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week 13
MTH-264 Week 13 (March 31-April 6)
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outline
Outline
Appendix B Power Series: The Ultimate Guess
- recommended:
4, 5, 7, 8, 10, 11, 12, 17, 18
- remembering power series
- the method of (infinitely many) undetermined coefficients
- recurrence relations
- linear differential equations with non-constant coefficients
6.1 Laplace Transforms
- 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
- the inverse laplace transform
- basic examples
- emphasizing the power of linearity
- "juggling" constants in inverse transforms
- simple differential equations
- ... but why build the machine?
6.2 Discontinuous Functions
- 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[ eatf(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[ ua(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!
semesters >
winter 2024 >
mth264 >
week 13 >
assessments
Assessments
- Deadlines and File Submission
- All assessments are due by 11:59pm on the date indicated
- Assessments are submitted online to our
MTH-264 Assignments
folder.
- No late assessments are accepted.
- Homework
- due Thursday, April 4:
3.6 - ,
4.1 - ,
4.2 - ,
4.3 - ,
4.4 -
- due Thursday, April 11:
Appendix B - ,
6.1 -
- due Thursday, April 18:
6.2 - ,
6.3 - ,
6.4 -
- Exams
- due Thursday, April 25: Exam 3
- Exam 3
(solutions)
- Exam 3 covers sections 3.6, 4.1-4.4, appendix B, and 6.1-6.5
- Exam 3 will be released by 11:59pm on Tuesday, April 23 and will
be written in class on Thursday, April 25.
semesters >
winter 2024 >
mth264 >
week 13 >
handouts
Handouts
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- Laplace Transforms
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technology
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