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Lessons | ||

logID |
Lesson Name |
Topics Covered |

calitbx | calculus 2 TOOLBOX* |
notes and hints on all course topics |

FUNDAMENTAL CONCEPTS | ||

cali1 | antiderivatives | antidifferentiating and differential equations. |

cali1.1 | areas with Riemann sums | basic priciples of integration: summing rectangles |

alg12 | summations | summation theorems and formulae |

TECHNIQUES OF INTEGRATION | ||

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 |

APPLICATIONS OF THE DEFINITE INTEGRAL | ||

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 |

INDETERMINATE FORMS, IMPROPER INTEGRALS | ||

cali5 | l'Hopital's rule |
limits of indeterminate forms with derivatives |

cali6 | improper integrals | infinite limits of integration, discontinuities on integrand |

INFINITE SERIES | ||

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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