Author: Jonas Reitz (Page 1 of 7)

Final Grades are posted – Farewell!

Hi everyone,

Your letter grades have been submitted to CUNYFirst, and you can find your final exam score and your overall course average in the OpenLab Gradebook.

It’s been a real pleasure working with you all this semester, and I wish you the best of luck as you pursue your education goals!

Happy Holidays,

Prof. Reitz

Happy Holidays everybody!

Day 25 In-Class Group Work – Laplace and Inverse Laplace Transforms

Choose one member of your group to be the scribe. The scribe should record your group’s work as you complete the examples below. You may wish to refer to this Table of Laplace Transforms when working on the problems below.

Example 1.  Find the Laplace Transform of each function, and determine the interval on which it is defined.

  1. $t^{2}+4 t^{3}-7 t^{6}$
  2. $\sin t+\cos 3 t$
  3. $5 e^{2 t}-4 \sin 3 t$
  4. $5 t^{2}+3 \sin 5 t-2 e^{6 t} \cos 2 t$

Find the inverse Laplace Transform

Now we consider the inverse problem – if I give you the Laplace Transform of a function, can you find the function it came from?

Example 2. Find the inverse Laplace Transform of each function.

  1. $\frac{3}{s}+\frac{4 !}{s^{5}}+\frac{1}{s-7}, \quad s>7$
  2. $\frac{1}{s^{2}+25}+\frac{s}{s^{2}+25}, \quad s>0$
  3. $\frac{1}{(s-4)^{2}+9}, \quad \mathrm{~s}>2$
  4. $\frac{1}{(s-6)^{7}}+\frac{5}{2 s-7}, s>6$
  5. $\frac{5}{s^{2}-8 s+41}, s>4$
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