IB Maths AA 5.13 Definitions

This page contains our IB Maths AA definitions for 5.13. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Maclaurin series'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Advanced Derivatives 5.4: Introduction To Integration 5.5: Advanced Integration 5.6: Kinematics (HL)5.7: Advanced limits (HL)5.8: Implicit differentiation (HL)5.9: Challenging derivatives (HL)5.10: Challenging integration (HL)5.11: Applying integration (HL)5.12: Differential equations (HL)5.13: Maclaurin series

approximation

Using a truncated Maclaurin series (a finite number of terms) to estimate a function value near

x=0

differential equation

An equation involving a function and one of its derivatives, so it describes how the function changes rather than giving the function directly.

differentiation

A process that can be applied term-by-term to a power series to create a new series for the derivative, within the interval where the original series is valid.

integration

The reverse of differentiation, used to rebuild a function from its derivative and to calculate accumulated change such as area.

integration by substitution

Replacing one expression with another to simplify a differential equation, such as using '

y=vx

' so that '

\frac{dy}{dx}=v+x\frac{dv}{dx}

Maclaurin formula

An expression that builds the Maclaurin series using derivatives at

0

f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^2+\frac{f^{(3)}(0)}{3!}x^3+\cdots

Maclaurin series

A power series representation of a function centred at

x=0

, written as

f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n

, giving a polynomial-style approximation near

x=0

power series

An infinite series of the form $\sum_{n=0}^{\infty} a_n x^n$ for constants $a_n$ , used to represent a function as powers of $x$ .

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