# 1.1 determine power series values for common scie

## 1.1 determine power series values for common scientific and engineering functions

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Learning outcomes

On successful completion of

this unit a learner will:

Assessment criteria for pass

The learner can:

LO1 Be able to analyse and

model engineering

situations and solve

engineering problems using

series and numerical

methods for the solution of

ordinary differential

equations

1.1 determine power series values for common

scientific and engineering functions

1.2 solve ordinary differential equations using power

series methods

1.3 solve ordinary differential equations using numerical

methods

1.4 model engineering situations, formulate differential

equations and determine solutions to these

equations using power series and numerical

methods

LO2 Be able to analyse and

model engineering

situations and solve

engineering problems using

Laplace transforms

2.1 determine Laplace transforms and their inverse

using tables and partial fractions

2.2 solve first and second order differential equations

using Laplace transforms

2.3 model and analyse engineering systems and

determine system behaviour using Laplace

transforms

LO3 Be able to analyse and

model engineering

situations and solve

engineering problems using

Fourier series

3.1 determine Fourier coefficients and represent

periodic functions as infinite series

3.2 apply the Fourier series approach to the exponential

form and model phasor behaviour

3.3 apply Fourier series to the analysis of engineering

problems

3.4 use numerical integration methods to determine

Fourier coefficients from tabulated data and solve

engineering problems using numerical harmonic

analysis

LO4 Be able to analyse and

model engineering

situations and solve

engineering problems using

partial differential

equations

4.1 solve rates of change problems and problems

involving stationary values using partial

differentiation

4.2 solve partial differential equations using direct

partial integration and separation of variables

methods

4.3 model and analyse engineering situations using

partial differential equations.