- Departmental picnic coming up!
- Reserve Sunday, September 21, starting at 4:30 pm for our fall picnic. This year it will be at Highlands Park in Fort Thomas. We will send out more details closer to that time.
- This is for majors, minors, and anyone who might be interested in becoming one of either. Don't be shy! Come on out and meet us.
- How are things going with the on-line homework program with the first homework assignment? I know that some of you have tried it out. Thank you. Some things I'm discovering:
- I can see your "failed attempts", so I could use this system and assign partial credit.
- Again, let's see how it goes:
- Create a username, password, and provide other info
- Course ID: 6
- Key: 882928
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- Demonstration of the derivative property of exponential functions (that an
exponential function is its own derivative, up to a constant multiple).
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- Example of Newton's method:
- First a summary of Newton's method:
- Objective: finding roots; that is, values of x such that f(x)=0.
- Strategy:
- given a good guess, x=a,
- find the linearization (tangent line) about
- solve L(x)=0 to find the iterative formula
- Does it work? With four "iterates", we can compute the square root of 7 to 8 decimal accuracy, starting from an initial guess of 2.
- Your calculator uses it...
- And now an example: #54, p. 349 (this link may work for students enrolled in our on-line homework system)
- First a summary of Newton's method:
- Examples:
- p. 349, #2,4,6,8
- p. 349, #17
- p. 349, #28
- p. 349, #55-67 odd
- Why study inverse functions?
- Pollution
- Forensics
- Ballistics
- Etc.!
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Proof: using the definition of the inverse, and the chain rule.
- Examples:
- #8, p. 356
- #9-16, p. 357
- #20, p. 357
- #22, p. 357
- #31, p. 357
- #33, p. 357
- #42, p. 358
