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Laplace from tables: e^(at), cos(bt), sin(bt).

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rebelmaths

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(a) Using the tables,  $L[e^{\\var{a}t}]=\\frac{1}{s-\\var{a}}$

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(b) Using the tables,  $L[e^{\\var{b}t}]=\\frac{1}{s-(\\var{b})}$

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(c) Using the tables,  $L[e^{\\var{c}t}+e^{\\var{d}t}]=\\frac{1}{s-(\\var{c})}+\\frac{1}{s-\\var{d}}$

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Find the laplace transform of $e^{\\var{a}t}$

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Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$

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$L\\{e^{at}\\}=\\frac{1}{s-a}$

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Find the laplace transform of $e^{\\var{b}t}$

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Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$

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$L\\{e^{at}\\}=\\frac{1}{s-a}$

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Find the laplace transform of $ { e^{ \\var{c} t}+e^{ \\var{d} t} }$

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When you have the Laplace transform of two functions added together you just get the Laplace transform of each function and add the two answers.

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$L\\{f(t)+g(t)\\}=L\\{f(t)\\}+L\\{g(t)\\}$

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You may use a table of Laplace transforms in order to answer the following questions.

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Laplace transform of e^{at}

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rebelmaths

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See 'show steps'.

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Find $L\\{\\var{a} \\}$.

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$L\\{k\\}=\\frac{k}{s}$

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Find $L\\{\\var{b}t \\}$.

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$L\\{t\\}=\\frac{1}{s^2}$

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Find $L\\{\\var{a}+\\var{b}t \\}$.

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$L\\{k\\}=\\frac{k}{s}$

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$L\\{t\\}=\\frac{1}{s^2}$

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Find $L\\{t^\\var{a}\\}$.

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$L\\{t^n\\}=\\frac{n!}{s^{n+1}}$

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Find $L\\{\\var{a}t^\\var{c}+\\var{b}t^\\var{d}\\}$.

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$L\\{t^n\\}=\\frac{n!}{s^{n+1}}$

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You may use a table of Laplace transforms in order to answer the following questions.

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Laplace of constants and powers of t

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rebelmaths

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