Hi everyone! Read through the material below and watch the videos, then give the WeBWorK assignment a try.
Lesson 26: Inverse Laplace Transform
Learning Outcomes: At the end of this lesson you will be able to find the inverse Laplace transform of functions
Topic. This lesson covers section 8.2: The Inverse Laplace Transform.
WeBWorK. There is one WeBWorK assignment on today’s material: Inverse Laplace Transforms
Review: Finding the Laplace Transform of a function
You may wish to refer to this Table of Laplace Transforms during today’s lesson.
Example 1. Find the Laplace Transform of each function, and determine the interval on which it is defined.
- $t^{2}+4 t^{3}-7 t^{6}$
- $\sin t+\cos 3 t$
- $5 e^{2 t}-4 \sin 3 t$
- $5 t^{2}+3 \sin 5 t-2 e^{6 t} \cos 2 t$
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.
- $\frac{3}{s}+\frac{4 !}{s^{5}}+\frac{1}{s-7}, \quad s>7$
- $\frac{1}{s^{2}+25}+\frac{s}{s^{2}+25}, \quad s>0$
- $\frac{1}{(s-4)^{2}+9}, \quad \mathrm{~s}>2$
- $\frac{1}{(s-6)^{7}}+\frac{5}{2 s-7}, s>6$
- $\frac{5}{s^{2}-8 s+41}, s>4$
That’s it for today! Try out the WeBWorK assignment, and let your professor know if you have questions.
Having trouble with derivatives and integrals in this class? First, don’t panic – it’s a lot to remember!! But do be prepared to put in some time re-learning stuff from Calculus I and II. I’ve collected a few topics that will be essential in this course, and linked to the corresponding online lessons in our Course Hubs from Calc I and Calc II.
If you’d like to see an example or two of how to solve a problem with these techniques, look for the videos embedded in each online lesson.
Continue reading
Go to the MAT 2680 Course Hub
About the MAT 2680 Course Hub
The Course Hub is a central resource created by the Mathematics Department for information and resources related to MAT 2680 Differential Equations. Whether you are a student in the course or a faculty member teaching it, we hope you will find useful material there. Some of the resources you will find include:
- Online Lessons. Here you will find (optional) online lessons for each day of class. If you missed a day of class, or you have questions, this is a great place to go!
- WeBWorK Resources for Students and Faculty. Need help with WeBWorK? Whether you are a student stuck on a problem in the homework, or a faculty member trying to create a quiz, there are resources to help.
- Video Resources. Stuck on a topic? Already looked at the online lesson? You can find additional videos for most topics here, including many examples worked out in full, created or selected by City Tech faculty.
- Faculty Training and Support. Includes more general (non-WeBWorK) topics like: How do I create a discussion board in my course? How do I collect student work using DropBox? Etc.
Go to the MAT 2680 Course Hub
Here are some helpful links:
Didn’t find what you need? The College website provides links to all student services.
Recent Comments