## Laplace Transforms

Skill Type Description Source
20.1 Causal Functions Workbook Explain what a causal function is + be able to apply the step function to "switch on" and "switch off" signals HELM
20.2 The Transform and its Inverse Workbook Find the Laplace transform of many commonly occurrring causal functions + obtain the inverse Laplace transform using techniques involving; (i) a table of transforms, (ii) partial fractions, (iii) completing the square, (iv) the first shift theorem HELM
20.3 Further Laplace Transforms Workbook Use the second shift theorem to obtain Laplace transforms and inverse Laplace transforms + find the Laplace transform of the derivative of a causal function HELM
20.4 Solving Differential Equations Workbook Solve initial-value problems using the Laplace transform method HELM
20.5 The Convolution Theorem Workbook Calculate the convolution of simple functions + apply the convolution theorem to obtain inverse Laplace transforms HELM
20.6 Transfer Functions Workbook Find a transfer function of a linear system + show how some linear systems may be combined together by combining appropriate transfer functions + obtain the impulse response and the general response to a linear engineering system HELM

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