Calculus II MathRoom

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logID Lesson Name Topics Covered
calitbx calculus 2 TOOLBOX* notes and hints on all course topics
cali1 antiderivatives antidifferentiating and differential equations.
cali1.1 areas with Riemann sums basic priciples of integration: summing rectangles
alg12 summations summation theorems and formulae
cali2 integration by parts includes "boomerang" integral
cali2.1 the "boomerang" integral integrals that come back to you
cali3 integration by substitution change of variable
cali3.1 trig integrals techniques for integrating trig functions
cali3.2 partial fraction decomposition techniques for integrating rational functions
cali3.3 quadratic expression integrands integrating irreducible quadratics
cali4 trig substitutions x = a sin h, x = a tan h, and x = a sec h
cali1.0 area finding area between curves
cali1.2 volumes by disk method solids of revolution, volume, cylindrical disks
cali1.3 volumes by shell method solids of revolution, volume, cylindrical shells
cali1.4 arc length finding length of an arc segment along a curve
cali1.5 volumes by slicing volumes of solids by summing area of slices
cali5 l'Hopital's rule limits of indeterminate forms with derivatives
cali6 improper integrals infinite limits of integration, discontinuities on integrand
cali7 testing infinite series-1 geometric series, p-series, integral & nth term test
cali7.1 testing infinite series-2 basic & limit comparison, ratio & root tests.
cali7.2 alternating series test testing series with alternating signs -- simple test
cali7.3 absolute & conditional convergence series that can be convergent and/or divergent
srststs guide to tests on infinite series table of info on the infinite series tests
Practice Exercises & Assignments
logID Exercise or Assignment Topics Covered
asgn1 assignment # 1 Mean Value Theorem, integration by substitution
asgn2 assignment # 2 area, volumes by revolving and slicing, arc length
asgn3 assignment # 3 all techniques of integration
asgn4 assignment # 4 l'Hopital's rule, improper integrals
asgn5 assignment # 5 testing infinite series for convergence
intprac integral practice exercise all techniques of integration with solutions
Tests and Exams
calitst1 Calculus II test #1 integrals, area, volumes, Mean Value Theorem,
calitst1sl Solutions: Calculus II test #1 solutions for test #1
cal2infosh information & formulas for test #2 trig integrals, inverse trig integrals, identities
calitst2 Calculus II test #2 integration techniques, volume, arc length
calitst2sl Solutions: Calculus II test #2 solutions for test #2
cal2tst3 Calculus II test #3 integration techniques, l'Hopital, convergence
cal2tst3sl Solutions: Calculus II test #3 solutions for test #3
califnl Final exam all topics on cal II course (science)
califnlsl Solutions for Final exam skimpy solutions -- by now you don't need more!
prctexams practice-exams 3 recent finals from Dawson



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