Dave's Web Corner

MTH-264 Week 13 (March 30-April 5)

recommended: 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25
definition and major transforms
- a "function of functions"
- \( L[f(t)]=F(s) \)
the linearity of the laplace transform
- \( L[cf(t)+dg(t)]=cL[f(t)]+dL[g(t)] \)
the laplace transform and derivatives
- \( L[y']=sL[y]-y(0) \)
the inverse laplace transform
- \( L^{-1}[F(s)]=f(t) \)
basic examples
- emphasizing the power of linearity
- "juggling" constants in inverse transforms
- simple differential equations
- ... but why build the machine?

recommended: 1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18
the heaviside function
- the "on" (and "off"!) switch
efficient descriptions of piecewise functions
- instead of thinking about where pieces "begin" and "end" ...
- ... think about where to turn functions "on" and "off"!
the first shifting theorem
- If L[ f(t) ] = F(s), then L[ e^atf(t) ] = F(s-a)
- "wrapping a function in an exponential envelope results in shifting its transform"
the second shifting theorem
- If L[ f(t) ] = F(s), then L[ u_a(t) f(t-a) ] = e^-asF(s)
- "wrapping a transform in an exponential envelope is the result of a 'shift and delay' of the original function"
discontinuous forcing functions
- ... the reason we built the machine!

Deadlines and File Submission
- Submit your assessment as a single PDF file to the Assessment Folder inside your assigned Google Drive folder by 11:59pm on the date indicated.
- No late assessments are accepted. If you have a conflict with a deadline, contact me before the deadline.
- Solutions are posted under these links after the deadline.
Homework
- due Wednesday, April 2: 3.6 - 20 alt, 4.1 - 38 alt, 4.2 - 14 alt, 19 alt, 4.3 - 18 alt, 4.4 - 4 alt
- due Wednesday, April 9: Appendix B - 12 alt, 18 alt, 6.1 - 22 alt, 25 alt, 6.2 - 13 alt, 14 alt
- due Wednesday, April 16: 6.3 - , 6.4 -
Exams
- due Wednesday, April 23: Exam 3
  - Exam 3 (solutions)
  - Exam 3 covers sections 3.6, 4.1-4.4, appendix B, and 6.1-6.5