Paul's Online Math Notes
[Notes]
Differential Equations - Notes

Internet Explorer 10 & 11 Users : If you have been using Internet Explorer 10 or 11 to view the site (or did at one point anyway) then you know that the equations were not properly placed on the pages unless you put IE into "Compatibility Mode". I beleive that I have partially figured out a way around that and have implimented the "fix" in the Algebra notes (not the practice/assignment problems yet). It's not perfect as some equations that are "inline" (i.e. equations that are in sentences as opposed to those on lines by themselves) are now shifted upwards or downwards slightly but it is better than it was.

If you wish to test this out please make sure the IE is not in Compatibility Mode and give it a test run in the Algebra notes. If you run into any problems please let me know. If things go well over the next week or two then I'll push the fix the full site. I'll also continue to see if I can get the inline equations to display properly.
 Second Order DE's Previous Chapter Next Chapter Systems of DE's Convolution Integrals Previous Section Next Section Systems of DE's (Introduction)

Table of Laplace Transforms

 1. 1 2. 3. 4. , p > -1 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. Heaviside Function 26. Dirac Delta Function 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

Table Notes

1. This list is not a complete listing of Laplace transforms and only contains some of the more commonly used Laplace transforms and formulas.

1. Recall the definition of hyperbolic functions.

1. Be careful when using “normal” trig function vs. hyperbolic functions.  The only difference in the formulas is the “+ a2” for the “normal” trig functions becomes a “- a2” for the hyperbolic functions!

1. Formula #4 uses the Gamma function which is defined as

If n is a positive integer then,

The Gamma function is an extension of the normal factorial function.  Here are a couple of quick facts for the Gamma function

 Convolution Integrals Previous Section Next Section Systems of DE's (Introduction) Second Order DE's Previous Chapter Next Chapter Systems of DE's

[Notes]

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