Laplace-transform

# Laplace-transform - Notes on Laplace transform In a rst...

This preview shows pages 1–2. Sign up to view the full content.

Notes on Laplace transform In a first approximation, Laplace transform is quite analogous to logarithms. The main property of logarithms is that ”taking logarithms” we transform products into sums and powers into products. log( a · b ) = log( a ) + log( b ) log( a b ) = b log( a ) This allows us to transform equations involving powers into equations involving prod- ucts, which may be more approachable. For example, if given the equation 7 x = 5 we realize that this is equivalent to log(7 x ) = log(5), which using the properties of loga- rithms is equivalent to x log(7) = log(5); x = log(5) / log(7) . 8270874753 Note that in the last step, we had to resort to a calculator that gives us the logarithms. (In older days, you had to resort to looking them up in a table.) Note that an important properties of logarithms is that knowing the logarithm of a number identifies the number. Laplace transform plays a similar role in differential equations. Taking Laplace trans- form of a an initial value problem for a linear diffferential equation with constant coefficients reduces the problem to an algebraic problem. Remember that a differential equation is an equation whose unknown is a function. Laplace transform will be a gadget that given a function produces another function.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern