MATH 181 (CALC I) -- Winter 2011
Topics Covered:
Review:
Real numbers (rational and irrational) and the real number line: preparing
for calculus (X lectures)
Limits
Introduction and definitions, properties, evaluation techniques, continuity,
one-sided limits, infinite limits (7 lectures)
Derivatives:
Tangent lines and definitions, velocity, acceleration, other rates of change,
rules: constant multiples, sums, powers, products, quotients, trigonometric,
chain; implicit differentiation, related rates (7 lectures)
Applications of differentiation:
Extrema on an interval, Rolle's Theorem and the MVT, first & second derivative
tests, concavity, limits at infinity, curve sketching, optimization, Newton's
Method, differentials (10 lectures)
Integration:
Antiderivatives, area, Riemann sums, the definite integral,
The Fundamental Theorem of Calculus (5 lectures)
WRITING UP HOMEWORK SOLUTIONS: For the
handwritten
homework, you are expected to show
all
essential steps in solving a problem. Draw appropriate figures. If
in
doubt,
PUT
IT IN! Make your solution flow. Ask yourself the question: "If
I
were
the reader, how would I score this problem?'' Numerical answers
alone,
single words "yes" or "no", etc., are NEVER, EVER acceptable as
complete
answers. One of the skills you are expected to learn in this class
is
that
of communicating mathematics clearly and completely
in
writing.
Writing up homework exercises is your opportunity to hone these
skills.
Your
grade depends on it!
Weekly handwritten HW assignments:
A. p.8: 11,14,27,65,77; p.16: 13,22,25,33; p.27: 7,11,16,23,49-54,63 (never due, BUT KNOW HOW
TO DO!)
B. p.8: 58; p.17: 40,48,74; p.27: 30 (due Tuesday, 4 Jan)
1. p.47: 6; p.55: 14,18 (due Monday, 10 Jan)
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