Click here for the First Exam for
Spring '00, and click
here for the solutions.
Review Materials for First Midterm Exam Spring '00
The first exam will be held on Tuesday, March 14, from 6:30pm to 8:30pm
in Science Center C.
On this first midterm you should be prepared to answer
questions from any of the following topics: (note the first test just covers
material from Section 7.4 and Chapter 11 in the text; you will not be tested
on the new material on integration (parts of chapter 7 besides 7.4)
which you might have covered
before the exam)
-
Basic infinite series information: definition of convergence/divergence
(i.e. know what partial sums are), sigma notation
-
Geometric series: know how to recognize them,
and how to find the sum of a convergent geometric series
-
P-series: know what values of p do they converge
-
Harmonic series: basic example of a diverging series whose
individual terms diminish to zero
-
Convergence Tests:
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Comparison Tests (including limit comparison test),
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Ratio Tests,
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Root Tests,
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Divergence Test,
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Alternating Series Test
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Alternating series: for converging alternating series know
how to bound the difference between a partial sum and the actual sum
-
Conditional versus Absolute convergence
-
Power series: know what they are, know how to find intervals/radii
of convergence (check your endpoints for convergence!)
-
Taylor/Maclaurin series (note a Maclaurin series is simply
a Taylor series around the point x=0):
-
know how to calculate Taylor series by taking
derivatives
-
know how they "evolve" from the best linear, quadratic, cubic,
etc. approximations of functions,
-
know how to find new series from old ones by substitutions
and simple algebraic manipulations,
-
know how to differentiate/integrate series to find series
for new functions (note the radius of convergence stays the same, but you
need to recheck the endpoints for convergence!)
-
know your basic Taylor series for sin x, cos x, e^x, log x,
(1+x)^m, 1/(1-x), etc. (log without a subscript means the natural
log)
-
Taylor Series error estimations based
on material from section 11.9
Old Exams for practice: