Mathematics 36, section 1 -- AP Analysis
Information on Final Exam
December 8, 1997
Background
The final exam for this section of AP Analysis will be given at
8:30 a.m. on Tuesday, December 16, in
our regular classroom -- Swords 359. The exam will be comprehensive,
covering all the material we have studied since the beginning of the
semester. I will write the exam to be roughly twice the length of the
in-class midterms. However, you will have the full three-hour
period 8:30 - 11:30 a.m. to work on the exam if you need that much time.
The questions will be similar to those on the 3 inclass exams.
I may include some questions asking for definitions
of terms or statements of theorems.
Topics to be Covered
- Functions defined by graphs, tables, formulas,
the ``library of functions''
- Derivatives (know the definition): know how to sketch
the graph of the derivative of a function defined by a graph,
how to approximate values of the derivative given a table for the
function, how to use the derivative rules on functions defined by
formulas.
- The meaning of the signs of f'(x), f''(x).
- Differentiability = local linearity, tangent lines,
etc.
- Taylor polynomials, approximations, the error bound
- Taylor series,
- Total change of a function, Riemann sums, the definite
integral (know the definition), antiderivatives
- The Fundamental Theorem of Calculus, and,
- Integration by substitution, by parts, using the
table. A copy of the table of integrals
from the text will be provided with the exam; any integral you
need to compute will be do-able by some combination of substitution,
integration by parts, and/or consultation with the table).
- Applications of integration (setting up problems via
Riemann sums; in limit a definite integral is obtained) -- volumes
by slices, arclengths, physical examples like work, mass from
non-constant density functions, etc.
- Differential equations -- slope fields and solutions
- Solving differential equations via separation of variables
and integration, including population growth models.
- Phase-plane analysis for systems of differential
equations and parametric curves.
Suggestion on How to Study
Begin by reviewing the class notes and the discussion write-ups
and lab reports from
your groups' work. Look at the in-class midterm problems and try to
work out solutions for those again, without refering to your previous
work. Look over some of the problems from the text from the
previous review sheets. Then take a couple of hours and try the practice
exam problems below.
Practice final exam:
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