (1685–1731) and Colin Maclaurin.

Find a Taylor or Maclaurin series for a function.
Find a binomial series.
Use a basic list of Taylor series to find other Taylor series.

Find the sum of a given series.
Find the Taylor series of a given function.
Find the Maclaurin series of a given function.
Use Maclaurin series to;
calculate limits,
approximate the values of some constants,
approximate an irrational number,
approximate logarithmic number,
approximate trigonometric number of an angle,
approximate the roots of a given equation.

Course Content

Finite series

Infinite series

Test for convergence of series

Power series

Taylor and Maclaurin series

Taylor series by using Maclaurin series

Calculation of limits

Estimation of the number e

Estimation of the number π

Estimation of trigonometric number of an angle

Estimation of an irrational number

Estimation of a natural logarithm number

Estimation of roots of equations

Final Exam

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S6 UNIT 3: Taylor and Maclaurin’s Expansions